3.1.1 Efficient methods for testing and characterizing quantum systems

Obtaining an accurate mathematical characterization of the quantum systems that are prepared in the lab is a pressing question for quantum technologies. For this reason, there has been very important progress on such statistical questions in the last few years. This includes the answer to foundational questions such as the number of samples needed to characterize an unknown quantum state, improved methods for characterizing quantum devices, and very recently techniques that can very efficiently predict multiple relevant properties of quantum systems. We plan to contribute to these lines of work by considering several questions all going in the direction of better characterization of quantum systems.

First, we will consider basic statistical questions related to testing relevant properties of quantum states. In particular, given a description of an ideal target state $|\psi \rangle$, how to efficiently test whether the state prepared by the device complies with $|\psi \rangle$? Another question is how to test whether the state prepared by the device is entangled or not? These are fundamental questions and for some of them the best known algorithm is to learn the whole state by performing a complete quantum tomography. We believe that this is far from optimal and that a better understanding of the geometry of quantum states can be turned into a significantly more efficient testing algorithm. Techniques from high-dimensional convex geometry 61 are likely to play an important role.

Building on that, we will then develop tools to characterize the noise affecting quantum devices. As the number of parameters and samples required to characterize an arbitrary noisy process grows exponentially in the number of qubits 97, it is of paramount importance to devise protocols to find an effective ansatz for the underlying structure. The first step we will take in this direction will be to devise scalable protocols that are able to identify the correlation structure of the noise. By singling out on which parts of the device the noise acts independently and on which the noise is correlated it is possible to substantially reduce the number of parameters that are required to effectively describe it, bringing it to a tractable number. Although finding the conditional independence structure of a set of random variables to a high precision is a difficult problem even classically, we will generalize to the quantum setting efficient classical techniques that employ convex relaxations 77 to obtain good approximate solutions.

The next step will then be to devise protocols inspired from machine learning techniques that can exploit the knowledge of the underlying correlation structure to efficiently learn its parameters. This will be combined with randomized benchmarking techniques 88, 92, 86. Randomized benchmarking techniques are known to be robust and experimentally friendly, however current results either give very limited information or require stringent assumptions on the structure of the underlying noise. Thus, the goal of this part will be to overcome these two limitations, providing experimentalists with much needed tools to efficiently characterize large noisy quantum devices.

Such a line of research certainly also profits from inputs from experimentalists to test the algorithms on real quantum hardware. Thus, we plan to work with the local experimental group led by Benjamin Huard to test such methods on the devices they build. Moreover, it is invaluable to obtain input from experimentalists regarding what are the limitations and challenges they face in the lab when characterizing their devices.

An important aspect in this direction that we will consider is the design of measurements that can probe the physical property of interest without disturbing the state by much. This is the so-called quantum non-demolition measurement (QND) and is important when one has a continuous signal which one wants to measure, since one has to measure the same system repeatedly over time and, ideally, one wants the outcomes of later measurements to depend solely on the quantity one intends to measure, and not on any disturbances caused by prior measurements. QNDs have found usages in many areas, including quantum computing and, most prominently, proposals for gravitational wave detectors with improved sensitivity. We view the problem through the lens of quantum information theory, and in this way, it can be seen that the quantum system involved in the QND, is a quantum reference frame. What’s more, there is a one-to-one relation between the reference frame imperfections, and its ability to act as a system for QND measurements. In 65, 115, we gave a construction of a QND where the error is a function of energy and dimension. Going forward, our objective is to determine whether this construction is optimal, determine the optimal tradeoff between error and energy and dimension and assess the extent to which such constructions can lead to an advantage for quantum sensing.

3.1.2 Limitations on the computational power of noisy quantum devices

In order to establish a quantum advantage for noisy quantum computers, it is important to study when noisy quantum computers can be simulated classically. Intuitively, it is clear that the noise present in a quantum device imposes a limit on the circuit depth we can implement before the device loses its usefulness when compared to classical devices. In order to understand the potential of noisy quantum devices, it is crucial to develop tools to characterize when this happens given a problem and noise model. In the context of optimization, such bounds were achieved by our work 87. In short, the results of 87 show that sampling from the output of noisy quantum devices quickly becomes comparable to sampling from Gibbs states that are easy to simulate classically by giving stringent explicit bounds. This is showcased Figure 1, where we plot at which density of corrupted qubits the noisy quantum device loses advantage against classical methods.

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Estimate as to when a noisy quantum device loses advantage compared to established efficient classical methods in terms of the density of uncorrupted qubits for one instance of the GSET (a set of instances of hard combinatorial optimization problems that are used to benchmark solvers). We see that even when only a fraction of the qubits have been corrupted (roughly one in 4), the noisy quantum computer is already expected to loose advantage against heuristic methods.

However, in their current version, our methods only allow for an analysis of the first moments. To extend the analysis and conclusions beyond optimization to other fields like quantum machine learning, it is imperative to obtain results for higher moments and concentration inequalities for the outputs of noisy quantum circuits. That is, to quantify how much noise a quantum system can tolerate before it behaves like a state that can be easily sampled from classically. To achieve this goal, we intend to resort to and further develop methods from the emerging field of quantum optimal transport 102, 78. Optimal transport techniques are by now a well-established method to show powerful concentration inequalities 108. They are known to combine well with other areas of expertise of the group, such as entropic and semigroup methods.

3.1.3 Efficient optimization using noisy quantum computers

Identifying good use cases for the noisy quantum devices expected to be available in the near future is one of the main current challenges faced by the quantum computing community. One possible candidate for such an application are quantum Gibbs state-sampling based methods. Quantum Gibbs states are at the core of powerful classical and quantum algorithms for optimization and machine learning based on mirror descent or the matrix multiplicative weight method 70, 67, 66. These iterative algorithms can be understood as a variation of simulated annealing, in which one starts with a (quantum) Gibbs state at infinite temperature and decreases the temperature to converge to the solution of an optimization problem. That is, we begin with a state that is supported everywhere on the state space and slowly zoom into regions that contain solutions to the problem of interest by tuning the Gibbs state. This intuitive picture conveys one feature of such methods: they are robust, especially at the first iterations, as we only need to ensure that we are zooming in the right direction. This robustness translates into them only requiring the preparation of states with relatively small precision to make progress.

On the other hand, this picture also showcases the issue noise imposes for such methods: after a while, the noise will make it impossible to zoom in further, imposing fundamental barriers onto how well we can characterize the region of solutions. Thus, it is expected that noisy quantum computers can offer useful advice as to which direction to go up to a level that naturally depends on the noise present in the device. Thus, we will design hybrid quantum-classical algorithms that explicitly take into account this limitation. They will only use the quantum computer to identify a region of a relatively small dimension that contains the solution.

At this stage, it is then possible to use powerful randomized linear algebra techniques to take advantage of the initial zooming in performed by the noisy quantum device. Techniques from randomized linear algebra offer significant speedups for basic operations under the promise that the involved matrices are supported on a small dimensional space 113. Thus, after doing the first iterations efficiently on the noisy quantum device and identifying a low-dimensional space that contains the solutions, a classical device takes over with this input and runs the later iterations much faster. Such a hybrid algorithm would lead to more efficient solvers for convex optimization problems. Although such problems can usually be solved in polynomial time, in practice it is still challenging to solve larger dimensional instances, impeding their more widespread use. Such a hybrid algorithm will increase the practicality of solving large-dimensional semidefinite programs, as the classical computer would only have to operate in the low-dimensional regime. It would also lead to provable speedups for quantum devices under noise, a goal that has so far remained elusive.

The main technical challenges that need to be overcome for the success of such an algorithm are threefold: first, carrying out a detailed analysis of the trade-offs as to when it becomes more efficient to transition from performing the optimization on the noisy quantum device to the classical computer. Second, the development of improved quantum Gibbs sampler for noisy devices to prepare the required states. Third, the identification of practically relevant problems that offer a good opportunity window for quantum speedups. The first and third challenges will profit from and are connected to the result of the previously discussed Goals 3.1.1 and 3.1.2. The second, the development of better quantum Gibbs samplers, as current proposals for Gibbs samplers require quantum circuits that are unlikely to be implementable in the near term, will certainly yield results that find applications in many other directions. Indeed, efficient classical Gibbs samplers are the bread the butter of most Monte Carlo techniques, and it is to be expected that quantum Gibbs samplers will find similar widespread application.

3.1.4 Certification of quantum devices

In the device-independent framework of quantum cryptography, protocols offer security by relying on minimal assumptions. Namely, they are secure even when the devices used within the protocol are completely untrusted or uncharacterized. The main idea behind many device-independent protocols, such as randomness expansion and quantum key distribution, is that there are certain correlations between multiple separate systems that ($i$) could only have been produced by entangled quantum systems and $\left(ii\right)$ are intrinsically random. The fundamental question underlying the analysis of such protocols is how to certify entanglement or randomness from the observed measurement statistics of the untrusted device?

This question of certification is recurrent when assessing the behaviour of quantum devices (and particularly of noisy ones), as highlighted by the issues that Goals 3.1.1 and 3.1.2 address. We plan to develop techniques to address the certification of quantum systems with minimal assumptions. Our objective is to first build mathematical tools in the continuity of the Entropy Accumulation Theorem 81 that allow us to make accurate statistical statements about large quantum systems. The second objective is to design computational methods 69 to certify in a quantitative way the relevant quantum properties that are consistent with the observed statistics.

For the context of device-independent cryptography, this will allow us to obtain protocols with improved noise tolerance and finite-length analysis to reach the realm of what can be done with current quantum technologies. But we believe these techniques will be applicable in the wider setting of certifying properties of quantum networks and quantum computing devices.

3.2.1 Optimal error correction tailored to noise model

Shannon's 1948 seminal theorem 104 modeled the problem of communication (or storage) over a given noisy channel and determined precisely its ultimate limit. Shannon's noisy coding theorem relates the maximum rate at which information can be transmitted reliably over a noisy channel ${𝒲}_{X\to Y}$ to a simple entropic expression $I(X:Y)$ measuring the correlations between the input and output of the channel. More precisely, it states that as $n\to \infty$, the maximum number of bits that can be sent using $n$ independent copies of ${𝒲}_{X\to Y}$ is asymptotically given by

where the right hand side is a maximization over distributions $P_X$ over the input of the channel and $I(X:Y)$ is a correlation measure, the exact definition of which we will omit in this document. Setting the fundamental limits for reliable communication, Shannon's theorem was instrumental in the discovery of good error correcting codes which are used in virtually every device or communication link today. One of the goals of the field of information theory is to characterize the optimal communication rates in the form (1) for various information processing tasks.

Devices that make use of the laws of quantum theory are also affected by noise, in fact even more so. Determining the optimal method in order to communicate (or store information) reliably over a noisy quantum channel is thus of fundamental importance in order to exploit the full potential of a quantum computer, or more generally a quantum device. However, despite the problem's importance and more than 40 years of efforts in quantum information theory 94, 112, it is fair to say that we do not have a quantum analogue of Shannon's theorem Eq. (1). Indeed, a formula analogous to Eq. (1) for quantum channels is known only in very special cases. As an illustration, even for the simplest possible quantum channel, called the qubit depolarizing channel, the asymptotic maximum rate of quantum communication is still unknown 79. The qubit depolarizing channel can be thought of as the quantum analogue of the channel that flips the input bit with some probability $f$.

The main difficulty in understanding the ability of a quantum channel in transmitting information is the non-additivity of the quantum entropic quantities having the form of the right hand side of Eq. (1) 79, 95, 93, 105. This challenge is due in many cases to the quantum property of entanglement and we believe that a new approach is needed to overcome this difficulty.

Faced with these difficulties, we propose a new framework for studying communication over noisy channels. Instead of trying to determine the optimal rate of communication asymptotically as the number of channel uses $n\to \infty$ (as in the left hand side of Eq. (1)), we assume we have a description of a finite channel ${\overline{𝒲}}_{\overline{X}\to \overline{Y}}$ (a particular case of which is ${\overline{𝒲}}_{\overline{X}\to \overline{Y}}={𝒲}_{X\to Y}^{\otimes n}$ for some finite $n$, but it could be much more general). Our objective is then to design an efficient algorithm that determines the maximum number of bits or qubits that can be sent reliably using ${\overline{𝒲}}_{\overline{X}\to \overline{Y}}$.

For the problem of classical communication over a classical channel, we have characterized this computational complexity precisely in our previous work 64 and this led to interesting connections between information theory and combinatorial optimization. The main objective here is to extend this approach to quantum channels, thereby designing algorithms that can find the best error correction schemes for a given noise model. These algorithms can naturally then be used on the noise models that are estimated using the methods developed in Axis 3.1.1. In particular, we will focus on relevant noise models that appear in current devices. For this we plan to collaborate with Benjamin Huard in the physics lab of ENS Lyon, and the presence of Cyril Élouard in the team significantly helps in this regard. To start in this direction, Cyril has given talks within the group to explain the mathematics of superconducting qubits and we are at the moment discussing specific dissipative models that can be reasonably implemented in hardware and for such different models compare their ability to store quantum information reliably.

3.2.2 Error correction and fault-tolerance with LDPC codes

Having a coding strategy for a given noise model with good performance is not enough: for a strategy to be applicable, it is important to be able to implement the error correction operations efficiently. An efficient decoding algorithm is not only important to establish fast and reliable communication networks but it is also crucial for fault-tolerant computing. In fact, the basic idea of fault-tolerant computing schemes is to perform computations on data encoded in an error correcting code. To prevent the errors that occurred during the computation from spreading, a decoding operation has to be regularly applied to correct these errors. For this reason, it is crucial for the decoding operation to be very fast to prevent the accumulation of errors. We focus here on an important class of quantum error correcting codes called Low-Density Parity-Check (LDPC) codes 71, 106 defined by two sparse binary parity-check matrices $H_X$ and $H_Z$ satisfying $H_X{H}_Z^T=0$. Our first objective is to design efficient decoding algorithms for quantum LDPC codes.

Quantum LDPC codes are particularly well suited to achieve fault-tolerant quantum computation. This is because the sparsity of the parity check matrices allows us to bound the error rate of the syndrome measurements. In fact, currently the leading candidate error correcting code to be used in future quantum computers is the surface code, a special kind of LDPC code. Even though the surface code can be embedded on a surface with only nearest neighbour interactions, it suffers from a very poor encoding rate, and thus using it for fault-tolerant constructions incurs a very large memory overhead. Our previous work 85 shows that in principle the memory overhead can be significantly reduced by using constant-rate LDPC codes based on expander graphs. The general idea of using constant-rate codes is illustrated in Figure 2. Our objective is to make fault-tolerant constructions with LDPC codes practical by finding fault-tolerant gadgets for such codes and using decoding algorithms with better performance.

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When using the surface code for fault-tolerance, each qubit of the original circuit is encoded in a separate block, leading to a large memory overhead. When using constant-rate codes, all the qubits of the original circuit are encoded in the same block which leads to important savings in terms of overhead.

3.2.3 New approaches for fault-tolerance

As mentioned before, the currently leading approach for fault-tolerance is using surface codes. In contrast to the previous goal 3.2.2, our objective here is to explore radically different approaches to fault-tolerance that could provide new avenues towards achieving fault-tolerance. In particular, we will look at one based on quantum polar codes and the other one based on quantum reference frames.

The class of quantum polar codes that has recently been proposed in 82 can be promising candidates for fault-tolerant quantum computing. The construction relies on a channel combining and splitting procedure, where a two-qubit gate randomly chosen from the Clifford group is used to combine two single-qubit channels. Applied recursively, this procedure allows synthesizing a set of so-called virtual channels from several instances of the quantum channel. When the code length goes to infinity, the virtual channels polarize, in the sense that they tend to become either noiseless or completely noisy. Interestingly, polar codes feature several extremely desirable properties: they protect a high number of logical qubits, and they have efficient decoding algorithms. In addition, logical Clifford operations can be easily performed by using code deformation like techniques. However, there are a number of challenging issues to be addressed in the fault-tolerant computing context. First, quantum channel polarization needs to be investigated by taking into account the fact that Clifford gates used for channel-combining are faulty. Second, we need to construct a universal set of fault-tolerant gates, which can be tackled by using magic state distillation. For this approach, we plan to collaborate closely with Mehdi Mhalla (CNRS, LIG).

The second approach we consider here is based one a way of circumventing the famous Eastin-Knill theorem. In the early days of quantum computing, one of the key ideas for building a quantum computer whose errors can be corrected, was the notion of transversal logic gates. The idea was to devise a scheme in which all the gates needed for universal quantum computation could be applied on non-overlapping subspaces in such a way that all the locally occurring errors were correctable. More specifically, the objective is to find an encoding $ℰ$ mapping the logical space to the physical space such that for any unitary $𝒱$ acting on the logical space, there exist unitaries ${𝒱}_1,\cdots ,{𝒱}_n$ acting on the physical space such that

This scheme would allow for errors in the implementation of the gates to be corrected before they have propagated through the computation and rendered its results useless. Unfortunately, transversality of all the gates needed for universal computation and local correctability within the blocks cannot both be simultaneously satisfied for finite dimensional codes. This was proven by Eastin and Knill in a landmark paper in 2009 83. Subsequently, workarounds have been found. For example, one of the current frontrunner approaches is to apply all but one of the gates needed for universal computation transversally, while the remaining gate is applied in a non-transversal way using other costly techniques.

We have developed in a series of two papers 114, 116, a new method for quantum error correction which is not based on this approach. In this technique, all of the gates in the set needed for universal computation are treated on an equal footing. More precisely, rather than circumventing the Eastin-Knill theorem by having one non-transversal gate, all gates from the universal set can be applied transversally, and local errors corrected, but at the price of an error in the decoding. As long as the error in the decoding is kept small, it will not disrupt the computation and is thus not significant from a practical point of view. To do so, it uses quantum reference frames and randomness to encode the information about which gate was applied during the computation. As the quality of the reference frame increases, the error in the decoding approaches zero. The concept of a quantum reference frame was introduced in the field of quantum foundations in the context of sharing so-called “unspeakable information”, such as the relative orientation of two distant observes. While it has been used over the years in various problems in quantum information theory, its use in quantum error correction has yet to be fully explored.

While this work on the circumvention of the Eastin-Knill theorem has attracted a lot of attention and follow up work by other research groups (see e.g. Refs. 99, 117, 109 and 98), it is not yet ready for primetime. The reason for this, it that while the encoded states are readily fault tolerant (due to the transversality of its gates), the current protocol for applying the encoding and decoding channels are not fault tolerant. This is down to the method in which the quantum reference frames are constructed. However, we believe that finding protocols for implementing the encoder and decoder in a fault tolerant way is a surmountable challenge. We plan to use a recent construction of unitary $t$-designs that use a constant number of non-Clifford gates. Implementing the Clifford gates in the circuit can be done in a transversal way and for the non-Clifford gates, a constant number of magic states can be used. This is analogous in some ways to the entanglement needed to perform magic state distillation 68, which is the building block of one of the leading proposals for fault tolerant quantum computation. However, there are many potential benefits to the proposed use of the initial entanglement resource over that of the magic state distillation approach — it is these benefits, which are the key to why this approach could become the chosen method to implement error correction. This includes the fact that the amount of entanglement needed is independent of the computation as well as the high adaptability of this method.

3.3.1 Quantum control in quantum information processing

One of the intrinsic limitations of the standard quantum circuit model is that the structure of the circuit, and hence of the flow of information, is fixed prior to computation; quantum circuits do not allow for the possibility of a “quantum if-statement”. In this research goal we study new models to quantum computation that, in contrast, have explicit quantum control structures. These models, in particular, have the potential to provide new approaches to mitigate noise can lead to stronger quantum advantages in certain applications.

To study quantum control structures we work within the framework of higher-order quantum operations 72, 101, which formalise the types of ways quantum circuits or channels can themselves be transformed within quantum theory. This approach has developed rapidly in recent years 110 since it was first used to show that one can indeed formulate quantum computations in which the order of two quantum gates is superposed with the help of a quantum control system, a gadget known as the quantum switch 73 (see Fig. 3).

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By allowing the structure of a circuit to be controlled by a quantum system, one can perform certain computations more efficiently. Such “quantum control structures” can be formally studied as higher-order quantum operations, leading to a generalisation of quantum circuits.

The quantum switch and related computations have since been shown to provide new types of quantum advantages in several information-theoretical tasks 75, 60, 91, where they outperform even “standard” quantum circuits. Moreover, its relevance for improving noise tolerance has recently come to light in a number of works showing how quantum control can be used to improve communication over noisy quantum channels 84, 74,59.

This progress emphasises the potential benefits in studying such models of quantum information processing, and motivates a more systematic study of quantum control models in this context. In a first step in this direction we recently formalised a computational model strictly generalising quantum circuits, called quantum circuits with quantum control of causal order (QC-QC) that incorporate – and generalise – quantum control structures 111. This model will serve as the base for a systematic study of the computational power of quantum computations exploiting quantum control, allowing us to understand the types of advantages this new resource of quantum control can provide.

With a better understanding of quantum computations with quantumly controlled operations, we will aim to develop algorithms for several problems where quantum control appears to be a promising problem. Of particular interest, we will look to use it to provide new algorithms for quantum metrology and parameter estimation – both key problems that are seen as near-to-mid-term applications for quantum information – that are more efficient than existing approaches and, in particular, are more robust in the noisy versions of these problems. An important first step we are undertaking in this direction is to generalise existing advantages obtainable with quantum circuits with quantum control of causal order from problems in a noiseless regime – where the controlled operations are unitary – to a noisy regime, where the controlled operations are noisy quantum channels.

In order to obtain such results, the mathematical tools being studied and developed in the other research axes of the proposed team, most notably convex optimisation, will be of utmost importance (e.g., Goals 3.1.3, 3.1.4 and 3.2.1). These research goals also build on existing collaborations on quantum control of causal order with physicists at the Institut Néel in Grenoble (including on the development of QC-QCs 111), in order to transfer physical insight on quantum control towards new application for information processing. We likewise plan to collaborate with the CAPP team at LIG to study diagrammatic calculi to understand how these new types of computations can be composed and compiled, building on existing collaborations with Mehdi Mhalla on quantum control 59.

The quantum control of quantum operations has potential as a resource throughout quantum information processing: not just for quantum computation but, e.g., also for quantum communication 91. As an example, it can be used to send messages through a quantum network in a superposition of different paths, amounting to a novel extension of quantum Shannon theory 74. By doing so, it has recently been shown in a simple, proof-of-principle setting, that one can notably reduce the effect of noise on the message as it traverses a network8459 and the effect experimentally verified 103. We will study this possibility further, looking at how it can be extended to practical network topologies and aim to show how it can be exploited to improve quantum communication protocols and lead to novel approaches for quantum cryptography.

One can also generalize the model of computation one step further. In causally indefinite models of computations such as QC-QCs the relative order between gates is rendered indefinite through the use of quantum control systems. Nonetheless, the computation itself still proceeds in the presence of a fixed, causal clock or external control. We will seek to go one step further in the quantum-classical divide and allow for this external control to also be quantum and autonomous. This would require the addition of another quantum system implementing the quantum gates themselves. In the case of a fixed causal order, this autonomous device needs its own internal notion of time, hence it should also be an accurate quantum clock 115. Since it is quantum, this clock which controls the interactions can be prepared in a superposition of different time states, leading to new types of non-casually implemented gates and potentially novel applications.

3.3.2 Multipartite entanglement and its applications

Multipartite entanglement plays an important role in quantum protocols and in quantum games, and is likewise a key resource for measurement-based quantum computing. Nonetheless, our understanding of multipartite entanglement as a resource is much less developed than for the simpler, but important, case of bipartite entanglement. The objective of this task is develop our understanding of multipartite entanglement, how it can contribute to reducing the effect of noise in communication, computation and more generally how it can improve coordination in multipartite scenarios.

In particular, we plan consider communication problems over noisy classical networks and quantify the extent to which multipartite nonlocality can improve the transmission rates 100. Focussing on relevant classical network communication scenarios, we will ask whether entanglement between some of the involved parties significantly improve the rates.

In a related direction, we plan to study game-theoretic settings with players with divergent interests and the advantage that can be achieved by using multipartite entangled states and, in particular, quantum graph states 90. In collaboration with Mehdi Mhalla, we will aim to use such advantages to provide new approaches to certify multipartite entangled states, and in particular to self-test quantum graph states – important resources in certain quantum computational models – by certifying them solely from the correlations they produce 63, 62. We plan to use progress towards Goal 3.1.4 to provide a finer analysis of the problem.

3.3.3 Quantum frequential computing

This is a new reserach direction of the team, which focuses on developing a new type of quantum computer that achieves speed-ups in both quantum and classical computation. In a nutshell, it will focus on showing that when the bit/qubit control is quantum, then a large quadratic speedup, as a fuction of the underlying resources, is achievable. This constitutes a new type of quantum resource since traditioanlly the bit/qubit control is considered to be classical or semi-calssical.

We are developing two intertwined directions of research with this objective in mind:

Learning quantum states beyond the i.i.d. assumption

In 16, we develop a framework for learning properties of quantum states beyond the assumption of independent and identically distributed (i.i.d.) input states. We prove that, given any learning problem (under reasonable assumptions), an algorithm designed for i.i.d. input states can be adapted to handle input states of any nature, albeit at the expense of a polynomial increase in training data size (aka sample complexity). Importantly, this polynomial increase in sample complexity can be substantially improved to polylogarithmic if the learning algorithm in question only requires non-adaptive, single-copy measurements. Among other applications, this allows us to generalize the classical shadow framework to the non-i.i.d. setting while only incurring a comparatively small loss in sample efficiency. We use rigorous quantum information theory to prove our main results. In particular, we leverage permutation invariance and randomized single-copy measurements to derive a new quantum de Finetti theorem that mainly addresses measurement outcome statistics and, in turn, scales much more favorably in Hilbert space dimension.

Classical algorithms for estimating equilibriuim properties of quantum system

Predicting observables in equilibrium states is a central yet notoriously hard question in quantum many-body systems. In the physically relevant thermodynamic limit, certain mathematical formulations of this task have even been shown to result in undecidable problems. Using a finite-size scaling of algorithms devised for finite systems often fails due to the lack of certified convergence bounds for this limit. In 13, we design certified algorithms for computing expectation values of observables in the equilibrium states of local quantum Hamiltonians, both at zero and positive temperature. Importantly, our algorithms output rigorous lower and upper bounds on these values. This allows us to show that expectation values of local observables can be approximated in finite time, contrasting related undecidability results. When the Hamiltonian is commuting on a 2-dimensional lattice, we prove fast convergence of the hierarchy at high temperature and as a result for a desired precision ε, local observables can be approximated by a convex optimization program of quasi-polynomial size in

Security of differential phase shift quantum key distribution

The design of quantum protocols for secure key generation poses many challenges: On the one hand, they need to be practical concerning experimental realisations. On the other hand, their theoretical description must be simple enough to allow for a security proof against all possible attacks. Often, these two requirements are in conflict with each other, and the differential phase shift (DPS) QKD protocol exemplifies these difficulties: It is designed to be implementable with current optical telecommunication technology, which, for this protocol, comes at the cost that many standard security proof techniques do not apply to it. After about 20 years since its invention, 28 presents the first full security proof of DPS QKD against general attacks, including finite-size effects. The proof combines techniques from quantum information theory, quantum optics, and relativity. We first give a security proof of a QKD protocol whose security stems from relativistic constraints. We then show that security of DPS QKD can be reduced to security of the relativistic protocol. In addition, we show that coherent attacks on the DPS protocol are, in fact, stronger than collective attacks. Our results have broad implications for the development of secure and reliable quantum communication technologies, as they shed light on the range of applicability of stateof-the-art security proof techniques.

Fault-tolerant quantum input/output

Usual scenarios of fault-tolerant computation are concerned with the fault-tolerant realization of quantum algorithms that compute classical functions, such as Shor's algorithm for factoring. In particular, this means that input and output to the quantum algorithm are classical. In contrast to stand-alone single-core quantum computers, in many distributed scenarios, quantum information might have to be passed on from one quantum information processing system to another one, possibly via noisy quantum communication channels with noise levels above fault-tolerant thresholds. In such situations, quantum information processing devices will have quantum inputs, quantum outputs or even both, which pass qubits among each other. Working in the fault-tolerant framework of 96, we show in 40 that any quantum circuit with quantum input and output can be transformed into a fault-tolerant circuit that produces the ideal circuit with some controlled noise applied at the input and output. The framework allows the direct composition of the statements, enabling versatile future applications. We illustrate this with two concrete applications. The first one concerns communication over a noisy channel with faulty encoding and decoding operations 76. For communication codes with linear minimum distance, we construct fault-tolerant encoders and decoders for general noise (including coherent errors). For the weaker, but standard, model of local stochastic noise, we obtain fault-tolerant encoders and decoders for any communication code that can correct a constant fraction random errors. In the second application, we use our result for a state preparation circuit within the construction of 89 to establish that fault-tolerant quantum computation for general noise can be achieved with constant space overhead.

A Shannon theory approach to dynamic quantum error correction

Given a quantum Markovian noise model, we study in 45 the maximum dimension of a classical or quantum system that can be stored for arbitrarily large time. We show that, unlike the fixed time setting, in the limit of infinite time, the classical and quantum capacities are characterized by efficiently computable properties of the peripheral spectrum of the quantum channel. In addition, the capacities are additive under tensor product, which implies in the language of Shannon theory that the one-shot and the asymptotic i.i.d. capacities are the same.

Norm estimates for $k$-positive maps

Quantum entanglement can be characterized as the discepancy between the classes of positive vs completely positive maps. When interpolating between these families, we obtain the classes of $k$-positive maps, parametrized by an integer $k$. In 9 we studied the discrepancy between the norm and the completely bounded norm of a map between matrix algebras under assumptions of $k$-positivity, using techniques from operator algebra.

Entanglement resources in quantum games

Entanglement is one of the primary quantum resources behind many quantum advantages, but many applications focus on bipartite entanglement shared between only two parties, in part due to the simplicity of this setting. In 6 we studied multipartite entanglement in the context of non-collaborative game theory, to understand how it can be used as a resource in tasks where there are conflicts of interest. We showed how quantum entanglement can lead to higher “social welfare” – a measure of the quality of a Nash equilibrium – than could be obtained with classical resources. Moreover, this setting allowed us to uncover surprising and nuanced differences between having direct access to quantum resources, and indirect access via some idealised black boxes. Technically, a key novelty of this work was to use the technique of self-testing correlations in a new way to show the separation between these types of quantum resource.

Connecting causal inference and space-time geometry via information-theoretic signalling

Causality is pivotal across scientific disciplines, presenting itself in different forms: information-theoretic, linked to information flow, and relativistic linked to the structure of space-time. Causal modelling and inference is a prominent approach for the former, which has seen applications across classical data-driven disciplines and recent growing interest in quantum information. In 47, we study the interplay between causal models and space-time structure in general theories of information-processing, which has been relatively little understood on a formal level. First, we improve the characterization of information-theoretic signalling relations studied in 107, introducing conditions for operationally identifying redundant information in different parts of such a relation. We thereby introduce new techniques for causal inference in unfaithful causal models (where the observable data does not "faithfully" reflect the causal dependences) which demonstrates the possibility of causal inference using the absence of signalling between certain nodes. Second, we define an order-theoretic property called conicality, that distinguishes the geometry of light cones in Minkowski space-times with $d>1$ vs $d=1$ spatial dimensions. Finally, we study the embedding of information-theoretic causal models in space-time without violating relativistic principles such as no superluminal signalling (NSS). In general, we observe that constraints imposed by NSS in a space-time and those imposed by purely information-theoretic causal inference behave differently. However, we demonstrate that in conical space-times and in faithful causal models, these two types of constraints exhibit certain similar and useful properties. This offers new insights on the fundamental role of different space-time geometries for information processing possibilities, while generating new causal inference methods which could have independent applications in classical statistics.

How relativistic principles constrain information-processing tasks

Relativistic causality principles fundamentally constrain information processing possibilities in space-time. No superluminal causation (NSC) and no superluminal signaling (NSS) are two such principles which, although often conflated, are distinct. In 54, we study the consequence of these principles for information-processing by considering the tasks of generating non-classical correlations within two space-time configurations. We show that the first task is impossible in any classical theory while the second is impossible in any (possibly non-classical) theory constrained by NSC. However, we construct a protocol enabling non-classical correlations to be generated in both configurations in a theory restricted by the NSS principle (which is weaker than NSC). We show that in any theory that admits this protocol, the violation of NSC without violating NSS would be operationally verifiable, and these findings link two distinct post-quantum resources: jamming non-local correlations and PR-box correlations. Our work informs a new research direction while providing insights and methods to explore it: how different relativistic principles lead to distinct constraints on the information processing power of physical theories.

Bridging indefinite causality and composable quantum protocols in space-time

The concept of quantum processes with indefinite causal orders (ICO) have garnered much interest due to their potential advantages for information processing. However, there have remained longstanding open questions regarding the physical realisability of ICO processes. Moreover, it was previously observed that composition of such processes is not so straightforward, which raises the question of how this connects with the observed composability of physical experiments. In 27, we address these questions by bridging these information-theoretic approaches for causality, with spacetime structure which constraints physical implementations. Specifically, we connect the formalism of quantum circuits with quantum control of causal order (QC-QC), which models an important class of ICO processes, with that of causal boxes, which models composable quantum information protocols in spacetime. We incorporate the set-up assumptions of the QC-QC framework into the spatiotemporal perspective and show that every QC-QC can be mapped to a causal box that satisfies these set up assumptions and acts on a Fock space while reproducing the QC-QC's behaviour in a relevant subspace. We show that the causal box corresponds to a fine-grained description of the QC-QC, which unravels the original ICO of the QC-QC into a set of quantum operations with a well-defined and acyclic causal order, compatible with the spacetime's light cone structure. Through this mapping, we clarify how the composability of physical experiments is recovered, and the role of relativistic causality.

Device-independent certification of indefinite causal orders

The strongest form of certification possible in quantum information theory is device-independent certification, which certifies the presence of a resource without making any assumptions about the devices used to perform the certification. This type of certification has been well-studied for entanglement and is exploited in cryptographic applications, for example, and there has been growing interest in applying it to different resources. While it is known that the causal indefiniteness of some quantum processes can be certified in a device-independent way through the violation of causal inequalities, it has been unclear whether more physical processes such as QC-QCs – which do not violate causal inequalities – can be certified in this way. Building on our previous work showing how one can certify causal indefiniteness in a "semi-device-independent" manner 80, we showed in 12 how this certification can be made stronger and transformed into a fully device-independent certification technique, in which no assumptions are made about the devices being used, other than the network structure describing how certain devices are connected. This shows that some important processes, like the quantum switch, can be certified in a device-indepndent manner, despite this being believed impossible until recently.

Query complexity of causally indefinite computation

Indefinite causal order opens interesting possibilities for information processing, such as the possibility to obtain computational advantages using causally indefinite quantum computations beyond what is possible with standards (causally ordered) quantum circuits. In 7 we study the computational advantages of causal indefiniteness in query complexity problems using the framework of quantum supermaps. Using semi-definite programming approaches, we are able to calculate the exact query complexity of different types of computations for small input sizes (4-bit Boolean functions with 2 queries to the oracle): standard quantum circuits, circuits with quantum control of causal order, and more general causally indefinite supermaps. We find that, for certain functions, causally indefinite supermaps can provide an advantage in query complexity, uncovering a new computational advantage of causal indefiniteness that, in contrast to previously known advantages, is formulated in a more standard complexity-theoretic setting. However, we prove that the class of quantum circuits with quantum control of causal order is unable to improve upon standard quantum circuits in this query complexity setting. In a work in preparation we study causally indefinite classical processes, and show that in this setting an asymptotic advantage in deterministic query complexity can be obtained.

Consistent multi-agent reasoning in Wigner's Friend Scenarios

It is natural to expect a complete physical theory to have the ability to consistently model agents as physical systems of the theory. With this motivation, Extended Wigner's Friend Scenarios (EWFSs) consider multiple quantum agents, who can perform quantum agents on each others' labs. These have been the subject of several no-go theorems: Frauchiger and Renner (FR) identified logical paradoxes arising from reasoning quantum agents, while other results highlight challenges for having an objective notion of measurement events and for causal reasoning in EWFSs. This raises the question: is it possible to reliably make and test scientific predictions, and consistently reason about the world when applying quantum theory universally? In 56, we give a positive answer by developing a general quantum circuit framework for EWFSs. By formalising the concept of Heisenberg cuts, we prove that FR-type paradoxes can be fully resolved and thereby provide concrete rules by which quantum agents can reason and make predictions in a logically and causally consistent manner. Our framework describes all predictions of an EWFS within a single, well-defined causal structure, while allowing events to be fundamentally subjective. Yet we show that an objective notion of measurement events emerges in real-world experiments. This provides a platform to consistently extend quantum information methods to Wigner's Friend Scenarios, and establishes that quantum computers playing the role of reasoning agents can in-principle be programmed consistently, while preserving the axioms of quantum theory and those of classical logic and probability theory.

Quadratically increasing computation speed without increasing interaction strengh nor power consumed

In 58, an initial invertigation kicking-off the research of Direction A of the quantum frequential computing program, has been performed. It was demostrated that there is indeed an advantage concerning the speed at which computation can be performed, if the control of the qubits/bits is quantum mechanical as opposed to the conventional setting where it is classical. It was proven that there is a quadratic speedup for quantum and classical algorithms alike, when the optimal quantum control state is used. The quantum advantage stems from the quantum resource of squeezing.

7.1.1 Visits of international scientists

Frédéric Dupuis

• Status
  Associate Professor
• Institution of origin:
  Université de Montréal
• Country:
  Canada
• Dates:
  April 15 - May 15
• Context of the visit:
  Research collaboration on security proofs for quantum cryptography
• Mobility program/type of mobility:
  Sabbatical research stay

7.2.1 Horizon Europe

7.2.2 H2020 projects

7.2.3 Other european programs/initiatives

PEPR DIQKD

• Title:
  Device-independent quantum key distribution
• Program:
  PEPR on Quantum Technologies
• Contact Inria:
  O. Fawzi
• Partners:
  CEA (coordinator), CNRS, Université Côte D’Azur, Sorbonne Université
• Duration:
  July 1, 2022 - June 30 2026

PEPR NISQ2LSQ

• Title:
  From NISQ to LSQ: Bosonic and LDPC codes
• Program:
  PEPR on Quantum Technologies
• Contact Inria:
  A. Leverrier (team COSMIQ)
• Contact QInfo:
  O. Fawzi
• Partners:
  Inria (coordinator), CNRS, CEA
• Duration:
  January 1, 2022 - December 2026

PEPR EPIQ

• Title:
  Study of the quantum stack: Algorithm, models, and simulation for quantum computing
• Program:
  PEPR on Quantum Technologies
• Contact Inria:
  S. Perdrix (team MOCQUA)
• Contact QInfo:
  O. Fawzi
• Partners:
  Inria (coordinator), CNRS, CEA
• Duration:
  January 1, 2022 - December 2026

PEPR HQI

• Title:
  Hybrid HPC Quantum Initiative
• Program:
  PEPR on Quantum Technologies
• Contact QInfo:
  D. Stilck Franca
• Partners:
  Inria, CPU, GENCI, CNRS, CEA (coordinator)
• Duration:
  April 1, 2023 - March 2028

ANR TaQC

• Title:
  Taming Quantum Causality
• Program:
  AAP Générique 2022
• Contact QInfo:
  A. Abbott
• Partners:
  CNRS (Institut Néel; coordinator), Inria QINFO, Université Paris-Saclay (LMF, Inria QUACS), CEA (IRFU/LARSIM)
• Duration:
  January 1, 2023 - December 2026

8.1.1 Scientific events: organisation

8.1.2 Scientific events: selection

8.1.3 Journal

8.1.4 Invited talks

• G. Aubrun, course given at the research school Random quantum channels: entanglement and entropies, Marseille (CIRM), July 2024
• G. Aubrun, invited speaker at the International Congress on Mathematical Physics, Strasbourg, July 2024
• G. Aubrun, mini-course given at the conference Random tensors and related topics, Paris (IHP), Oct 2024
• O. Fawzi, Symposium on Quantum Optimization and Geometry, Amsterdam, January 2024
• O. Fawzi, Quantum Information Workshop, Les Diablerets, February 2024
• O. Fawzi, Workshop Quantum Cryptography and Quantum Networks, Berlin, May 2024
• O. Fawzi, Quantum Error Correction meets Operator Algebras, Oslo, June 2024
• O. Fawzi, Focused workshop on quantum Reńyi divergences, July 2024
• O. Fawzi, Fault-Tolerant Quantum Technologies, Benasque, August 2024
• O. Fawzi, IWOTA 2024, Canterbury, August 2024
• O. Fawzi, Journées Scientifiques Inria, Grenoble, August 2024
• O. Fawzi, Workshop on Machine Learning and Quantum Information, Marseille (CIRM), September 2024
• O. Fawzi, Séminaire Parisien d'Optimisation, December 2024
• V. Vilasini, From Quantum Materials to Quantum Information: Symposium on Trans-Scale Quantum Science and Quantum Materials Synthesis (QMQI2024) held at Okinawa Institute for Science and Technology in November 2024.
• V. Vilasini, Vienna Foundations Conference, Vienna in September 2024.
• V. Vilasini, Invited Plenary talk at Relativistic Quantum Information North, Prague in August 2024.
• V. Vilasini, Emergence of Classicality: New Perspectives on Measurements in Quantum Theory, held at Trinity College Dublin in July 2024.
• V. Vilasini, A look at the interface between gravity and quantum theory, held in San Vito di Cadore in July 2024.
• V. Vilasini, Invited talk at Laboratoire Kastler Brossel, Paris in June 2024.
• D. Stilck Franca, Quantum Gibbs Sampling Tutorial, Simons Instute Berkeley, April 2024.
• M. Woods, invited speaker at Geometry of Quantum States, Siegen, August 2024
• M. Woods, invited speaker at Foundations of Quantum Computing, Royal Holloway, University of London, September 2024.
• M. Woods, invited speaker at QMQI, Okinawa Institute of Science and Technology, Japan November 2024.

8.1.5 Leadership within the scientific community

• V. Vilasini is a co-leader of a research working group in the European COST Action for Relativistic Quantum Information

8.1.6 Scientific expertise

• Alastair Abbott : Member of the selection committee for Inria CRCN and ISFP recrutement competitions, Inria Saclay Centre
• Alastair Abbott : Member of the selection committee for Assistant Professor in Quantum Computing, CentraleSupélec
• Omar Fawzi : Member of the selection commitee for Inria CRCN and ISFP recruitment competitions, Inria Paris
• Omar Fawzi : Member of the selection commitee for a Professor at ENS de Lyon.

8.1.7 Research administration

• Alastair Abbott is a member of the governing board of the QuantAlps Research Federation
• Alastair Abbott is a member of the governing board of the TIQuA CD Tools Programme

8.2.1 Teaching

• L3: G. Aubrun, Probability, 32 hours, course given for the first year students in computer science, ENS Lyon.
• Master: A. Abbott, Fundamental Computer Science. M1 MOSIG/M1 INFO UGA, 27 hours lectures and tutorials.
• Master: O. Fawzi, Quantum Computer Science. Master 1 Informatique ENS Lyon, 28 hours lectures.

8.2.2 Supervision

• PhD: Raphaël Mothe, Causal indefiniteness and dynamicality in quantum mechanics (A. Abbott with C. Branciard)
• PhD: Sarah Timhadjelt, Liberté asymptotique forte de matrices de perturbations aléatoires, indépendantes et uniformes (G. Aubrun, co-supervisor)
• PhD in progress: Pierre Pocreau, Implications of causal indefiniteness for quantum communication (A. Abbott with M. Mhalla)
• PhD in progress: Maarten Grothus, Exploiting causal indefiniteness in quantum computational models (A. Abbott with C. Branciard)
• PhD in progress: Raphaël le Bihan, Compositionality and applications of quantum supermaps (A. Abbott with M. Echenim)
• PhD in progress: Emilien de Bank, (V. Vilasini with C. Branciard)
• PhD in progress: Amanda Maria Fonseca, (V. Vilasini with C. Branciard)
• PhD in progress: Pablo Alvarez Dominguez, (M. Woods)
• PhD in progress: Emily Beatty, Quantum Optimal Transposrt (G. Aubrun, D. Stilck Franca)
• PhD in progress: Victor Martinez, Quantum algorithms and combinatorial optimization (O. Fawzi, D. Stilck Franca)
• PhD in progress: Mostafa Taheri, (O. Fawzi)
• PhD in progress: Idris Delsol, (O. Fawzi)
• PhD thesis submitted (defense on 17th February 2025): Victor Gitton, ETH Zürich (co-supervisor: V. Vilasini with supervisor: Renato Renner)
• Master's internship: Raphaël le Bihan, Compositionality of quantum supermaps (A. Abbott)

8.2.3 Juries

• PhD: Harold Nieuwboer, Classical and quantum algorithms for scaling problems, University of Amsterdam, 31 January 2024
• PhD: Gergely Bunth, On quantum Rényi divergences, Budapest University of Technology and Economics, 23 July 2024
• PhD: Emanuel-Cristian Boghiu Crihan, Bell non-locality and causal networks, Institute of Photonic Sciences (ICFO) Barcelona, 9th July 2024 (V. Vilasini, external examiner).
• PhD: Raphaël Mothe, Causal indefiniteness and dynamicality in quantum mechanics, Université Grenoble Alpes, 18th October 2024 (V. Vilasini, internal examiner)
• PhD: Isaac Friend, Causal identification for quantum networks, University of Oxford, U.K., 6th of December 2024 (V. Vilasini, external examiner)
• HDR: Alantha Newman, Cuts, orders and partitions through the lens of relaxation, rounding and approximation, Université Grenoble Alpes, 4 December 2024 (O. Fawzi examiner)

8.3.1 Productions (articles, videos, podcasts, serious games, ...)

• V. Vilasini, popular science article in Phys.org and Physicsworld based on recent publications 29, 30 and interview with science journalist.
• A. Abbott, Explorations Quantiques 2050, les récits. Technological analysis of scenarios and their basis in the scientific literature 32.
• M. Woods, interview with science jouralist Karmela Padavic-Callaghan for comments in her popular science article in New Scientist.

8.3.2 Participation in Live events

• Alastair Abbott, invited introductory talk for general public and researchers in social sciences and humanities in a program creating dialogue with citizens about the implications of quantum technologies, “Quantum Dates: Quantique, Cybersecurité et Data” (November 2024).
• Emily Beatty and Mizanur Rahaman organized a booth in the event "Science is Wonderful" that is held each year by the EU for the Marie-Curie fellows. In this event, researchers are chosen to explain their scientific work to the public (mainly high school students) through interactive experiments, hands-on activities, science shows, games and quizzes. More than 500 students visiting our booth who came and participated in our presentation.

International journals

• 6 articleA. A.Alastair A. Abbott, M.Mehdi Mhalla and P.Pierre Pocreau. Improving social welfare in non-cooperative games with different types of quantum resources.Quantum8June 2024, 1376HALDOIback to text
• 7 articleA. A.Alastair A. Abbott, M.Mehdi Mhalla and P.Pierre Pocreau. Quantum query complexity of Boolean functions under indefinite causal order.Physical Review Research63July 2024, L032020HALDOIback to text
• 8 articleG.Guillaume Aubrun, K.Kenneth Davidson, A.Alexander Müller-Hermes, V.Vern Paulsen and M.Mizanur Rahaman. Completely bounded norms of k-positive maps.Journal of the London Mathematical Society1096June 2024, e12936HALDOI
• 9 articleG.Guillaume Aubrun, A.Alexander Müller-Hermes and M.Martin Plávala. Monogamy of entanglement between cones.Math.Ann.39112025, 1591-1609HALDOIback to text
• 10 articleS.Stefan Bäuml, C.Carlos Pascual-García, V.Victoria Wright, O.Omar Fawzi and A.Antonio Acín. Security of discrete-modulated continuous-variable quantum key distribution.Quantum8July 2024, 1-37HALDOI
• 11 articleP.Peter Brown, H.Hamza Fawzi and O.Omar Fawzi. Device-independent lower bounds on the conditional von Neumann entropy.Quantum8August 2024, 1445HALDOI
• 12 articleH.Hippolyte Dourdent, A. A.Alastair A. Abbott, I.Ivan Šupić and C.Cyril Branciard. Network-Device-Independent Certification of Causal Nonseparability.Quantum8October 2024, 1-24HALDOIback to text
• 13 articleH.Hamza Fawzi, O.Omar Fawzi and S. O.Samuel O Scalet. Certified algorithms for equilibrium states of local quantum Hamiltonians.Nature Communications1512024, 7394HALDOIback to text
• 14 articleH.Hamza Fawzi, O.Omar Fawzi and S.Samuel Scalet. Entropy constraints for ground energy optimization.Journal of Mathematical Physics6532024, 032201HALDOI
• 15 articleO.Omar Fawzi and P.Paul Fermé. Broadcast Channel Coding: Algorithmic Aspects and Non-Signaling Assistance.IEEE Transactions on Information Theory70November 2024, 7563 - 7580HALDOI
• 16 articleO.Omar Fawzi, R.Richard Kueng, D.Damian Markham and A.Aadil Oufkir. Learning properties of quantum states without the IID assumption.Nature Communications151November 2024, 9677HALDOIback to text
• 17 articleV.Victor Gitton and M. P.Mischa P Woods. On the System loophole of generalized noncontextuality.Physical Review Research64December 2024, 043289HALDOI
• 18 articleD.Dylan Harley, I.Ishaun Datta, F. R.Frederik Ravn Klausen, A.Andreas Bluhm, D.Daniel Stilck França, A. H.Albert H Werner and M.Matthias Christandl. Going beyond gadgets: the importance of scalability for analogue quantum simulators.Nature Communications151August 2024, 6527HALDOI
• 19 articleY.Yanglin Hu, M.Maximilian Lock and M.Mischa Woods. On the feasibility of detecting quantum delocalization effects on relativistic time dilation in optical clocks.Quantum Science and Technology9September 2024, 045052HALDOI
• 20 articleD.David Kribs, J.Jeremy Levick, R.Rajesh Pereira and M.Mizanur Rahaman. Operator algebra generalization of a theorem of Watrous and mixed unitary quantum channels.Journal of Physics A: Mathematical and Theoretical57March 2024, 115303HALDOI
• 21 articleL. A.Liubov A. Markovich, V. V.V. V. Dobrovitski, A. H.Albert H. Werner, J.Johannes Borregaard and D.Daniel Stilck França. Efficient and robust estimation of many-qubit Hamiltonians.Nature Communications15311January 2024HALDOI
• 22 articleT.Tony Metger, O.Omar Fawzi, D.David Sutter and R.Renato Renner. Generalised Entropy Accumulation.Communications in Mathematical Physics40511October 2024, 261HALDOI
• 23 articleR.Raphaël Mothe, C.Cyril Branciard and A. A.Alastair A. Abbott. Reassessing the advantage of indefinite causal orders for quantum metrology.Physical Review A1096June 2024, 062435HALDOI
• 24 articleA.Amélie Piveteau, A. A.Alastair A. Abbott, S.Sadiq Muhammad, M.Mohamed Bourennane and A.Armin Tavakoli. Weak entanglement improves quantum communication using only product measurements.Physical Review Applied21March 2024, 034053HALDOI
• 25 articleC.Cambyse Rouzé and D.Daniel Stilck França. Learning quantum many-body systems from a few copies.Quantum82024, 1319HALDOI
• 26 articleC.Cambyse Rouzé, D.Daniel Stilck França, E.Emilio Onorati and J.James Watson. Efficient learning of ground and thermal states within phases of matter.Nature Communications151September 2024, 7755HALDOI
• 27 articleM.Matthias Salzger and V.Vilasini Venkatesh. Mapping indefinite causal order processes to composable quantum protocols in a spacetime.New Journal of Physics2025, 1-54In press. HALDOIback to text
• 28 articleM.Martin Sandfuchs, M.Marcus Haberland, V.V. Vilasini and R.Ramona Wolf. Security of differential phase shift QKD from relativistic principles.Quantum2025. In press. HALback to text
• 29 articleV.V. Vilasini and R.Renato Renner. Embedding cyclic information-theoretic structures in acyclic space-times: No-go results for indefinite causality.Physical Review A1102August 2024, 022227HALDOIback to text
• 30 articleV.V. Vilasini and R.Renato Renner. Fundamental Limits for Realizing Quantum Processes in Spacetime.Physical Review Letters1338August 2024, 080201HALDOIback to text

International peer-reviewed conferences

• 31 inproceedingsM.Mario Berta, O.Omar Fawzi and A.Aadil Oufkir. Optimality of meta-converse for channel simulation.ISIT 2024 - IEEE International Symposium on Information TheoryAthens, GreeceIEEEOctober 2024, 1209-1214HALDOI

Scientific book chapters

• 32 inbookA. A.Alastair A. Abbott, P.Pierre Engerran, F.Fabrice Forest, O.Oscar Gravier and R. S.Robert S. Whitney. L'analyse technologique.Explorations quantiques 2050: Les récitsMarch 2024HALback to text

Reports & preprints

• 33 miscK.Kanat Abdukhalikov, T.Tushar Bag and D.Daniel Panario. Quantum Codes from Group Ring Codes.December 2024HAL
• 34 miscA.Adam Artymowicz, H.Hamza Fawzi, O.Omar Fawzi and S. O.Samuel O. Scalet. Certified algorithms for quantum Hamiltonian learning via energy-entropy inequalities.October 2024HAL
• 35 miscG.Guillaume Aubrun and A.Alexander Müller-Hermes. Limit formulas for norms of tensor power operators.October 2024HAL
• 36 miscT.Tushar Bag, H. Q.Hai Q Dinh and D.Daniel Panario. Some New Non-binary Quantum Codes from One-generator Quasi-cyclic Codes.December 2024HAL
• 37 miscE.Emily Beatty and D.Daniel Stilck França. Order p quantum Wasserstein distances from couplings.February 2024HAL
• 38 miscS.Simon Becker, N.Niklas Galke, R.Robert Salzmann and L.Lauritz van Luijk. Convergence rates for the Trotter-Kato splitting.July 2024HAL
• 39 miscH.-C.Hao-Chung Cheng, N.Nilanjana Datta, N.Nana Liu, T.Theshani Nuradha, R.Robert Salzmann and M. M.Mark M Wilde. An invitation to the sample complexity of quantum hypothesis testing.May 2024HAL
• 40 miscM.Matthias Christandl, O.Omar Fawzi and A.Ashutosh Goswami. Fault-tolerant quantum input/output.2024HALback to text
• 41 miscK.Kun Fang, H.Hamza Fawzi and O.Omar Fawzi. Generalized quantum asymptotic equipartition.November 2024HAL
• 42 miscM.Marco Fanizza, C.Cambyse Rouzé and D. S.Daniel Stilck França. Efficient Hamiltonian, structure and trace distance learning of Gaussian states.2024HALDOI
• 43 miscO.Omar Fawzi, A.Aadil Oufkir and R.Robert Salzmann. Optimal Fidelity Estimation from Binary Measurements for Discrete and Continuous Variable Systems.September 2024HAL
• 44 miscO.Omar Fawzi, M.Mizanur Rahaman and M.Mostafa Taheri. Capacities of quantum Markovian noise for large times.2024HALDOI
• 45 miscO.Omar Fawzi, M.Mizanur Rahaman and M.Mostafa Taheri. Capacities of quantum Markovian noise for large times.2024HALDOIback to text
• 46 miscL.Li Gao and M.Mizanur Rahaman. Generalized Stein's lemma and asymptotic equipartition property for subalgebra entropies.2024HALDOI
• 47 miscM.Maarten Grothus and V.V. Vilasini. Characterizing Signalling: Connections between Causal Inference and Space-time Geometry.2024HALback to text
• 48 miscC.Cambyse Rouzé, D. S.Daniel Stilck França and Á.Álvaro Alhambra. Efficient thermalization and universal quantum computing with quantum Gibbs samplers.2024HALDOI
• 49 miscC.Cambyse Rouzé, D. S.Daniel Stilck França and Á.Álvaro Alhambra. Optimal quantum algorithm for Gibbs state preparation.2024HALDOI
• 50 miscT. L.Tristan Le Roy-Deloison, E. P.Edwin Peter Lobo, J.Jef Pauwels and S.Stefano Pironio. Device-independent quantum key distribution based on routed Bell tests.April 2024HAL
• 51 miscR.Robert Salzmann, B.Bjarne Bergh and N.Nilanjana Datta. Robustness of Fixed Points of Quantum Channels and Application to Approximate Quantum Markov Chains.May 2024HAL
• 52 miscR.Robert Salzmann. Quantitative Quantum Zeno and Strong Damping Limits in Strong Topology.September 2024HAL
• 53 miscS.Satvik Singh, M.Mizanur Rahaman and N.Nilanjana Datta. Zero-error communication under discrete-time Markovian dynamics.2024HALDOI
• 54 miscV.V. Vilasini and R.Roger Colbeck. Information-processing in theories constrained by no superluminal causation vs no superluminal signalling.February 2024HALback to text
• 55 miscV.V. Vilasini and R.Roger Colbeck. The standard no-signalling constraints in Bell scenarios are neither sufficient nor necessary for preventing superluminal signalling with general interventions.January 2025HAL
• 56 miscV.V Vilasini and M. P.Mischa P Woods. A general quantum circuit framework for Extended Wigner's Friend Scenarios: logically and causally consistent reasoning without absolute measurement events.November 2024HALback to text
• 57 miscG.Guoming Wang, D. S.Daniel Stilck França, G.Gumaro Rendon and P.Peter Johnson. Faster ground state energy estimation on early fault-tolerant quantum computers via rejection sampling.January 2024HALDOI
• 58 miscM.Mischa Woods. Quantum Frequential Computing: a quadratic run time advantage for all algorithms.2024HALDOIback to text