QUROPE Quantum Information Processing and Communication in Europe

Levitated nanoparticles in vacuum are prime candidates for generating macroscopic quantum superposition states of massive objects. Most protocols for preparing these states necessitate coherent expansion beyond the scale of the zero-point motion to produce sufficiently delocalized and pure phase-space distributions. Here, we spatially expand and subsequently recontract the thermal state of a levitated nanoparticle by modifying the stiffness of the trap holding the particle. We achieve state-expansion factors of 25 in standard deviation for a particle initially feedback-cooled to a center-of-mass thermal state of \SI{155}{\milli\kelvin}. Our method relies on a hybrid scheme combining an optical trap, for cooling and measuring the particle's motion, with a Paul trap for expanding its state. Consequently, state expansion occurs devoid of measurement backaction from photon recoil, making this approach suitable for coherent wavefunction expansion in future experiments.

We study the optimal placement of wind turbines within a windfarm to maximize the power produced by mapping the system to a Quadratic Unconstrained Binary Optimisation (QUBO) problem. We investigate solving the resulting QUBO problem using the Variational Quantum Eigensolver (VQE) on a quantum computer simulator and compare the results to those from two classical optimisation methods: simulated annealing and the Gurobi solver. The maximum grid size we study is 4 $\times$ 4, which requires 16 qubits.

Adiabatic processes can keep the quantum system in its instantaneous eigenstate, which is robust to noises and dissipation. However, it is limited by sufficiently slow evolution. Here, we experimentally demonstrate the transitionless quantum driving (TLQD) of the shortcuts to adiabaticity (STA) in gate-defined semiconductor quantum dots (QDs) to greatly accelerate the conventional adiabatic passage for the first time. For a given efficiency of quantum state transfer, the acceleration can be more than 2-fold. The dynamic properties also prove that the TLQD can guarantee fast and high-fidelity quantum state transfer. In order to compensate for the diabatic errors caused by dephasing noises, the modified TLQD is proposed and demonstrated in experiment by enlarging the width of the counter-diabatic drivings. The benchmarking shows that the state transfer fidelity of 97.8% can be achieved. This work will greatly promote researches and applications about quantum simulations and adiabatic quantum computation based on the gate-defined QDs.

Measurement-based quantum computation (MBQC) is a paradigm for quantum computation where computation is driven by local measurements on a suitably entangled resource state. In this work we show that MBQC is related to a model of quantum computation based on Clifford quantum cellular automata (CQCA). Specifically, we show that certain MBQCs can be directly constructed from CQCAs which yields a simple and intuitive circuit model representation of MBQC in terms of quantum computation based on CQCA. We apply this description to construct various MBQC-based Ans\"atze for parameterized quantum circuits, demonstrating that the different Ans\"atze may lead to significantly different performances on different learning tasks. In this way, MBQC yields a family of Hardware-efficient Ans\"atze that may be adapted to specific problem settings and is particularly well suited for architectures with translationally invariant gates such as neutral atoms.

In a recent paper (Balbino-de Freitas-Rana-FT, arXiv:2309.00965) we proved that the supercharges of the supersymmetric quantum mechanics can be statistically transmuted and accommodated into a $Z_2^n$-graded parastatistics. In this talk I derive the $6=1+2+3$ transmuted spectrum-generating algebras (whose respective $Z_2^n$ gradings are $n=0,1,2$) of the ${\cal N}=2$ Superconformal Quantum Mechanics. These spectrum-generating algebras allow to compute, in the corresponding multiparticle sectors of the de Alfaro-Fubini-Furlan deformed oscillator, the degeneracies of each energy level. The levels induced by the $Z_2\times Z_2$-graded paraparticles cannot be reproduced by the ordinary bosons/fermions statistics. This implies the theoretical detectability of the $Z_2\times Z_2$-graded parastatistics.

The interplay between the algebraic structure (operator algebras) for the quantum observables and the convex structure of the state space has been explored for a long time and most advanced results are due to Alfsen and Shultz. Here we present a more elementary approach with a more generic structure for the observables, which focuses on the transition probability of the quantum logical atoms. The binary case gives rise to the generalized qubit models and was fully developed in a preceding paper. Here we consider any case with finite information capacity (binary means that the information capacity is 2). A novel geometric property that makes any compact convex set a matching state space is presented. Generally, the transition probability is not symmetric; if it is symmetric, we get an inner product and a self-dual cone. The emerging mathematical structure comes close to the Euclidean Jordan algebras and becomes a new mathematical model for a potential extension of quantum theory.

In this manuscript we present a pedagogical introduction to continuously monitored quantum systems. We start by giving a simplified derivation of the Markovian master equation in Lindblad form, in the spirit of collision models and input-output theory, which describes the unconditional dynamics of a continuously monitored system. The same formalism is then exploited to derive stochastic master equations that describe the conditional dynamics. We focus on the two most paradigmatic examples of continuous monitoring: continuous photodetection, leading to a discontinuous dynamics with "quantum jumps", and continuous homodyne measurements, leading to a diffusive dynamics. We then present a derivation of feedback master equations that describe the dynamics (either conditional or unconditional) when the continuous measurement photocurrents are fed back to the system as a linear driving Hamiltonian, a paradigm known as linear Markovian feedback. In the second part of the manuscript we focus on continuous-variable Gaussian systems: we first present the equations for first and second moments describing the dynamics under continuous general-dyne measurements, and we then discuss in more detail the conditional and unconditional dynamics under Markovian and state-based feedback.

We propose a scheme for two-qubit gates between a flying photon and an atom in a cavity. The atom-photon gate setup consists of a cavity and a Mach-Zehnder interferometer with doubly degenerate ground and excited state energy levels mediating the atom-light interaction. We provide an error analysis of the gate and model important errors, including spatial mode mismatch between the photon and the cavity, spontaneous emission, cavity losses, detunings, and random fluctuations of the cavity parameters and frequencies. Error analysis shows that the gate protocol is more robust against experimental errors compared to previous atom-photon gates and achieves higher fidelity.

Studies of the dynamics of a quantum system coupled to a bath are typically performed by utilizing the Nakajima-Zwanzig memory kernel (${\mathcal{K}}$) or the influence functions ($\mathbf{{I}}$), especially when the dynamics exhibit memory effects (i.e., non-Markovian). Despite their significance, the formal connection between the memory kernel and the influence functions has not been explicitly made. We reveal their relation through the observation of a diagrammatic structure underlying the system propagator, $\mathbf{{I}}$, and ${\mathcal{K}}$. Based on this, we propose a non-perturbative, diagrammatic approach to construct ${\mathcal{K}}$ from $\mathbf{{I}}$ for (driven) systems interacting with harmonic baths without the use of any projection-free dynamics inputs required by standard approaches. With this construction, we also show how approximate path integral methods can be understood in terms of approximate memory kernels. Furthermore, we demonstrate a Hamiltonian learning procedure to extract the bath spectral density from a set of reduced system trajectories obtained experimentally or by numerically exact methods, opening new avenues in quantum sensing and engineering. The insights we provide in this work will significantly advance the understanding of non-Markovian dynamics, and they will be an important stepping stone for theoretical and experimental developments in this area.

Measurement-based quantum computing (MBQC) is a promising approach to reducing circuit depth in noisy intermediate-scale quantum algorithms such as the Variational Quantum Eigensolver (VQE). Unlike gate-based computing, MBQC employs local measurements on a preprepared resource state, offering a trade-off between circuit depth and qubit count. Ensuring determinism is crucial to MBQC, particularly in the VQE context, as a lack of flow in measurement patterns leads to evaluating the cost function at irrelevant locations. This study introduces MBVQE-ans\"atze that respect determinism and resemble the widely used problem-agnostic hardware-efficient VQE ansatz. We evaluate our approach using ideal simulations on the Schwinger Hamiltonian and $XY$-model and perform experiments on IBM hardware with an adaptive measurement capability. In our use case, we find that ensuring determinism works better via postselection than by adaptive measurements at the expense of increased sampling cost. Additionally, we propose an efficient MBQC-inspired method to prepare the resource state, specifically the cluster state, on hardware with heavy-hex connectivity, requiring a single measurement round, and implement this scheme on quantum computers with $27$ and $127$ qubits. We observe notable improvements for larger cluster states, although direct gate-based implementation achieves higher fidelity for smaller instances.

The notion of probability plays a crucial role in quantum mechanics. It appears in quantum mechanics as the Born rule. In modern mathematics which describes quantum mechanics, however, probability theory means nothing other than measure theory, and therefore any operational characterization of the notion of probability is still missing in quantum mechanics. In our former works [K. Tadaki, arXiv:1804.10174], based on the toolkit of algorithmic randomness, we presented a refinement of the Born rule, called the principle of typicality, for specifying the property of results of measurements in an operational way. In this paper, we make an application of our framework to the argument of local realism versus quantum mechanics for refining it, in order to demonstrate how properly our framework works in practical problems in quantum mechanics.

Geometric deep learning refers to the scenario in which the symmetries of a dataset are used to constrain the parameter space of a neural network and thus, improve their trainability and generalization. Recently this idea has been incorporated into the field of quantum machine learning, which has given rise to equivariant quantum neural networks (EQNNs). In this work, we investigate the role of classical-to-quantum embedding on the performance of equivariant quantum convolutional neural networks (EQCNNs) for the classification of images. We discuss the connection between the data embedding method and the resulting representation of a symmetry group and analyze how changing representation affects the expressibility of an EQCNN. We numerically compare the classification accuracy of EQCNNs with three different basis-permuted amplitude embeddings to the one obtained from a non-equivariant quantum convolutional neural network (QCNN). Our results show that all the EQCNNs achieve higher classification accuracy than the non-equivariant QCNN for small numbers of training iterations, while for large iterations this improvement crucially depends on the used embedding. It is expected that the results of this work can be useful to the community for a better understanding of the importance of data embedding choice in the context of geometric quantum machine learning.

We first review the problem of a rigorous justification of Kubo's formula for transport coefficients in gapped extended Hamiltonian quantum systems at zero temperature. In particular, the theoretical understanding of the quantum Hall effect rests on the validity of Kubo's formula for such systems, a connection that we review briefly as well. We then highlight an approach to linear response theory based on non-equilibrium almost-stationary states (NEASS) and on a corresponding adiabatic theorem for such systems that was recently proposed and worked out by one of us in [51] for interacting fermionic systems on finite lattices. In the second part of our paper we show how to lift the results of [51] to infinite systems by taking a thermodynamic limit.

We show that recent results on adiabatic theory for interacting gapped many-body systems on finite lattices remain valid in the thermodynamic limit. More precisely, we prove a generalised super-adiabatic theorem for the automorphism group describing the infinite volume dynamics on the quasi-local algebra of observables. The key assumption is the existence of a sequence of gapped finite volume Hamiltonians which generates the same infinite volume dynamics in the thermodynamic limit. Our adiabatic theorem holds also for certain perturbations of gapped ground states that close the spectral gap (so it is an adiabatic theorem also for resonances and in this sense `generalised'), and it provides an adiabatic approximation to all orders in the adiabatic parameter (a property often called `super-adiabatic'). In addition to existing results for finite lattices, we also perform a resummation of the adiabatic expansion and allow for observables that are not strictly local. Finally, as an application, we prove the validity of linear and higher order response theory for our class of perturbations also for infinite systems.

While we consider the result and its proof as new and interesting in itself, they also lay the foundation for the proof of an adiabatic theorem for systems with a gap only in the bulk, which will be presented in a follow-up article.

We prove a generalised super-adiabatic theorem for extended fermionic systems assuming a spectral gap only in the bulk. More precisely, we assume that the infinite system has a unique ground state and that the corresponding GNS-Hamiltonian has a spectral gap above its eigenvalue zero. Moreover, we show that a similar adiabatic theorem also holds in the bulk of finite systems up to errors that vanish faster than any inverse power of the system size, although the corresponding finite volume Hamiltonians need not have a spectral gap.

Although free-fermion systems are considered exactly solvable, they generically do not admit closed expressions for nonlocal quantities such as topological string correlations or entanglement measures. We derive closed expressions for such quantities for a dense subclass of certain classes of topological fermionic wires (classes BDI and AIII). Our results also apply to spin chains called generalised cluster models. While there is a bijection between general models in these classes and Laurent polynomials, restricting to polynomials with degenerate zeros leads to a plethora of exact results: (1) we derive closed expressions for the string correlation functions - the order parameters for the topological phases in these classes; (2) we obtain an exact formula for the characteristic polynomial of the correlation matrix, giving insight into ground state entanglement; (3) the latter implies that the ground state can be described by a matrix product state (MPS) with a finite bond dimension in the thermodynamic limit - an independent and explicit construction for the BDI class is given in a concurrent work [Phys. Rev. Res. 3 (2021), 033265, 26 pages, arXiv:2105.12143]; (4) for BDI models with even integer topological invariant, all non-zero eigenvalues of the transfer matrix are identified as products of zeros and inverse zeros of the aforementioned polynomial. General models in these classes can be obtained by taking limits of the models we analyse, giving a further application of our results. To the best of our knowledge, these results constitute the first application of Day's formula and Gorodetsky's formula for Toeplitz determinants to many-body quantum physics.

Recent advances in practical quantum computing have led to a variety of cloud-based quantum computing platforms that allow researchers to evaluate their algorithms on noisy intermediate-scale quantum (NISQ) devices. A common property of quantum computers is that they can exhibit instances of true randomness as opposed to pseudo-randomness obtained from classical systems. Investigating the effects of such true quantum randomness in the context of machine learning is appealing, and recent results vaguely suggest that benefits can indeed be achieved from the use of quantum random numbers. To shed some more light on this topic, we empirically study the effects of hardware-biased quantum random numbers on the initialization of artificial neural network weights in numerical experiments. We find no statistically significant difference in comparison with unbiased quantum random numbers as well as biased and unbiased random numbers from a classical pseudo-random number generator. The quantum random numbers for our experiments are obtained from real quantum hardware.

Quantum machine learning has emerged as a promising utilization of near-term quantum computation devices. However, algorithmic classes such as variational quantum algorithms have been shown to suffer from barren plateaus due to vanishing gradients in their parameters spaces. We present an approach to quantum algorithm optimization that is based on trainable Fourier coefficients of Hamiltonian system parameters. Our ansatz is exclusive to the extension of discrete quantum variational algorithms to analog quantum optimal control schemes and is non-local in time. We demonstrate the viability of our ansatz on the objectives of compiling the quantum Fourier transform and preparing ground states of random problem Hamiltonians. In comparison to the temporally local discretization ans\"atze in quantum optimal control and parameterized circuits, our ansatz exhibits faster and more consistent convergence. We uniformly sample objective gradients across the parameter space and find that in our ansatz the variance decays at a non-exponential rate with the number of qubits, while it decays at an exponential rate in the temporally local benchmark ansatz. This indicates the mitigation of barren plateaus in our ansatz. We propose our ansatz as a viable candidate for near-term quantum machine learning.

Random numbers are central to cryptography and various other tasks. The intrinsic probabilistic nature of quantum mechanics has allowed us to construct a large number of quantum random number generators (QRNGs) that are distinct from the traditional true number generators. This article provides a review of the existing QRNGs with a focus on their various possible features (e.g., device independence, semi-device independence) that are not achievable in the classical world. It also discusses the origin, applicability, and other facets of randomness. Specifically, the origin of randomness is explored from the perspective of a set of hierarchical axioms for quantum mechanics, implying that succeeding axioms can be regarded as a superstructure constructed on top of a structure built by the preceding axioms. The axioms considered are: (Q1) incompatibility and uncertainty; (Q2) contextuality; (Q3) entanglement; (Q4) nonlocality and (Q5) indistinguishability of identical particles. Relevant toy generalized probability theories (GPTs) are introduced, and it is shown that the origin of random numbers in different types of QRNGs known today are associated with different layers of nonclassical theories and all of them do not require all the features of quantum mechanics. Further, classification of the available QRNGs has been done and the technological challenges associated with each class are critically analyzed. Commercially available QRNGs are also compared.

A surprising 'converse to the polynomial method' of Aaronson et al. (CCC'16) shows that any bounded quadratic polynomial can be computed exactly in expectation by a 1-query algorithm up to a universal multiplicative factor related to the famous Grothendieck constant. A natural question posed there asks if bounded quartic polynomials can be approximated by $2$-query quantum algorithms. Arunachalam, Palazuelos and the first author showed that there is no direct analogue of the result of Aaronson et al. in this case. We improve on this result in the following ways: First, we point out and fix a small error in the construction that has to do with a translation from cubic to quartic polynomials. Second, we give a completely explicit example based on techniques from additive combinatorics. Third, we show that the result still holds when we allow for a small additive error. For this, we apply an SDP characterization of Gribling and Laurent (QIP'19) for the completely-bounded approximate degree.