QUROPE Quantum Information Processing and Communication in Europe

We propose an efficient protocol to estimate the fidelity of an $n$-qubit entangled measurement device, requiring only qubit state preparations and classical data post-processing. It works by measuring the eigenstates of Pauli operators, which are strategically selected according to their importance weights and collectively contributed by all measurement operators. We rigorously analyze the protocol's performance and demonstrate that its sample complexity is uniquely determined by the number of Pauli operators possessing non-zero expectation values with respect to the target measurement. Moreover, from a resource-theoretic perspective, we introduce the stabilizer R\'enyi entropy of quantum measurements as a precise metric to quantify the inherent difficulty of estimating measurement fidelity.

Resonance fluorescence (RF) serves as a fundamental path for matter to coherently interact with light. Accompanying this coherent process, recent studies suggested parallel existence of an incoherent scattering channel in order to explain the long-standing paradox of joint observation of a laser-like spectrum and anti-bunching in the RF of a weakly driven two-level emitter. If truly present, this incoherent process would cast doubt over RF's prospects in quantum information applications. Here, we exploit the concept of single-photon time-energy entanglement and have thus revolved the paradox without reliance on any incoherent scattering process. We derive a dimensionless dependence of the first-order coherence of the RF on the driving strength, followed by experimental verification on a cavity-enhanced quantum dot device with near-perfect light coupling. Furthermore, we perform the first phase-dependent two-photon interference experiment and observe peculiar coincidence bunching that is explained by single-photon time-energy entanglement. Our work reveals a new dimension in the understanding of photonic quantum superposition and may stimulate new applications.

The equilibrium state of a closed system in contact with a heat reservoir can be described in terms of the Helmholtz free energy ($F$). Mathematically, $F$ is related to the entropy ($S$) of the system by the Legendre transform where the independent variable is changed from the energy ($U$) of the system to its inverse temperature ($1/T$). This mathematical structure is preserved in the statistical framework of canonical ensemble where the system energy and entropy are defined in terms of expectation values over the canonical probability distribution. In this paper, we present the microscopic form of the Legendre transform ($\mathscr{L}_{\!\mathscr{M}}^{}$) by treating the microstate probabilities and the energies (scaled by the inverse temperature) as conjugate variables. The transform $\mathscr{L}_{\!\mathscr{M}}^{}$ requires that the canonical entropy be redefined by explicitly incorporating the normalization constraint on the probabilities and underscores the exact differential property of the canonical entropy. Canonical distribution may be derived as a consequence of this transform. Other approaches, in particular, Jaynes' maximum entropy principle is compared with the present approach. The relevance of $\mathscr{L}_{\!\mathscr{M}}^{}$ is explored based on the thermodynamics of a system in contact with a heat reservoir.

Quantum Reinforcement Learning (QRL) emerged as a branch of reinforcement learning (RL) that uses quantum submodules in the architecture of the algorithm. One branch of QRL focuses on the replacement of neural networks (NN) by variational quantum circuits (VQC) as function approximators. Initial works have shown promising results on classical environments with discrete action spaces, but many of the proposed architectural design choices of the VQC lack a detailed investigation. Hence, in this work we investigate the impact of VQC design choices such as angle embedding, encoding block architecture and postprocessesing on the training capabilities of QRL agents. We show that VQC design greatly influences training performance and heuristically derive enhancements for the analyzed components. Additionally, we show how to design a QRL agent in order to solve classical environments with continuous action spaces and benchmark our agents against classical feed-forward NNs.

We generalize the notion of joint measurability to continuous variable systems by extending a recently introduced compression algorithm of quantum measurements to this realm. The extension results in a property that asks for the minimal dimensional quantum system required for representing a given set of quantum measurements. To illustrate the concept, we show that the canonical pair of position and momentum is completely incompressible. We translate the concept of measurement compression to the realm of quantum correlations, where it results in a generalisation of continuous variable quantum steering. In contrast to the steering scenario, which detects entanglement, the generalisation detects the dimensionality of entanglement. We illustrate the bridge between the concepts by showing that an analogue of the original EPR argument is genuinely infinite-dimensional with respect to our figure of merit, and that a fundamental discrete variable result on preparability of unsteerable state assemblages with separable states does not directly carry over to the continuous variable setting. We further prove a representation result for partially entanglement breaking channels that can be of independent interest.

We analyze the spectrum of a periodic quantum graph of the Cairo lattice form. The used vertex coupling violates the time reversal invariance and its high-energy behavior depends on the vertex degree parity; in the considered example both odd and even parities are involved. The presence of the former implies that the spectrum is dominated by gaps. In addition, we discuss two modifications of the model in which this is not the case, the zero limit of the length parameter in the coupling, and the sign switch of the coupling matrix at the vertices of degree three; while different they both yield the same probability that a randomly chosen positive energy lies in the spectrum.

We experimentally demonstrate adaptive reconciliation for continuous-variable quantum key distribution over a turbulent free-space optical channel. Additionally, we propose a method for optimising the reconciliation efficiency, increasing secret key rates by up to 8.1%.

Two matrix product states (MPS) are in the same phase in the presence of symmetries if they can be transformed into one another via symmetric short-depth circuits. We consider how symmetry-preserving measurements with feedforward alter the phase classification of MPS in the presence of global on-site symmetries. We demonstrate that, for all finite abelian symmetries, any two symmetric MPS belong to the same phase. We give an explicit protocol that achieves a transformation between any two phases and that uses only a depth-two symmetric circuit, two rounds of symmetric measurements, and a constant number of auxiliary systems per site. In the case of non-abelian symmetries, symmetry protection prevents one from deterministically transforming symmetry-protected topological (SPT) states to product states directly via measurements, thereby complicating the analysis. Nonetheless, we provide protocols that allow for asymptotically deterministic transformations between the trivial phase and certain SPT phases.

Quantum computers exhibit an inherent randomness, so it seems natural to consider them for procedural content generation. In this work, a quantum version of the famous (classical) wave function collapse algorithm is proposed. This quantum wave function collapse algorithm is based on the idea that a quantum circuit can be prepared in such a way that it acts as a special-purpose random generator for content of a desired form. The proposed method is presented theoretically and investigated experimentally on simulators and actual IBM Quantum devices.

Variational quantum algorithms (VQAs) are hybrid quantum-classical approaches used for tackling a wide range of problems on noisy intermediate-scale quantum (NISQ) devices. Testing these algorithms on relevant hardware is crucial to investigate the effect of noise and imperfections and to assess their practical value. Here, we implement a variational algorithm designed for optimized parameter estimation on a continuous variable platform based on squeezed light, a key component for high-precision optical phase estimation. We investigate the ability of the algorithm to identify the optimal metrology process, including the optimization of the probe state and measurement strategy for small-angle optical phase sensing. Two different optimization strategies are employed, the first being a gradient descent optimizer using Gaussian parameter shift rules to estimate the gradient of the cost function directly from the measurements. The second strategy involves a gradient-free Bayesian optimizer, fine-tuning the system using the same cost function and trained on the data acquired through the gradient-dependent algorithm. We find that both algorithms can steer the experiment towards the optimal metrology process. However, they find minima not predicted by our theoretical model, demonstrating the strength of variational algorithms in modelling complex noise environments, a non-trivial task.

Due to their conceptual appeal and computational convenience, two-level systems (TLS) and their generalisations are often used to investigate nonlinear behavior in quantum optics, and to assess the applicability of theoretical methods. Here the focus is on second harmonic generation (SHG) and, as system of interest, on the Dicke model, which consists of several TLSs inside an optical cavity. The main aspect addressed is the scope of non-equilibrium Green's function (NEGF) to describe the effect of disorder and electron-electron (e-e) interactions on the SHG signal. For benchmarking purposes, exact diagonalization (ED) results are also presented and discussed. SHG spectra obtained with NEGF and ED are found to be in very good mutual agreement in most situations. Furthermore, inhomogeneity in the TLS and e-e interactions reduce the strength of SHG, and the reduction is stronger with inhomogeneity than with interactions. This trend is consistently noted across different (small to large) system sizes. Finally, a modified NEGF approach is proposed to account for cavity leakage, where the quantum photon fields are coupled to a bath of classical oscillators. As to be expected, within this mixed quantum-classical scheme a decrease in the intensity of the fluorescent spectra takes place depending on the entity of cavity leakage.

In order to alleviate the computational costs of fully quantum nonadiabatic dynamics, we present a mixed quantum-classical (MQC) particle method based on the theory of Koopman wavefunctions. Although conventional MQC models often suffer from consistency issues such as the violation of Heisenberg's principle, we overcame these difficulties by blending Koopman's classical mechanics on Hilbert spaces with methods in symplectic geometry. The resulting continuum model enjoys both a variational and a Hamiltonian structure, while its nonlinear character calls for suitable closures. Benefiting from the underlying action principle, here we apply a regularization technique previously developed within our team. This step allows for a singular solution ansatz which introduces the trajectories of computational particles - the koopmons - sampling the Lagrangian classical paths in phase space. In the case of Tully's nonadiabatic problems, the method reproduces the results of fully quantum simulations with levels of accuracy that are not achieved by standard MQC Ehrenfest simulations. In addition, the koopmon method is computationally advantageous over similar fully quantum approaches, which are also considered in our study. As a further step, we probe the limits of the method by considering the Rabi problem in both the ultrastrong and the deep strong coupling regimes, where MQC treatments appear hardly applicable. In this case, the method succeeds in reproducing parts of the fully quantum results.

The quantum kicked rotor is a paradigmatic model system in quantum physics. As a driven quantum system, it is used to study the transition from the classical to the quantum world and to elucidate the emergence of chaos and diffusion. In contrast to its classical counterpart, it features dynamical localization, specifically Anderson localization in momentum space. The interacting many-body kicked rotor is believed to break localization, as recent experiments suggest. Here, we present evidence for many-body dynamical localization for the Lieb-Liniger version of the many-body quantum kicked rotor. After some initial evolution, the momentum distribution of interacting quantum-degenerate bosonic atoms in one-dimensional geometry, kicked hundreds of times by means of a pulsed sinusoidal potential, stops spreading. We quantify the arrested evolution by analysing the energy and the information entropy of the system as the interaction strength is tuned. In the limiting cases of vanishing and strong interactions, the first-order correlation function exhibits a very different decay behavior. Our results shed light on the boundary between the classical, chaotic world and the realm of quantum physics.

We introduce a quantum algorithm to efficiently prepare states with an arbitrarily small energy variance at the target energy. We achieve it by filtering a product state at the given energy with a Lorentzian filter of width $\delta$. Given a local Hamiltonian on $N$ qubits, we construct a parent Hamiltonian whose ground state corresponds to the filtered product state with variable energy variance proportional to $\delta\sqrt{N}$. We prove that the parent Hamiltonian is gapped and its ground state can be efficiently implemented in $\mathrm{poly}(N,1/\delta)$ time via adiabatic evolution. We numerically benchmark the algorithm for a particular non-integrable model and find that the adiabatic evolution time to prepare the filtered state with a width $\delta$ is independent of the system size $N$. Furthermore, the adiabatic evolution can be implemented with circuit depth $\mathcal{O}(N^2\delta^{-4})$. Our algorithm provides a way to study the finite energy regime of many body systems in quantum simulators by directly preparing a finite energy state, providing access to an approximation of the microcanonical properties at an arbitrary energy.

Linear response (LR) theory is a powerful tool in classic quantum chemistry crucial to understanding photo-induced processes in chemistry and biology. However, performing simulations for large systems and in the case of strong electron correlation remains challenging. Quantum computers are poised to facilitate the simulation of such systems, and recently, a quantum linear response formulation (qLR) was introduced. To apply qLR to near-term quantum computers beyond a minimal basis set, we here introduce a resource-efficient qLR theory using a truncated active-space version of the multi-configurational self-consistent field LR ansatz. Therein, we investigate eight different near-term qLR formalisms that utilize novel operator transformations that allow the qLR equations to be performed on near-term hardware. Simulating excited state potential energy curves and absorption spectra for various test cases, we identify two promising candidates dubbed ``proj LRSD'' and ``all-proj LRSD''.

We present a consistent formalism to describe the dynamics of hybrid systems with mixed classical and quantum degrees of freedom. The probability function of the system, which, in general, will be a combination of the classical distribution function and the quantum density matrix, is described in terms of its corresponding moments. We then define a hybrid Poisson bracket, such that the dynamics of the moments is ruled by an effective Hamiltonian. In particular, a closed formula for the Poisson brackets between any two moments for an arbitrary number of degrees of freedom is presented, which corrects previous expressions derived in the literature for the purely quantum case. This formula is of special relevance for practical applications of the formalism. Finally, we study the dynamics of a particular hybrid system given by two coupled oscillators, one being quantum and the other classical. Due to the coupling, specific quantum and classical properties are transferred between different sectors. In particular, the quantum sector is allowed to violate the uncertainty relation, though we explicitly show that there exists a minimum positive bound of the total uncertainty of the hybrid system.

The development of quantum acoustics has enabled the cooling of mechanical objects to their quantum ground state, generation of mechanical Fock-states, and Schrodinger cat states. Such demonstrations have made mechanical resonators attractive candidates for quantum information processing, metrology, and tests of quantum gravity theories. Here, we experimentally demonstrate a direct quantum-acoustic equivalent of a single-atom laser. A single superconducting qubit coupled to a high-overtone bulk acoustic resonator is used to drive the onset of phonon lasing. We observe the absence of a sharp lower lasing threshold and characteristic upper lasing threshold, unique predictions of single-atom lasing. Lasing of an object with an unprecedented 25 ug mass represents a new regime of laser physics and provides a foundation for integrating phonon lasers with on-chip devices.

We propose an interferometric method to probe pair correlations in a gas of spin-1/2 fermions. The method consists of a Ramsey sequence where both spin states of the Fermi gas are set in a superposition of a state at rest and a state with a large recoil velocity. The two-body density matrix is extracted via the fluctuations of the transferred fraction to the recoiled state. In the pair-condensed phase, the off-diagonal long-range order is directly reflected in the asymptotic behavior of the interferometric signal for long interrogation times. The method also allows to probe the spatial structure of the condensed pairs: the interferometric signal is an oscillating function of the interrogation time in the Bardeen-Cooper-Schrieffer regime; it becomes an overdamped function in the molecular Bose-Einstein condensate regime.

Operator systems connect operator algebra, free semialgebraic geometry and quantum information theory. In this work we generalize operator systems and many of their theorems. While positive semidefinite matrices form the underlying structure of operator systems, our work shows that these can be promoted to far more general structures. For instance, we prove a general extension theorem which unifies the well-known homomorphism theorem, Riesz' extension theorem, Farkas' lemma and Arveson's extension theorem. On the other hand, the same theorem gives rise to new vector-valued extension theorems, even for invariant maps, when applied to other underlying structures. We also prove generalized versions of the Choi-Kraus representation, Choi-Effros theorem, duality of operator systems, factorizations of completely positive maps, and more, leading to new results even for operator systems themselves. In addition, our proofs are shorter and simpler, revealing the interplay between cones and tensor products, captured elegantly in terms of star autonomous categories. This perspective gives rise to new connections between group representations, mapping cones and topological quantum field theory, as they correspond to different instances of our framework and are thus siblings of operator systems.

We present the null test of the dimension of bipartite quantum systems using local measurements on each party, assuming no-signaling. We find the dimension being dependent on classical and quantum limits and finite statistics error. The test is performed on IBM quantum computers, in perfect agreement with two-level Hilbert spaces. However, in one of test we observe a moderate violation of no-signaling, requiring further tests.