QUROPE Quantum Information Processing and Communication in Europe

Developing superior quantum sensing strategies ranging from ultra-high precision measurement to complex structural analysis is at the heart of quantum technologies. While strategies using quantum resources, such as entanglement among sensors, to enhance the sensing precision have been abundantly demonstrated, the signal correlation among quantum sensors is rarely exploited. Here we develop a novel sensing paradigm exploiting the signal correlation among multiple quantum sensors to resolve overlapping signals from multiple targets that individual sensors can't resolve and complex structural construction struggles with. With three nitrogen-vacancy centers as a quantum electrometer system, we demonstrate this multi-sensor paradigm by resolving individual defects' fluctuating electric fields from ensemble signals. We image the three-dimensional distribution of 16 dark electronic point-defects in diamond with accuracy approaching 1.7 nm via a GPS-like localization method. Furthermore, we obtain the real-time charge dynamics of individual point defects and visualize how the dynamics induce the well-known optical spectral diffusion. The multi-sensor paradigm extends the quantum sensing toolbox and offers new possibilities for structural analysis.

The relativistic Doppler effect comes from the fact that observers in different inertial reference frames experience space and time differently, while the speed of light remains always the same. Consequently, a wave packet of light exhibits different frequencies, wavelengths, and amplitudes. In this paper, we present a local approach to the relativistic Doppler effect based on relativity, spatial and time translational symmetries, and energy conservation. Afterward, we investigate the implications of the relativistic Doppler effect for the quantum state transformations of wave packets of light and show that a local photon is a local photon at the same point in the spacetime diagram in all inertial frames.

It is generally considered that the signal output by a quantum circuit is attenuated exponentially fast in the number of gates. This letter explores how algorithms using mid-circuit measurements and classical conditioning as computational tools (and not as error mitigation or correction subroutines) can be naturally resilient to complete decoherence, and maintain quantum states with useful properties even for infinitely deep noisy circuits. Specifically, we introduce a quantum channel built out of mid-circuit measurements and feed-forward, that can be used to compute dynamical correlations at infinite temperature and canonical ensemble expectation values for any Hamiltonian. The unusual property of this algorithm is that in the presence of a depolarizing channel it still displays a meaningful, non-zero signal in the large depth limit. We showcase the noise resilience of this quantum channel on Quantinuum's H1-1 ion-trap quantum computer.

Due to its significant application in reducing algorithm depth, fSim gates have attracted a lot of attention, while one-step implementation of fSim gates remains an unresolved issue. In this manuscript, we propose a one-step implementation of holonomic fSim gates in a tunable superconducting circuit based on the three lowest energy levels. Numerical simulations demonstrate the feasibility of our scheme. This scheme may provide a promising path toward quantum computation and simulation.

Nonreciprocal devices, allowing to manipulate one-way signals, are crucial to quantum information processing and quantum network. Here we propose a nonlinear cavity-magnon system, consisting of a microwave cavity coupled to one or two yttrium-iron-garnet (YIG) spheres supporting magnons with Kerr nonlinearity, to investigate nonreciprocal photon blockade. The nonreciprocity originates from the direction-dependent Kerr effect, distinctly different from previous proposals with spinning cavities and dissipative couplings. For a single sphere case, nonreciprocal photon blockade can be realized by manipulating the nonreciprocal destructive interference between two active paths, via vary the Kerr coefficient from positive to negative, or vice versa. By optimizing the system parameters, the perfect and well tuned nonreciprocal photon blockade can be predicted. For the case of two spheres with opposite Kerr effects, only reciprocal photon blockade can be observed when two cavity-magnon coupling strengths Kerr strengths are symmetric. However, when coupling strengths or Kerr strengths become asymmetric, nonreciprocal photon blockade appears. This implies that two-sphere nonlinear cavity-magnon systems can be used to switch the transition between reciprocal and nonreciprocal photon blockades. Our study offers a potential platform for investigating nonreciprocal photon blockade effect in nonlinear cavity magnonics.

Bennett et al. proposed a family of protocols for entanglement distillation, namely, hashing, recurrence and breeding protocols. The last one was considered inefficient and has been investigated little, because it was considered inferior to the hashing protocol. In this paper, we propose a general framework of converting a stabilizer quantum error-correcting code to a breeding protocol. Then, we show an example of a stabilizer that gives a breeding protocol better than hashing protocols.

This article delves into an analysis of the intrinsic entanglement and separability feature in quantum states as depicted by graph Laplacian. We show that the presence or absence of edges in the graph plays a pivotal role in defining the entanglement or separability of these states. We propose a set of criteria for ascertaining the separability of quantum states comprising $n$-qubit within a composite Hilbert space, indicated as $H=H_1 \otimes H_2 \otimes \dots \otimes H_n$. This determination is achieved through a combination of unitary operators, neighbourhood sets, and equivalence relations.

Satellite-based quantum communications including quantum key distribution (QKD) represent one of the most promising approaches toward global-scale quantum communications. To determine the viability of transmitting quantum signals through the atmosphere, it is essential to conduct atmospheric simulations for both uplink and downlink quantum communications. In the case of the uplink scenario, the initial phase of the beam's propagation involves interaction with the atmosphere, making simulation particularly critical. To analyze the atmosphere over the Indian subcontinent, we begin by validating our approach by utilizing atmospheric data obtained from the experiments carried out in the Canary Islands within the framework of Quantum Communication (QC). We also verify our simulation methodology by reproducing simulation outcomes from diverse Canadian locations, taking into account both uplink and downlink scenarios in Low Earth Orbit (LEO). In this manuscript, we explore the practicality of utilizing three different ground station locations in India for uplink-based QC, while also considering beacon signals for both uplink and downlink scenarios. The atmospheric conditions of various geographical regions in India are simulated, and a dedicated link budget analysis is performed for each location, specifically focusing on three renowned observatories: IAO Hanle, Aries Nainital, and Mount Abu. The analysis involves computing the overall losses of the signal and beacon beams. The findings indicate that the IAO Hanle site is a more suitable choice for uplink-based QC when compared to the other two sites.

We present an analysis of interspecies interactions between Rydberg $d$-states of rubidium and cesium. We identify the F\"orster resonance channels offering the strongest interspecies couplings, demonstrating the viability for performing high-fidelity two- and multi-qubit $C_kZ$ gates up to $k=4$, including accounting for blockade errors evaluated via numerical diagonalization of the pair-potentials. Our results show $d$-state orbitals offer enhanced suppression of intraspecies couplings compared to $s$-states, making them well suited for use in large-scale neutral atom quantum processors.

Spontaneous parametric down-conversion is a common source of quantum photonic states that is a key enabling quantum technology. We show that the source characteristics can be optimized by adjusting the beam waists of the pump mode and the signal and idler collection modes. It is possible to obtain simultaneously near unity heralding efficiency and single-photon purity using a bulk crystal with both metrics approaching $\approx0.98$ under appropriate conditions. Importantly, our approach can be applied over a wide range of pump, signal, and idler wavelengths without requiring special crystal dispersion characteristics. As an example, we obtain a heralding efficiency of 0.98, a single-photon purity of 0.98, and a pair production rate of 10.9 pairs/(s$\textrm{ }$mW) using a 450-$\mu$m-long $\beta$-barium borate crystal pumped by a 405-nm-wavelength laser and nearly degenerate signal and idler wavelengths around 810 nm. Here, the pump mode has a waist of 310 $\mu$m and the signal and idler collection modes have a waist of 145.4 $\mu$m, which can be produced straightforwardly using standard laboratory components. Our work paves the way for realizing a simple approach to producing quantum photonic states with high purity and heralding efficiency.

The interference of single photons going through a double slit is a compelling demonstration of the wave and particle nature of light in the same experiment. Single photons produced by spontaneous parametric down-conversion can be used for this purpose. However, it is particularly challenging to implement due to coherency and resolution challenges. In this article, we present a tabletop laboratory arrangement suitable for the undergraduate instruction laboratory that overcomes these challenges. The apparatus scans a single detector to produce a plot showing the interference patterns of single photons. We include experimental data obtained using this setup demonstrating double-slit and single-slit interference as well as quantum erasing through the use of sheet polarizers.

The Variational Quantum Eigensolver (VQE) algorithm, as applied to finding the ground state of a Hamiltonian, is particularly well-suited for deployment on noisy intermediate-scale quantum (NISQ) devices. Here we utilize the VQE algorithm with a quantum circuit ansatz inspired by the Density Matrix Renormalization Group (DMRG) algorithm. To ameliorate the impact of realistic noise on the performance of the method we employ zero-noise extrapolation. We find that, with realistic error rates, our DMRG-VQE hybrid algorithm delivers good results for strongly correlated systems. We illustrate our approach with the Heisenberg model on a Kagome lattice patch and demonstrate that DMRG-VQE hybrid methods can locate, and faithfully represent the physics of, the ground state of such systems. Moreover, the parameterized ansatz circuit used in this work is low-depth and requires a reasonably small number of parameters, so is efficient for NISQ devices.

Despite the fundamental role the Quantum Satisfiability (QSAT) problem has played in quantum complexity theory, a central question remains open: At which local dimension does the complexity of QSAT transition from "easy" to "hard"? Here, we study QSAT with each constraint acting on a $k$-dimensional and $l$-dimensional qudit pair, denoted $(k,l)$-QSAT. Our first main result shows that, surprisingly, QSAT on qubits can remain $\mathsf{QMA}_1$-hard, in that $(2,5)$-QSAT is $\mathsf{QMA}_1$-complete. In contrast, $2$-SAT on qubits is well-known to be poly-time solvable [Bravyi, 2006]. Our second main result proves that $(3,d)$-QSAT on the 1D line with $d\in O(1)$ is also $\mathsf{QMA}_1$-hard. Finally, we initiate the study of 1D $(2,d)$-QSAT by giving a frustration-free 1D Hamiltonian with a unique, entangled ground state.

Our first result uses a direct embedding, combining a novel clock construction with the 2D circuit-to-Hamiltonian construction of [Gosset, Nagaj, 2013]. Of note is a new simplified and analytic proof for the latter (as opposed to a partially numeric proof in [GN13]). This exploits Unitary Labelled Graphs [Bausch, Cubitt, Ozols, 2017] together with a new "Nullspace Connection Lemma", allowing us to break low energy analyses into small patches of projectors, and to improve the soundness analysis of [GN13] from $\Omega(1/T^6)$ to $\Omega(1/T^2)$, for $T$ the number of gates. Our second result goes via black-box reduction: Given an arbitrary 1D Hamiltonian $H$ on $d'$-dimensional qudits, we show how to embed it into an effective null-space of a 1D $(3,d)$-QSAT instance, for $d\in O(1)$. Our approach may be viewed as a weaker notion of "simulation" (\`a la [Bravyi, Hastings 2017], [Cubitt, Montanaro, Piddock 2018]). As far as we are aware, this gives the first "black-box simulation"-based $\mathsf{QMA}_1$-hardness result, i.e. for frustration-free Hamiltonians.

A generalization of the quantum Rabi model is obtained by replacing the linear (dipole) coupling between the two-level system and the radiation mode by a non-linear expression in the creation and annihilation operators, corresponding to multi-photon excitations. If each spin flip involves $k$ photons, it is called the "$k$-photon" quantum Rabi model. While the formally symmetric Hamilton operator is self-adjoint in the case $k=2$, it is demonstrated here that the Hamiltonian is not self-adjoint for $k\ge 3$. Therefore it does not generate a unitary time evolution and is unphysical. This result cannot be obtained by numerical calculations in finite-dimensional spaces which attempt to approximate an unbounded operator by a finite-rank operator.

Special approximation technique for analysis of different characteristics of states of multipartite infinite-dimensional quantum systems is proposed and applied to the study of the relative entropy of $\pi$-entanglement and its regularisation.

In particular, by using this technique we obtain simple sufficient conditions for local continuity (convergence) of the regularized relative entropy of $\pi$-entanglement.

We establish a finite-dimensional approximation property for the relative entropy of entanglement and its regularization that allows us to generalize to the infinite-dimensional case the results proved in the finite-dimensional settings.

We also show that for any multipartite state with finite energy the infimum in the definition of the relative entropy of $\pi$-entanglement can be taken over the set of finitely-decomposable $\pi$-separable states with finite energy.

Most physical systems, whether classical or quantum mechanical, exhibit spherical symmetry. Angular momentum, denoted as $\ell$, is a conserved quantity that appears in the centrifugal potential when a particle moves under the influence of a central force. This study introduces a formalism in which $\ell$ plays a unifying role, consolidating solvable central potentials into a superpotential. This framework illustrates that the Coulomb potential emerges as a direct consequence of a homogenous ($r$-independent) isotropic superpotential. Conversely, a $\ell$-independent central superpotential results in the 3-Dimensional Harmonic Oscillator (3-DHO) potential. Moreover, a local $\ell$-dependent central superpotential generates potentials applicable to finite-range interactions such as molecular or nucleonic systems. Additionally, we discuss generalizations to arbitrary $D$ dimensions and investigate the properties of the superpotential to determine when supersymmetry is broken or unbroken. This scheme also explains that the free particle wave function in three dimensions is obtained from spontaneous breakdown of supersymmetry and clarifies how a positive 3-DHO potential, as an upside-down potential, can have a negative energy spectrum. We also present complex isospectral deformations of the central superpotential and superpartners, which can have interesting applications for open systems in dynamic equilibrium. Finally, as a practical application, we apply this formalism to specify a new effective potential for the deuteron.

The required precision to perform quantum simulations beyond the capabilities of classical computers imposes major experimental and theoretical challenges. The key to solving these issues are highly precise ways of characterizing analog quantum sim ulators. Here, we robustly estimate the free Hamiltonian parameters of bosonic excitations in a superconducting-qubit analog quantum simulator from measured time-series of single-mode canonical coordinates. We achieve the required levels of precision in estimating the Hamiltonian parameters by maximally exploiting the model structure, making it robust against noise and state-preparation and measurement (SPAM) errors. Importantly, we are also able to obtain tomographic information about those SPAM errors from the same data, crucial for the experimental applicability of Hamiltonian learning in dynamical quantum-quench experiments. Our learning algorithm is highly scalable both in terms of the required amounts of data and post-processing. To achieve this, we develop a new super-resolution technique coined tensorESPRIT for frequency extraction from matrix time-series. The algorithm then combines tensorESPRIT with constrained manifold optimization for the eigenspace reconstruction with pre- and post-processing stages. For up to 14 coupled superconducting qubits on two Sycamore processors, we identify the Hamiltonian parameters - verifying the implementation on one of them up to sub-MHz precision - and construct a spatial implementation error map for a grid of 27 qubits. Our results constitute a fully characterized, highly accurate implementation of an analog dynamical quantum simulation and introduce a diagnostic toolkit for understanding, calibrating, and improving analog quantum processors.

The Quantum Singular Value Transformation (QSVT) is a recent technique that gives a unified framework to describe most quantum algorithms discovered so far, and may lead to the development of novel quantum algorithms. In this paper we investigate the hardness of classically simulating the QSVT. A recent result by Chia, Gily\'en, Li, Lin, Tang and Wang (STOC 2020) showed that the QSVT can be efficiently "dequantized" for low-rank matrices, and discussed its implication to quantum machine learning. In this work, motivated by establishing the superiority of quantum algorithms for quantum chemistry and making progress on the quantum PCP conjecture, we focus on the other main class of matrices considered in applications of the QSVT, sparse matrices.

We first show how to efficiently "dequantize", with arbitrarily small constant precision, the QSVT associated with a low-degree polynomial. We apply this technique to design classical algorithms that estimate, with constant precision, the singular values of a sparse matrix. We show in particular that a central computational problem considered by quantum algorithms for quantum chemistry (estimating the ground state energy of a local Hamiltonian when given, as an additional input, a state sufficiently close to the ground state) can be solved efficiently with constant precision on a classical computer. As a complementary result, we prove that with inverse-polynomial precision, the same problem becomes BQP-complete. This gives theoretical evidence for the superiority of quantum algorithms for chemistry, and strongly suggests that said superiority stems from the improved precision achievable in the quantum setting. We also discuss how this dequantization technique may help make progress on the central quantum PCP conjecture.

In this article, we analyse the Bistritzer--MacDonald (BM) model (also known as the continuum model) of twisted bilayer graphene (TBG) with an additional external magnetic field. We provide an explicit semiclassical asymptotic expansion of the density of states (DOS) in the limit of strong magnetic fields. The explicit expansion of the DOS enables us to study magnetic response properties such as magnetic oscillations which includes Shubnikov-de Haas and de Haas-van Alphen oscillations as well as the integer quantum Hall effect. In particular, we elucidate the role played by different types of interlayer tunnelings ($AA^{\prime}$/$BB^{\prime}$ vs. $AB^{\prime}$/$BA^{\prime}$) in the study of the DOS, and magnetic properties.

Ground states of local Hamiltonians are of key interest in many-body physics and also in quantum information processing. Efficient verification of these states are crucial to many applications, but very challenging. Here we propose a simple, but powerful recipe for verifying the ground states of general frustration-free Hamiltonians based on local measurements. Moreover, we derive rigorous bounds on the sample complexity by virtue of the quantum detectability lemma (with improvement) and quantum union bound. Notably, the number of samples required does not increase with the system size when the underlying Hamiltonian is local and gapped, which is the case of most interest. As an application, we propose a general approach for verifying Affleck-Kennedy-Lieb-Tasaki (AKLT) states on arbitrary graphs based on local spin measurements, which requires only a constant number of samples for AKLT states defined on various lattices. Our work is of interest not only to many tasks in quantum information processing, but also to the study of many-body physics.