QUROPE Quantum Information Processing and Communication in Europe

We show that the basic non-relativistic quantum formulations can be derived from a least observability principle. The principle extends the least action principle from classical mechanics by factoring in two assumptions. First, the Planck constant defines the discrete amount of action a physical object needs to exhibit during its dynamics in order to be observable. Second, there is constant vacuum fluctuation along a classical trajectory. A novel method is introduced to define the information metrics that measures additional observable information due to vacuum fluctuations, which is then converted to the additional action through the first assumption. Applying the variation principle to minimize the total actions allows us to elegantly recover the basic quantum formulations including the uncertainty relation and the Schr\"{o}dinger equation in both position and momentum representations. Adding the no preferred representation assumption, we obtain the transformation formulation between position and momentum representations. The extended least action principle shows clearly how classical mechanics becomes quantum mechanics. Furthermore, it is a mathematical tool that can bring in new results. By defining the information metrics for vacuum fluctuations using more general definitions of relative entropy, we obtain a generalized Schr\"{o}dinger equation that depends on the order of relative entropy. The principle can be applied to derive more advance quantum formalism such as quantum scalar field theory.

We investigate what can be concluded about the quantum system when the sequential quantum measurements of its observable -- a prominent example of the so-called quantum stochastic process -- fulfill the Kolmogorov consistency condition, and thus, appear to an observer as a sampling of classical trajectory. We identify a set of physical conditions imposed on the system dynamics, that when satisfied lead to the aforementioned trajectory interpretation of the measurement results. Then, we show that when another quantum system is coupled to the observable, the operator representing it can be replaced by an external noise. Crucially, the realizations of this surrogate (classical) stochastic process are following the same trajectories as those measured by the observer. Therefore, it can be said that the trajectory interpretation suggested by the Kolmogorov consistent measurements also applies in contexts other than sequential measurements.

Whereas point-gap topological phases are responsible for exceptional phenomena intrinsic to non-Hermitian systems, their realization in quantum materials is still elusive. Here we propose a simple and universal platform of point-gap topological phases constructed from Hermitian topological insulators and superconductors. We show that (d-1)-dimensional point-gap topological phases are realized by making a boundary in d-dimensional topological insulators and superconductors dissipative. A crucial observation of the proposal is that adding a decay constant to boundary modes in d-dimensional topological insulators and superconductors is topologically equivalent to attaching a (d-1)-dimensional point-gap topological phase to the boundary. We furthermore establish the proposal from the extended version of the Nielsen-Ninomiya theorem, relating dissipative gapless modes to point-gap topological numbers. From the bulk-boundary correspondence of the point-gap topological phases, the resultant point-gap topological phases exhibit exceptional boundary states or in-gap higher-order non-Hermitian skin effects.

We discuss the construction of a microcanonical projection WOW of a quantum operator O induced by an energy window filter W, its spectrum, and the retrieval of canonical many-time correlations from it.

Fabrication errors pose a significant challenge in scaling up solid-state quantum devices to the sizes required for fault-tolerant (FT) quantum applications. To mitigate the resource overhead caused by fabrication errors, we combine two approaches: (1) leveraging the flexibility of a modular architecture, (2) adapting the procedure of quantum error correction (QEC) to account for fabrication defects. We simulate the surface code adapted to qubit arrays with arbitrarily distributed defects to find metrics that characterize how defects affect fidelity. We then determine the impact of defects on the resource overhead of realizing a fault-tolerant quantum computer, on a chiplet-based modular architecture. Our strategy for dealing with fabrication defects demonstrates an exponential suppression of logical failure where error rates of non-faulty physical qubits are ~0.1% in a circuit-based noise model. This is a typical regime where we imagine running the defect-free surface code. We use our numerical results to establish post-selection criteria for building a device from defective chiplets. Using our criteria, we then evaluate the resource overhead in terms of the average number of fabricated physical qubits per logical qubit. We find that an optimal choice of chiplet size, based on the defect rate and target fidelity, is essential to limiting any additional error correction overhead due to defects. When the optimal chiplet size is chosen, at a defect rate of 1% the resource overhead can be reduced to below 3X and 6X respectively for the two defect models we use, for a wide range of target performance. We also determine cutoff fidelity values that help identify whether a qubit should be disabled or kept as part of the error correction code.

In this work, we consider biased-noise qubits affected only by bit-flip errors, which is motivated by existing systems of stabilized cat qubits. This property allows us to design a class of noisy Hadamard-tests involving entangling and certain non-Clifford gates, which can be conducted reliably with only a polynomial overhead in algorithm repetitions. On the flip side we also found classical algorithms able to efficiently simulate both the noisy and noiseless versions of our specific variants of Hadamard test. We propose to use these algorithms as a simple benchmark of the biasness of the noise at the scale of large circuits. The bias being checked on a full computational task, it makes our benchmark sensitive to crosstalk or time-correlated errors, which are usually invisible from individual gate tomography. For realistic noise models, phase-flip will not be negligible, but in the Pauli-Twirling approximation, we show that our benchmark could check the correctness of circuits containing up to $10^6$ gates, several orders of magnitudes larger than circuits not exploiting a noise-bias. Our benchmark is applicable for an arbitrary noise-bias, beyond Pauli models.

Quantum alternating operator ansatz (QAOA) has a strong connection to the adiabatic algorithm, which it can approximate with sufficient depth. However, it is unclear to what extent the lessons from the adiabatic regime apply to QAOA as executed in practice with small to moderate depth. In this paper, we demonstrate that the intuition from the adiabatic algorithm applies to the task of choosing the QAOA initial state. Specifically, we observe that the best performance is obtained when the initial state of QAOA is set to be the ground state of the mixing Hamiltonian, as required by the adiabatic algorithm. We provide numerical evidence using the examples of constrained portfolio optimization problems with both low ($p\leq 3$) and high ($p = 100$) QAOA depth. Additionally, we successfully apply QAOA with XY mixer to portfolio optimization on a trapped-ion quantum processor using 32 qubits and discuss our findings in near-term experiments.

We introduce the concept of partial and full tunneling processes to explain the seemingly contradictory non-zero and vanishing tunneling times often reported in the literature. Our analysis starts by considering the traversal time of a quantum particle through a potential barrier, including both above and below-barrier traversals, using the theory of time-of-arrival operators. We then show that there are three traversal processes corresponding to non-tunneling, full-tunneling, and partial tunneling. The distinction between the three depends on the support of the incident wavepackets energy distribution in relation to the shape of the barrier. Non-tunneling happens when the energy distribution of the quantum particle lies above the maximum of the potential barrier. Otherwise, full-tunneling process occurs when the energy distribution of the particle is below the minimum of the potential barrier. For this process, the obtained traversal time is interpreted as the tunneling time. Finally, the partial-tunneling process occurs when the energy distribution lies between the minimum and maximum of the potential barrier. This signifies that the quantum particle tunneled only through some portions of the potential barrier. We argue that the duration for a partial-tunneling process should not be interpreted as the tunneling time but instead as a partial traversal time to differentiate it from the full-tunneling process. We then show that a full-tunneling process is always instantaneous, while a partial-tunneling process takes a non-zero amount of time. We are then led to the hypothesis that experimentally measured non-zero and vanishing tunneling times correspond to partial and full-tunneling processes, respectively.

Digital payments have replaced physical banknotes in many aspects of our daily lives. Similarly to banknotes, they should be easy to use, unique, tamper-resistant and untraceable, but additionally withstand digital attackers and data breaches. Current technology substitutes customers' sensitive data by randomized tokens, and secures the payment's uniqueness with a cryptographic function, called a cryptogram. However, computationally powerful attacks violate the security of these functions. Quantum technology comes with the potential to protect even against infinite computational power. Here, we show how quantum light can secure daily digital payments by generating inherently unforgeable quantum cryptograms. We implement the scheme over an urban optical fiber link, and show its robustness to noise and loss-dependent attacks. Unlike previously proposed protocols, our solution does not depend on long-term quantum storage or trusted agents and authenticated channels. It is practical with near-term technology and may herald an era of quantum-enabled security.

A recently introduced classical simulation method for universal quantum computation with magic states operates by repeated sampling from probability functions [M. Zurel et al. PRL 260404 (2020)]. This method is closely related to sampling algorithms based on Wigner functions, with the important distinction that Wigner functions can take negative values obstructing the sampling. Indeed, negativity in Wigner functions has been identified as a precondition for a quantum speed-up. However, in the present method of classical simulation, negativity of quasiprobability functions never arises. This model remains probabilistic for all quantum computations. In this paper, we analyze the amount of classical data that the simulation procedure must track. We find that this amount is small. Specifically, for any number $n$ of magic states, the number of bits that describe the quantum system at any given time is $2n^2+O(n)$.

Matrix Product States (MPS) and Operators (MPO) have been proven to be a powerful tool to study quantum many-body systems but are restricted to moderately entangled states as the number of parameters scales exponentially with the entanglement entropy. While MPS can efficiently find ground states of 1D systems, their capacities are limited when simulating their dynamics, where the entanglement can increase ballistically with time. On the other hand, quantum devices appear as a natural platform to encode and perform the time evolution of correlated many-body states. However, accessing the regime of long-time dynamics is hampered by quantum noise. In this study we use the best of worlds: the short-time dynamics is efficiently performed by MPSs, compiled into short-depth quantum circuits, and is performed further in time on a quantum computer thanks to efficient MPO-optimized quantum circuits. We quantify the capacities of this hybrid classical-quantum scheme in terms of fidelities taking into account a noise model. We show that using classical knowledge in the form of tensor networks provides a way to better use limited quantum resources and lowers drastically the noise requirements to reach a practical quantum advantage. Finally we successfully demonstrate our approach with an experimental realization of the technique. Combined with efficient circuit transpilation we simulate a 10-qubit system on an actual quantum device over a longer time scale than low-bond-dimension MPSs and purely quantum Trotter evolution.

Variational Quantum Algorithms are one of the most promising candidates to yield the first industrially relevant quantum advantage. Being capable of arbitrary function approximation, they are often referred to as Quantum Neural Networks (QNNs) when being used in analog settings as classical Artificial Neural Networks (ANNs). Similar to the early stages of classical machine learning, known schemes for efficient architectures of these networks are scarce. Exploring beyond existing design patterns, we propose a reduced-width circuit ansatz design, which is motivated by recent results gained in the analysis of dropout regularization in QNNs. More precisely, this exploits the insight, that the gates of overparameterized QNNs can be pruned substantially until their expressibility decreases. The results of our case study show, that the proposed design pattern can significantly reduce training time while maintaining the same result quality as the standard "full-width" design in the presence of noise.

The JPEG algorithm compresses a digital image by filtering its high spatial-frequency components. Similarly, we introduce a quantum algorithm that uses the quantum Fourier transform to discard the high spatial-frequency qubits of an image, downsampling it to a lower resolution. This allows one to capture, compress, and send images even with limited quantum resources for storage and communication. We show under which conditions this protocol is advantageous with respect to its classical counterpart.

The union-find decoder is a leading algorithmic approach to the correction of quantum errors on the surface code, achieving code thresholds comparable to minimum-weight perfect matching (MWPM) with amortised computational time scaling near-linearly in the number of physical qubits. This complexity is achieved via optimisations provided by the disjoint-set data structure. We demonstrate, however, that the behaviour of the decoder at scale underutilises this data structure for twofold analytic and algorithmic reasons, and that improvements and simplifications can be made to architectural designs to reduce resource overhead in practice. To reinforce this, we model the behaviour of erasure clusters formed by the decoder and show that there does not exist a percolation threshold within the data structure for any mode of operation. This yields a linear-time worst-case complexity for the decoder at scale, even with a naive implementation omitting popular optimisations.

Quantum tunneling is the phenomenon that makes superconducting circuits "quantum". Recently, there has been a renewed interest in using quantum tunneling in phase space of a Kerr parametric oscillator as a resource for quantum information processing. Here, we report a direct observation of quantum interference induced by such tunneling in a planar superconducting circuit through Wigner tomography. We experimentally elucidate all essential properties of this quantum interference, such as mapping from Fock states to cat states, a temporal oscillation due to the pump detuning, as well as its characteristic Rabi oscillations and Ramsey fringes. Finally, we perform gate operations as manipulations of the observed quantum interference. Our findings lay the groundwork for further studies on quantum properties of superconducting Kerr parametric oscillators and their use in quantum information technologies.

Because of their small size, low loss, and compatibility with magnetic fields and elevated temperatures, surface acoustic wave resonators hold significant potential as future quantum interconnects. Here, we design, fabricate, and characterize GHz-frequency surface acoustic wave resonators with the potential for strong capacitive coupling to nanoscale solid-state quantum systems, including semiconductor quantum dots. Strong capacitive coupling to such systems requires a large characteristic impedance, and the resonators we fabricate have impedance values above 100 $\Omega$. We achieve such high impedance values by tightly confining a Gaussian acoustic mode. At the same time, the resonators also have low loss, with quality factors of several thousand at millikelvin temperatures. These high-impedance resonators are expected to exhibit large vacuum electric-field fluctuations and have the potential for strong coupling to a variety of solid-state quantum systems.

Conventionally, the total correlations within a quantum system are quantified through distance-based expressions such as the relative entropy or the square-norm. Those expressions imply that a quantum state can contain both classical and quantum correlations. In this work, we provide an alternative method to quantify the total correlations through the Pearson correlation coefficient. Using this method, we argue that a quantum state can be correlated in either a classical or a quantum way, i.e., the two cases are mutually exclusive. We also illustrate that, at least for the case of two-qubit systems, the distribution of the correlations among certain locally incompatible pairs of observables provides insight in regards to whether a system contains classical or quantum correlations. Finally, we show how correlations in quantum systems are connected to the general entropic uncertainty principle.

We investigate how the breaking of charge conjugation symmetry $\mathcal{C}$ impacts on the dynamics of a half-filled fermionic lattice system after global quenches. We show that, when the initial state is insulating and the $\mathcal{C}$-symmetry is broken non-locally by a constant magnetic flux, local observables and correlations behave as if the symmetry were unbroken for a time interval proportional to the system size $L$. In particular, the local particle density of a quenched dimerized insulator remains pinned to $1/2$ in each lattice site for an extensively long time, while it starts to significantly fluctuate only afterwards. Due to its qualitative resemblance to the sudden arrival of rapidly rising ocean waves, we dub this phenomenon the ``tsunami effect". Notably, it occurs even though the chiral symmetry is dynamically broken right after the quench. Furthermore, we identify a way to quantify the amount of symmetry breaking in the quantum state, showing that in insulators perturbed by a flux it is exponentially suppressed as a function of the system size, while it is only algebraically suppressed in metals and in insulators with locally broken $\mathcal{C}$-symmetry. The robustness of the tsunami effect to weak disorder and interactions is demonstrated, and possible experimental realizations are proposed.

Based on the two-qubit Jaynes-Cummings model - a common cavity quantum electrodynamics model, and extending to modification of the three-qubit Tavis-Cummings model, we investigate the quantum correlation between light and matter in bipartite quantum systems. By resolving the quantum master equation, we are able to derive the dissipative dynamics in open systems. To gauge the degree of quantum entanglement, some entanglement measurements are introduced: von Neumann entropy, concurrence and quantum discord. In addition, consideration is given to the impacts of initial entanglement and dissipation strength on quantum discord. Finally we discussed two different cases of nuclei motion: quantum and classical.

We numerically simulate a non-Abelian lattice gauge theory in two spatial dimensions, with Tensor Networks (TN). We focus on the SU(2) Yang-Mills model in Hamiltonian formulation, with dynamical matter and minimally truncated gauge field (hardcore gluon). Thanks to the TN sign-problem-free approach, we characterize the phase diagram of the model at zero and finite baryon number as a function of the quark bare mass and color charge. Already at intermediate system sizes, we distinctly detect a liquid phase of quark-pair bound-state quasi-particles (baryons), whose mass is finite towards the continuum limit. Interesting phenomena arise at the transition boundary where color-electric and color-magnetic terms are maximally frustrated: for low quark masses, we see traces of potential deconfinement, while for high masses, signatures of a possible topological order.