QUROPE Quantum Information Processing and Communication in Europe

We introduce low-energy effective models for dense configurations of vortices in the Kitaev honeycomb model. Specifically, we consider configurations of vortices in which vortex-free plaquettes form triangular lattices against a vortex-full background. Depending on the vortex density, these "dual" configurations belong to either one of two families classified by translation and inversion symmetry. As a function of a time-reversal symmetry breaking term, one family exhibits gapped phases with even Chern numbers separated by extended gapless phases, while the other exhibits gapped phases with even or odd Chern numbers, separated by critical points. We construct an effective model for each family, determine the parameters of these models by fitting the integrated density of states, and reproduce energy spectra and Chern numbers of the Kitaev honeycomb model. We also derive phase diagrams and determine these models' validity.

We present the first hardware implementation of electrostatic interaction energies using a trapped-ion quantum computer. As test system for our computation, we focus on the reduction of $\mathrm{NO}$ to $\mathrm{N}_2\mathrm{O}$ catalyzed by a nitric oxide reductase (NOR). The quantum computer is used to generate an approximate ground state within the NOR active space. To efficiently measure the necessary one-particle density matrices, we incorporate fermionic basis rotations into the quantum circuit without extending the circuit length, laying the groundwork for further efficient measurement routines using factorizations. Measurements in the computational basis are then used as inputs for computing the electrostatic interaction energies on a classical computer. Our experimental results strongly agree with classical noise-less simulations of the same circuits, finding electrostatic interaction energies within chemical accuracy despite hardware noise. This work shows that algorithms tailored to specific observables of interest, such as interaction energies, may require significantly fewer quantum resources than individual ground state energies would in the straightforward supermolecular approach.

Quantum computing has attracted considerable attention in recent years because it promises speed-ups that conventional supercomputers cannot offer, at least for some applications. Though existing quantum computers are, in most cases, still too small to solve significant problems, their future impact on domain sciences is already being explored now. Within this context, we present a quantum computing concept for 1-D elastic wave propagation in heterogeneous media with two components: a theoretical formulation and an implementation on a real quantum computer. The method rests on a finite-difference approximation, followed by a sparsity-preserving transformation of the discrete elastic wave equation to a Schr\"{o}dinger equation, which can be simulated directly on a gate-based quantum computer. An implementation on an error-free quantum simulator verifies our approach and forms the basis of numerical experiments with small problems on the real quantum computer IBM Brisbane. The latter produce simulation results that qualitatively agree with the error-free version but are contaminated by quantum decoherence and noise effects. Complementing the discrete transformation to the Schr\"{o}dinger equation by a continuous version allows the replacement of finite differences by other spatial discretisation schemes, such as the spectral-element method. Anticipating the emergence of error-corrected quantum chips, an analogy between our method and analyses of coupled mass-spring systems suggests that our quantum computing approach may lead to wave field simulations that run exponentially faster than simulations on classical computers.

We obtain the reduced density matrix of a resistively shunted Josephson junction (RSJ), using the stochastic Liouville equation method in imaginary time - an exact numerical scheme based on the Feynman-Vernon influence functional. For all parameters looked at, we find a shunted junction is more superconducting than the same unshunted junction. We find no trace of Schmid's superconducting-insulating quantum phase transition long believed to occur in the RSJ. This work confirms theoretically a similar conclusion drawn in 2020 by Murani et al., based on experimental observations. We reveal that predictions of an insulating junction in previous works were due to considering Ohmic environments with no UV cutoff.

When subject to measurements, quantum systems evolve along stochastic quantum trajectories that can be naturally equipped with a geometric phase observable via a post-selection in a final projective measurement. When post-selecting the trajectories to form a close loop, the geometric phase undergoes a topological transition driven by the measurement strength. Here, we study the geometric phase of a subset of self-closing trajectories induced by a continuous Gaussian measurement of a single qubit system. We utilize a stochastic path integral that enables the analysis of rare self-closing events using action methods and develop the formalism to incorporate the measurement-induced geometric phase therein. We show that the geometric phase of the most likely trajectories undergoes a topological transition for self-closing trajectories as a function of the measurement strength parameter. Moreover, the inclusion of Gaussian corrections in the vicinity of the most probable self-closing trajectory quantitatively changes the transition point in agreement with results from numerical simulations of the full set of quantum trajectories.

In general, classical fully-connected systems are known to undergo violent relaxation. This phenomenon refers to the relaxation of observables to stationary, non-thermal, values on a finite timescale, despite their long-time dynamics being dominated by mean-field effects in the thermodynamic limit. Here, we analyze the ``quantum" violent relaxation by studying the dynamics of generic many-body systems with two-body, all-to-all, interactions in the thermodynamic limit. We show that, in order for violent relaxation to occur very specific conditions on the spectrum of the mean-field effective Hamiltonian have to be met. These conditions are hardly met and ``quantum" violent relaxation is observed rarely with respect to its classical counterpart. Our predictions are validated by the study of a spin model which, depending on the value of the coupling, shows a transition between violent-relaxation and a generic prethermal phase. We also analyze a spin version of the quantum Hamiltonian-Mean-Field model, which is shown not to exhibit violent-relaxation. Finally, we discuss how the violent-relaxation picture emerges back in the classical limit. Our results demonstrate how, even in the mean-field regime, quantum effects have a rather dramatic impact on the dynamics, paving the way to a better understanding of light-matter coupled systems.

Block encoding is a key ingredient in the recently developed quantum signal processing that forms a unifying framework for quantum algorithms. Initially showcased for simplifying and optimizing resource utilization in several problems, such as searching, amplitude estimation, and Hamiltonian simulation, the capabilities of the quantum signal processing go beyond these and offer untapped potential for devising new quantum algorithms. In this article, we utilize block encoding to substantially enhance two previously proposed quantum algorithms: largest eigenvalue estimation and quantum gradient descent. Unlike previous works that involve sophisticated procedures, our findings, using the unitary block encoding, demonstrate that even with elementary operations, these new quantum algorithms can eliminate major scaling factors present in their original counterparts. This yields much more efficient quantum algorithms capable of tackling complex computational problems with remarkable efficiency. Furthermore, we show how to extend our proposed method to different contexts, including matrix inversion and multiple eigenvalues estimation.

The quantum repeater cell is a basic building block for a quantum network, as it allows to overcome the distance limitations due to unavoidable fiber loss in direct transmission. We demonstrate the implementation of a quantum repeater cell, based on two free-space coupled $^{40}$Ca$^+$ ions in the same trap that act as quantum memories. We demonstrate the asynchronous generation of atom-photon and photon-photon entanglement by controlled emission of single photons from the individually addressed ions and entanglement swapping. We discuss the fidelity as well as the scaling of the generated rate.

In this expository paper we present a brief introduction to the geometrical modeling of some quantum computing problems. After a brief introduction to establish the terminology, we focus on quantum information geometry and ZX-calculus, establishing a connection between quantum computing questions and quantum groups, i.e. Hopf algebras.

The development of quantum-gas microscopes has brought novel ways of probing quantum degenerate many-body systems at the single-atom level. Until now, most of these setups have focused on alkali atoms. Expanding quantum-gas microscopy to alkaline-earth elements will provide new tools, such as SU(N)-symmetric fermionic isotopes or ultranarrow optical transitions, to the field of quantum simulation. Here, we demonstrate the site-resolved imaging of a $^{84}$Sr bosonic quantum gas in a Hubbard-regime optical lattice. The quantum gas is confined by a two-dimensional in-plane lattice and a light-sheet potential, which operate at the strontium clock-magic wavelength of 813.4 nm. We realize fluorescence imaging using the broad 461 nm transition, which provides high spatial resolution. Simultaneously, we perform attractive Sisyphus cooling with the narrow 689 nm intercombination line. We reconstruct the atomic occupation from the fluorescence images, obtaining imaging fidelities above 94%. Finally, we realize a $^{84}$Sr superfluid in the Bose-Hubbard regime. We observe its interference pattern upon expansion, a probe of phase coherence, with single-atom resolution. Our strontium quantum-gas microscope provides a new platform to study dissipative Hubbard models, quantum optics in atomic arrays, and SU(N) fermions at the microscopic level.

We have investigated the phonon dynamics of a single-molecule embedded in a mechanical resonator made of an organic crystal. The whole system is placed in an optical resonator within the bad cavity limit. We have found that the optical control of the molecular population affects the phonon dynamics. Long-lived phonons are obtained when slowing-down the decay dynamics of the molecule via modulation of the transition frequency. The discussed results are also valid for optomechanical setups based on other types of two-level emitters and mechanical resonators.

We address the problem of the reconstruction of quantum covariance matrices using the notion of Lagrangian and symplectic polar duality introduced in previous work. We apply our constructions to Gaussian quantum states which leads to a non-trivial generalization of Pauli's reconstruction problem and we state a simple tomographic characterization of such states.

Optical tweezer arrays of neutral atoms provide a versatile platform for quantum simulation due to the range of interactions and Hamiltonians that can be realized and explored. We propose to simulate a two-component Bose-Hubbard model with power-law hopping using arrays of multilevel Rydberg atoms featuring resonant dipolar interactions. The diversity of states that can be used to encode the local Hilbert space of the Bose-Hubbard model enables control of the relative hopping rate of each component and even the realization of spin-flip hopping. We use numerical simulations to show how multilevel Rydberg atoms provide an opportunity to explore the diverse non-equilibrium quench dynamics of the model. For example, we demonstrate a separation of the relaxation timescales of effective spin and charge degrees of freedom, and observe regimes of slow relaxation when the effective hopping rates of the two components are vastly different due to dynamical constraints arising from hardcore boson interactions. We discuss the technical details of realizing our proposal in state-of-the-art Rydberg tweezer arrays.

Parametric amplifiers have become a workhorse in superconducting quantum computing, however research and development of these devices has been hampered by inconsistent, and sometimes misleading noise performance characterization methodologies. The concepts behind noise characterization are deceptively simple, and there are many places where one can make mistakes, either in measurement or interpretation and analysis. In this article we cover the basics of noise performance characterization, and the special problems it presents in parametric amplifiers with limited power handling capability. We illustrate the issues with three specific examples: a high-electron mobility transistor amplifier, a Josephson traveling-wave parametric amplifier, and a Josephson parametric amplifier. We emphasize the use of a 50-$\Omega$ shot noise tunnel junction (SNTJ) as a broadband noise source, demonstrating its utility for cryogenic amplifier amplifications. These practical examples highlight the role of loss as well as the additional parametric amplifier `idler' input mode.

It has been shown that the entanglement between the system state and the ancillary state is not a strict requirement for performing ancilla-assisted process tomography(AAPT). Instead, it only requires that the system-ancilla state be faithful, which is equivalent to the invertibility of a certain matrix representing the state. However, it is difficult to distinguish between a faithful state that brings small error amplification and one that produces larger error amplification. Restricted to two-qubit system-ancilla states, we present a theoretical analysis to connect the invertibility problem to the concept of sinisterness, which classifies the correlation of two qubits. Using sinisterness, we provide a way of constructing all two qubits faithful mixed separable states with the smallest error amplification. We show that the maximally entangled states provided the smallest error amplification, while the separable Werner states produced an uneven error amplification larger than the maximally entangled state. Nevertheless, the error amplification due to inverting the separable Werner states or isotropic states is the best any mixed separable state can do.

Quantum computing promises to provide the next step up in computational power for diverse application areas. In this review, we examine the science behind the quantum hype and breakthroughs required to achieve true quantum advantage in real world applications. Areas that are likely to have the greatest impact on high performance computing (HPC) include simulation of quantum systems, optimisation, and machine learning. We draw our examples from materials simulations and computational fluid dynamics which account for a large fraction of current scientific and engineering use of HPC. Potential challenges include encoding and decoding classical data for quantum devices, and mismatched clock speeds between classical and quantum processors. Even a modest quantum enhancement to current classical techniques would have far-reaching impacts in areas such as weather forecasting, engineering, aerospace, drug design, and realising ``green'' materials for sustainable development. This requires significant effort from the computational science, engineering and quantum computing communities working together.

This work is a generalization of \cite{baldiotti2021} to Grassmann algebras of arbitrary dimensions. Here we present a covariant quantization scheme for pseudoclassical theories focused on non-hermitian quantum mechanics. The quantization maps canonically related pseudoclassical theories to equivalent quantum realizations in arbitrary dimensions. We apply the formalism to the problem of two coupled spins with Heisenberg interaction.

The implementation of physical symmetries into problem descriptions allows for the reduction of parameters and computational complexity. We show the integration of the permutation symmetry as the most restrictive discrete symmetry into quantum circuits. The permutation symmetry is the supergroup of all other discrete groups. We identify the permutation with a $\operatorname{SWAP}$ operation on the qubits. Based on the extension of the symmetry into the corresponding Lie algebra, quantum circuit element construction is shown via exponentiation. This allows for ready integration of the permutation group symmetry into quantum circuit ansatzes. The scaling of the number of parameters is found to be $\mathcal{O}(n^3)$, significantly lower than the general case and an indication that symmetry restricts the applicability of quantum computing. We also show how to adapt existing circuits to be invariant under a permutation symmetry by modification.

Density estimation is a central task in statistics and machine learning. This problem aims to determine the underlying probability density function that best aligns with an observed data set. Some of its applications include statistical inference, unsupervised learning, and anomaly detection. Despite its relevance, few works have explored the application of quantum computing to density estimation. In this article, we present a novel quantum-classical density matrix density estimation model, called Q-DEMDE, based on the expected values of density matrices and a novel quantum embedding called quantum Fourier features. The method uses quantum hardware to build probability distributions of training data via mixed quantum states. As a core subroutine, we propose a new algorithm to estimate the expected value of a mixed density matrix from its spectral decomposition on a quantum computer. In addition, we present an application of the method for quantum-classical anomaly detection. We evaluated the density estimation model with quantum random and quantum adaptive Fourier features on different data sets on a quantum simulator and a real quantum computer. An important result of this work is to show that it is possible to perform density estimation and anomaly detection with high performance on present-day quantum computers.

Dynamical Decoupling (DD) is perhaps the simplest and least resource-intensive error suppression strategy for improving quantum computer performance. Here we report on a large-scale survey of the performance of 60 different DD sequences from 10 families, including basic as well as advanced sequences with high order error cancellation properties and built-in robustness. The survey is performed using three different superconducting-qubit IBMQ devices, with the goal of assessing the relative performance of the different sequences in the setting of arbitrary quantum state preservation. We find that the high-order universally robust (UR) and quadratic DD (QDD) sequences generally outperform all other sequences across devices and pulse interval settings. Surprisingly, we find that DD performance for basic sequences such as CPMG and XY4 can be made to nearly match that of UR and QDD by optimizing the pulse interval, with the optimal interval being substantially larger than the minimum interval possible on each device.