QUROPE Quantum Information Processing and Communication in Europe

Several quantum hardware platforms, while being unable to perform fully fault-tolerant quantum computation, can still be operated as analogue quantum simulators for addressing many-body problems. However, due to the presence of errors, it is not clear to what extent those devices can provide us with an advantage with respect to classical computers. In this work we consider the use of noisy analogue quantum simulators for computing physically relevant properties of many-body systems both in equilibrium and undergoing dynamics. We first formulate a system-size independent notion of stability against extensive errors, which we prove for Gaussian fermion models, as well as for a restricted class of spin systems. Remarkably, for the Gaussian fermion models, our analysis shows the stability of critical models which have long-range correlations. Furthermore, we analyze how this stability may lead to a quantum advantage, for the problem of computing the thermodynamic limit of many-body models, in the presence of a constant error rate and without any explicit error correction.

Quantum error correction (QEC) plays an essential role in fault-tolerantly realizing quantum algorithms of practical interest. Among different approaches to QEC, encoding logical quantum information in harmonic oscillator modes has been shown to be promising and hardware efficient. In this work, we study multimode Gottesman-Kitaev-Preskill (GKP) codes, encoding a qubit in many oscillators, through a lattice perspective. In particular, we implement a closest point decoding strategy for correcting random Gaussian shift errors. For decoding a generic multimode GKP code, we first identify its corresponding lattice followed by finding the closest lattice point in its symplectic dual lattice to a candidate shift error compatible with the error syndrome. We use this method to characterize the error correction capabilities of several known multimode GKP codes, including their code distances and fidelities. We also perform numerical optimization of multimode GKP codes up to ten modes and find three instances (with three, seven and nine modes) with better code distances and fidelities compared to the known GKP codes with the same number of modes. While exact closest point decoding incurs exponential time cost in the number of modes for general unstructured GKP codes, we give several examples of structured GKP codes (i.e., of the repetition-rectangular GKP code types) where the closest point decoding can be performed exactly in linear time. For the surface-GKP code, we show that the closest point decoding can be performed exactly in polynomial time with the help of a minimum-weight-perfect-matching algorithm (MWPM). We show that this MWPM closest point decoder improves both the fidelity and the noise threshold of the surface-GKP code to 0.602 compared to the previously studied MWPM decoder assisted by log-likelihood analog information which yields a noise threshold of 0.599.

Krylov complexity is an important dynamical quantity with relevance to the study of operator growth and quantum chaos, and has recently been much studied for various time-independent systems. We initiate the study of K-complexity in time-dependent (driven) quantum systems. For periodic time-dependent (Floquet) systems, we develop a natural method for doing the Krylov construction and then define (state and operator) K-complexity for such systems. Focusing on kicked systems, in particular the quantum kicked rotor on a torus, we provide a detailed numerical study of the time dependence of Arnoldi coefficients as well as of the K-complexity with the system coupling constant interpolating between the weak and strong coupling regime. We also study the growth of the Krylov subspace dimension as a function of the system coupling constant.

Two non-identical quantum emitters, when placed within a cavity and coherently excited at the two-photon resonance, can reach stationary states of nearly maximal entanglement. In Vivas-Via\~na et al., we introduce a frequency-resolved Purcell effect stabilizing entangled $W$ states among strongly interacting quantum emitters embedded in a cavity. Here, we delve deeper into a specific configuration with a particularly rich phenomenology: two interacting quantum emitters under coherent excitation at the two-photon resonance. This scenario yields two resonant cavity frequencies where the combination of two-photon driving and Purcell-enhanced decay stabilizes the system into the sub- and superradiant states, respectively. By considering the case of non-degenerate emitters and exploring the parameter space of the system, we show that this mechanism is merely one among a complex family of phenomena that can generate both stationary and metastable entanglement when driving the emitters at the two-photon resonance. We provide a global perspective of this landscape of mechanisms and contribute analytical characterizations and insights into these phenomena, establishing connections with previous reports in the literature and discussing how some of these effects can be optically detected.

Enhancing the capabilities of superconducting quantum hardware, requires higher gate fidelities and lower crosstalk, particularly in larger scale devices, in which qubits are coupled to multiple neighbors. Progress towards both of these objectives would highly benefit from the ability to fully control all interactions between pairs of qubits. Here we propose a new coupler model that allows to fully decouple dispersively detuned Transmon qubits from each other, i.e. ZZ-crosstalk is completely suppressed while maintaining a maximal localization of the qubits' computational basis states. We further reason that, for a dispersively detuned Transmon system, this can only be the case if the anharmonicity of the coupler is positive at the idling point. A simulation of a 40ns CZ-gate for a lumped element model suggests that achievable process infidelity can be pushed below the limit imposed by state-of-the-art coherence times of Transmon qubits. On the other hand, idle gates between qubits are no longer limited by parasitic interactions. We show that our scheme can be applied to large integrated qubit grids, where it allows to fully isolate a pair of qubits, that undergoes a gate operation, from the rest of the chip while simultaneously pushing the fidelity of gates to the limit set by the coherence time of the individual qubits.

Variational wavefunction ans\"{a}tze are at the heart of solving quantum many-body problems in physics and chemistry. Previous designs of hardware-efficient ansatz (HEA) on quantum computers are largely based on heuristics and lack rigorous theoretical foundations. In this work, we introduce a physics-constrained approach for designing HEA with rigorous theoretical guarantees by imposing a few fundamental constraints. Specifically, we require that the target HEA to be universal, systematically improvable, and size-consistent, which is an important concept in quantum many-body theories for scalability, but has been overlooked in previous designs of HEA. We extend the notion of size-consistency to HEA, and present a concrete realization of HEA that satisfies all these fundamental constraints while only requiring linear qubit connectivity. The developed physics-constrained HEA is superior to other heuristically designed HEA in terms of both accuracy and scalability, as demonstrated numerically for the Heisenberg model and some typical molecules. In particular, we find that restoring size-consistency can significantly reduce the number of layers needed to reach certain accuracy. In contrast, the failure of other HEA to satisfy these constraints severely limits their scalability to larger systems with more than ten qubits. Our work highlights the importance of incorporating physical constraints into the design of HEA for efficiently solving many-body problems on quantum computers.

Atom interferometers allow determining inertial effects to high accuracy. Quantum-projection noise as well as systematic effects impose demands on large atomic flux as well as ultra-low expansion rates. Here we report on a high-flux source of ultra-cold atoms with free expansion rates near the Heisenberg limit directly upon release from the trap. Our results are achieved in a time-averaged optical dipole trap and enabled through dynamic tuning of the atomic scattering length across two orders of magnitude interaction strength via magnetic Feshbach resonances. We demonstrate BECs with more than $6\times 10^{4}$ particles after evaporative cooling for $170$ ms and their subsequent release with a minimal expansion energy of $4.5$ nK in one direction. Based on our results we estimate the performance of an atom interferometer and compare our source system to a high performance chip-trap, as readily available for ultra-precise measurements in micro-gravity environments.

Ascertaining whether a classical model can efficiently replace a given quantum model -- dequantization -- is crucial in assessing the true potential of quantum algorithms. In this work, we introduced the dequantizability of the function class of variational quantum-machine-learning~(VQML) models by employing the tensor network formalism, effectively identifying every VQML model as a subclass of matrix product state (MPS) model characterized by constrained coefficient MPS and tensor product-based feature maps. From this formalism, we identify the conditions for which a VQML model's function class is dequantizable or not. Furthermore, we introduce an efficient quantum kernel-induced classical kernel which is as expressive as given any quantum kernel, hinting at a possible way to dequantize quantum kernel methods. This presents a thorough analysis of VQML models and demonstrates the versatility of our tensor-network formalism to properly distinguish VQML models according to their genuine quantum characteristics, thereby unifying classical and quantum machine-learning models within a single framework.

We experimentally study collective decay of an extended disordered ensemble of $N$ atoms inside a hollow-core fiber. We observe up to $300$-fold enhanced decay rates, strong optical bursts and a coherent ringing. Due to inhomogeneities limiting the synchronization of atoms, the data does not show the typical scaling with $N$. We show that an effective number of collective emitters can be determined to recover the $N$ scaling known to homogeneous ensembles over a large parameter range. This provides physical insight into the limits of collective decay and allows for its optimization in extended ensembles as used, e.g., in quantum optics, precision time-keeping or waveguide QED.

The Quantum Sun model is an interacting model that exhibits sharp signatures of ergodicity breaking phase transition. Here, we show that the model exhibits a many-body mobility edge. We provide analytical arguments for its existence, complemented by the state-of-the-art numerical simulations analysing gap ratios, Thouless times as well as entanglement entropy of eigenstates. We also introduce the Quantum Sun model with particle number conservation, and we argue that it shares many similarities with his unrestricted predecessor.

Quantum mechanics is a theory that is as effective as it is counterintuitive. While quantum practices operate impeccably, they compel us to embrace enigmatic phenomena like the collapse of the state vector and non-locality, thereby pushing us towards untenable "hypotheses non fingo" stances. However, a century after its inception, we are presented with a promising interpretive key, intimated by Wheeler as early as 1974. The interpretative paradoxes of this theory might be resolved if we discern the relationship between logical undecidability and quantum undecidability. It will be demonstrated how both are intricately linked to an observer/observed relational issue, and how the idiosyncratic behaviours of quantum physics can be reconciled with the normative, following this path.

Understanding how errors deteriorate the information encoded in a many-body quantum system is a fundamental problem with practical implications for quantum technologies. Here, we investigate a class of encoding-decoding random circuits subject to local coherent and incoherent errors. We analytically demonstrate the existence of a phase transition from an error-protecting phase to an error-vulnerable phase occurring when the error strength is increased. This transition is accompanied by R\'enyi entropy transitions and by onset of multifractal features in the system. Our results provide a new perspective on storing and processing quantum information, while the introduced framework enables an analytic understanding of a dynamical critical phenomenon in a many-body system.

This report presents a practical approach to teaching quantum computing to Electrical Engineering & Computer Science (EECS) students through dedicated hands-on programming labs. The labs cover a diverse range of topics, encompassing fundamental elements, such as entanglement, quantum gates and circuits, as well as advanced algorithms including Quantum Key Distribution, Deutsch and Deutsch-Jozsa Algorithms, Simon's algorithm, and Grover's algorithm. As educators, we aim to share our teaching insights and resources with fellow instructors in the field. The full lab handouts and program templates are provided for interested instructors. Furthermore, the report elucidates the rationale behind the design of each experiment, enabling a deeper understanding of quantum computing.

Color centers in diamonds have emerged as a leading solid-state platform for advancing quantum technologies, satisfying the DiVincenzo criteria and recently achieving a quantum advantage in secret key distribution. Recent theoretical works estimate that general-purpose quantum computing using local quantum communication networks will require millions of physical qubits to encode thousands of logical qubits, which presents a substantial challenge to the hardware architecture at this scale. To address the unanswered scaling problem, in this work, we first introduce a scalable hardware modular architecture "Quantum System-on-Chip" (QSoC) that features compact two-dimensional arrays "quantum microchiplets" (QMCs) containing tin-vacancy (SnV-) spin qubits integrated on a cryogenic application-specific integrated circuit (ASIC). We demonstrate crucial architectural subcomponents, including (1) QSoC fabrication via a lock-and-release method for large-scale heterogeneous integration; (2) a high-throughput calibration of the QSoC for spin qubit spectral inhomogenous registration; (3) spin qubit spectral tuning functionality for inhomogenous compensation; (4) efficient spin-state preparation and measurement for improved spin and optical properties. QSoC architecture supports full connectivity for quantum memory arrays in a set of different resonant frequencies and offers the possibility for further scaling the number of solid-state physical qubits via larger and denser QMC arrays and optical frequency multiplexing networking.

Given any pair of quantum channels $\Phi_1,\Phi_2$ such that at least one of them has Kraus rank one, as well as any respective Stinespring isometries $V_1,V_2$, we prove that there exists a unitary $U$ on the environment such that $\|V_1-({\bf1}\otimes U)V_2\|_\infty\leq\sqrt{2\|\Phi_1-\Phi_2\|_\diamond}$. Moreover, we provide a simple example which shows that the factor $\sqrt2$ on the right-hand side is optimal, and we conjecture that this inequality holds for every pair of channels.

We propose a post-processing variationally scheduled quantum algorithm (pVSQA) for solving constrained combinatorial optimization problems (COPs). COPs are typically transformed into ground-state search problems of the Ising model on a quantum annealer or gate-type quantum device. Variational methods are used to find an optimal schedule function that leads to high-quality solutions in a short amount of time. Post-processing techniques convert the output solutions of the quantum devices to satisfy the constraints of the COPs. pVSQA combines the variational methods and the post-processing technique. We obtain a sufficient condition for constrained COPs to apply pVSQA based on a greedy post-processing algorithm. We apply the proposed method to two constrained NP-hard COPs: the graph partitioning problem and the quadratic knapsack problem. pVSQA on a simulator shows that a small number of variational parameters is sufficient to achieve a (near-)optimal performance within a predetermined operation time. Then building upon the simulator results, we implement pVSQA on a quantum annealer and a gate-type quantum device. The experimental results demonstrate the effectiveness of our proposed method.

In this work we introduce two different generalizations of the Fokker-Planck equation in (1+1) dimensions by replacing the spatial derivatives in terms of generalized Dunkl-type derivatives involving reflection operators. As applications of these results, we solve exactly the generalized Fokker-Planck equations for the harmonic oscillator and the centrifugal-type potentials.

Classical shadow tomography, harnessing randomized informationally complete (IC) measurements, provides an effective avenue for predicting many properties of unknown quantum states with sample-efficient precision. Projections onto $2^n+1$ mutually unbiased bases (MUBs) are widely recognized as minimal and optimal IC measurements for full-state tomography. We study how to use MUBs circuits as the ensemble in classical shadow tomography. For the general observables, the variance to predict their expectation value is shown to be exponential to the number of qubits $n$. However, for a special class termed as appropriate MUBs-average (AMA) observables, the variance decreases to $poly(n)$. Additionally, we find that through biased sampling of MUBs circuits, the variance for non-AMA observables can again be reduced to $poly(n)$ with the MUBs-sparse condition. The performance and complexity of using the MUBs and Clifford circuits as the ensemble in the classical shadow tomography are compared in the end.

We present a theoretical investigation of the Vavilov-Cherenkov (VC) radiation by a plane-wave or twisted electron. Special emphasis is put on the question whether and at what conditions the emitted VC photons can be twisted. For this aim we obtain a general expression in the coordinate and momentum representations for the quantum state of the final electron-photon system that is a result of the radiation process itself and does not depend on the properties of a detector. It is shown that this evolved state is an entangled state of an electron and a photon, and both particles can be twisted. A direct consequence of this result follows: if one uses a detector sensitive to the twisted electron (photon) with the definite projection of the total angular momentum (TAM), then the final photon (electron) also will be in the twisted state with a definite TAM projection. Further, we investigate the polarization properties of the final twisted photon in more general conditions than has been calculated before. Finally, we exploit a close similarity between the discussed VC radiation and the process of the equivalent photon emission in the Weizs\"acker-Williams method and find the corresponding final state.

GKP states, introduced by Gottesman, Kitaev, and Preskill, are continuous variable logical qubits that can be corrected for errors caused by phase space displacements. Their experimental realization is challenging, in particular using propagating fields, where quantum information is encoded in the quadratures of the electromagnetic field. However, travelling photons are essential in many applications of GKP codes involving the long-distance transmission of quantum information. We introduce a new method for encoding GKP states in propagating fields using single photons, each occupying a distinct auxiliary mode given by the propagation direction. The GKP states are defined as highly correlated states described by collective continuous modes, as time and frequency. We analyze how the error detection and correction protocol scales with the total photon number and the spectral width. We show that the obtained code can be corrected for displacements in time-frequency phase space - which correspond to dephasing, or rotations, in the quadrature phase space - and to photon losses. Most importantly, we show that generating two-photon GKP states is relatively simple, and that such states are currently produced and manipulated in several photonic platforms where frequency and time-bin biphoton entangled states can be engineered.