QUROPE Quantum Information Processing and Communication in Europe

We investigate the quantum analogue of the classical Sobolev inequalities in the phase space, with the quantum Sobolev norms defined in terms of Schatten norms of commutators. These inequalities provide an uncertainty principle for the Wigner-Yanase skew information, and also lead to new bounds on the Schatten norms of the Weyl quantization in terms of its symbol. As an intermediate tool, we obtain the analogue of Hardy-Littlewood-Sobolev's inequalities for a semiclassical analogue of the convolution, and introduce quantum Besov spaces. Explicit estimates are obtained on the optimal constants.

The relaxation dynamics of an open quantum system is determined by the competition between the coherent Hamiltonian dynamics of a system and the dissipative dynamics due to interactions with environments. It is therefore of fundamental interest to understand the transition from the coherent to incoherent regimes. We find that hitherto unrecognized quasiparticles -- incoherentons -- describe this coherent-to-incoherent transition in eigenmodes of a Liouvillian superoperator that governs the dynamics of an open quantum many-body system. Here, an incoherenton is defined as an interchain bound state in an auxiliary ladder system that represents the density matrix of a system. The Liouvillian eigenmodes are classified into groups with different decay rates that reflect the number of incoherentons involved therein. We also introduce a spectral gap -- quantum coherence gap -- that separates the different groups of eigenmodes. We demonstrate the existence of incoherentons in a lattice boson model subject to dephasing, and show that the quantum coherence gap closes when incoherentons are deconfined, which signals a dynamical transition from incoherent relaxation with exponential decay to coherent oscillatory relaxation. Furthermore, we discuss how the decoherence dynamics of quantum many-body systems can be understood in terms of the generation, localization, and diffusion of incoherentons.

State-of-the-art quantum computers can only reliably execute circuits with limited qubit numbers and computational depth. This severely reduces the scope of algorithms that can be run. While numerous techniques have been invented to exploit few-qubit devices, corresponding schemes for depth-limited computations are less explored. This work investigates to what extent we can mimic the performance of a deeper quantum computation by repeatedly using a shallower device. We propose a method for this purpose, inspired by Feynman simulation, where a given circuit is chopped in two pieces. The first piece is executed and measured early on, and the second piece is run based on the previous outcome. This method is inefficient if applied in a straightforward manner due to the high number of possible outcomes. To mitigate this issue, we propose a shallow variational circuit, whose purpose is to maintain the complexity of the method within pre-defined tolerable limits, and provide a novel optimisation method to find such circuit. The composition of these components of the methods is called reduce\&chop. As we discuss, this approach works for certain cases of interest. We believe this work may stimulate new research towards exploiting the potential of shallow quantum computers.

We show that the phase-space formulation of general probabilistic theories can be extended to include a generalized time-evolution and that it can describe a nonquantum hydrogen-like system which is stable, has discrete energy levels, and includes the Zeeman effect. This allows us to study dynamical effects such as excitations of the hydrogen-like system by a resonant laser and Rutherford scattering. Our construction demonstrates that classical theory and quantum theory can be seen as specific choices of general probabilistic theory in phase space and that other probabilistic theories also lead to measurable predictions.

A neural network is a powerful tool that can uncover hidden laws beyond human intuition. However, it often appears as a black box due to its complicated nonlinear structures. By drawing upon the Gutzwiller mean-field theory, we can showcase a principle of sign rules for ordered states in qubit lattice models. We introduce a shallow feed-forward neural network with a single hidden neuron to present these sign rules. We conduct systematical benchmarks in various models, including the generalized Ising, spin-$1/2$ XY, (frustrated) Heisenberg rings, triangular XY antiferromagnet on a torus, and the Fermi-Hubbard ring at an arbitrary filling. These benchmarks show that all the leading-order sign rule characteristics can be visualized in classical forms, such as pitch angles. Besides, quantum fluctuations can result in an imperfect accuracy rate quantitatively.

We propose a phase-space representation concept in terms of the Wigner function for a quantum harmonic oscillator model that exhibits the semiconfinement effect through its mass varying with the position. The new method is used to compute the Wigner distribution function exactly for such a semiconfinement quantum system. This method suppresses the divergence of the integrand in the definition of the quantum distribution function and leads to the computation of its analytical expressions for the stationary states of the semiconfined oscillator model. For this quantum system, both the presence and absence of the applied external homogenous field are studied. Obtained exact expressions of the Wigner distribution function are expressed through the Bessel function of the first kind and Laguerre polynomials. Furthermore, some of the special cases and limits are discussed in detail.

Unauthorized light injection has always been a vital threat to the practical security of a quantum key distribution (QKD) system. An optical power limiter (OPL) based on the thermo-optical defocusing effect has been proposed and implemented, limiting the injected hacking light. As a hardware countermeasure, the performance of the OPL under various light-injection attacks shall be tested to clarify the security boundary before being widely deployed. To investigate the OPL's security boundary in quantum cryptography, we comprehensively test and analyse the behavior of OPL under continuous-wave (c.w.) light-injection attacks and pulse illumination attacks with pulses' repetition rate at $0.5$-$\hertz$, $40$-$\mega\hertz$, and $1$-$\giga\hertz$. The testing results illuminate the security boundary of the OPL, which allows one to properly employ the OPL in the use cases. The methodology of testing and analysis proposed here is applicable to other power-limitation components in a QKD system.

Undesired coupling to the surrounding environment destroys long-range correlations on quantum processors and hinders the coherent evolution in the nominally available computational space. This incoherent noise is an outstanding challenge to fully leverage the computation power of near-term quantum processors. It has been shown that benchmarking Random Circuit Sampling (RCS) with Cross-Entropy Benchmarking (XEB) can provide a reliable estimate of the effective size of the Hilbert space coherently available. The extent to which the presence of noise can trivialize the outputs of a given quantum algorithm, i.e. making it spoofable by a classical computation, is an unanswered question. Here, by implementing an RCS algorithm we demonstrate experimentally that there are two phase transitions observable with XEB, which we explain theoretically with a statistical model. The first is a dynamical transition as a function of the number of cycles and is the continuation of the anti-concentration point in the noiseless case. The second is a quantum phase transition controlled by the error per cycle; to identify it analytically and experimentally, we create a weak link model which allows varying the strength of noise versus coherent evolution. Furthermore, by presenting an RCS experiment with 67 qubits at 32 cycles, we demonstrate that the computational cost of our experiment is beyond the capabilities of existing classical supercomputers, even when accounting for the inevitable presence of noise. Our experimental and theoretical work establishes the existence of transitions to a stable computationally complex phase that is reachable with current quantum processors.

The aim of this paper is to show that a two-dimensional Schr\"odinger operator with the potential in the form of a `ditch' of a fixed profile can have a geometrically induced discrete spectrum; this happens if such a potential channel has a single or multiple bends being straight outside a compact. Moreover, under stronger geometric restrictions the claim remains true in the presence of a potential bias at one of the channel `banks'.

We study a system of $N$ qubits with a random Hamiltonian obtained by drawing coupling constants from Gaussian distributions in various ways. This results in a rich class of systems which include the GUE and the fixed $q$ SYK theories. Our motivation is to understand the system at large $N$. In practice most of our calculations are carried out using exact diagonalisation techniques (up to $N=24$). Starting with the GUE, we study the resulting behaviour as the randomness is decreased. While in general the system goes from being chaotic to being more ordered as the randomness is decreased, the changes in various properties, including the density of states, the spectral form factor, the level statistics and out-of-time-ordered correlators, reveal interesting patterns. Subject to the limitations of our analysis which is mainly numerical, we find some evidence that the behaviour changes in an abrupt manner when the number of non-zero independent terms in the Hamiltonian is exponentially large in $N$. We also study the opposite limit of much reduced randomness obtained in a local version of the SYK model where the number of couplings scales linearly in $N$, and characterise its behaviour. Our investigation suggests that a more complete theoretical analysis of this class of systems will prove quite worthwhile.

Progress in superconducting device and detector technologies over the past decade have realized practical applications in quantum computers, detectors for far-infrared telescopes, and optical communications. Superconducting thin film materials, however, have remained largely unchanged, with aluminum still being the material of choice for superconducting qubits, and niobium compounds for high frequency/high kinetic inductance devices. Magnesium diboride ($\mathrm{MgB}_2$), known for its highest transition temperature ($\mathrm{T}_c$ = 39 K) among metallic superconductors, is a viable material for elevated temperature and higher frequency superconducting devices moving towards THz frequencies. However, difficulty in synthesizing wafer-scale thin films have prevented implementation of $\mathrm{MgB}_2$ devices into the application base of superconducting electronics. Here, we report ultra-smooth (< 0.5 nm root-mean-square roughness) and uniform $\mathrm{MgB}_2$ thin (< 100 nm) films over 100 mm in diameter for the first time and present prototype devices fabricated with these films demonstrating key superconducting properties including internal quality factor over $\mathrm{10}^4$ at 4.5 K and high tunable kinetic inductance in the order of tens of pH/sq in a 40 nm film. This groundbreaking advancement will enable development of elevated temperature, high frequency superconducting quantum circuits and devices.

Several extensions of the classical optimal transport distances to the quantum setting have been proposed. In this paper, we investigate the pseudometrics introduced by Golse, Mouhot and Paul in [Commun Math Phys 343:165-205, 2016] and by Golse and Paul in [Arch Ration Mech Anal 223:57-94, 2017]. These pseudometrics serve as a quantum analogue of the Monge-Kantorovich-Wasserstein distances of order $2$ on the phase space. We prove that they are comparable to negative Sobolev norms up to a small term due to a positive "self-distance" in the semiclassical approximation, which can be bounded above using the Wigner-Yanase skew information. This enables us to improve the known results in the context of the mean-field and semiclassical limits by requiring less regularity on the initial data.

We discuss stabilizer quantum-error correction codes implemented in a single multi-level qudit to avoid resource escalation typical of multi-qubit codes. These codes can be customized to the specific physical errors on the qudit, effectively suppressing them. We demonstrate a Fault-Tolerant implementation on molecular spin qudits, showcasing nearly exponential error suppression with only linear qudit size growth. Notably, this outperforms qubit codes using thousands of units. We also outline the required properties for a generic physical system to Fault-Tolerantly implement these embedded codes.

As quantum devices make steady progress towards intermediate scale and fault-tolerant quantum computing, it is essential to develop rigorous and efficient measurement protocols that account for known sources of noise. Most existing quantum characterization protocols such as gate set tomography and randomized benchmarking assume the noise acting on the qubits is Markovian. However, this assumption is often not valid, as for the case of 1/f charge noise or hyperfine nuclear spin noise. Here, we present a general framework for quantum process tomography (QPT) in the presence of time-correlated noise. We further introduce fidelity benchmarks that quantify the relative strength of different sources of Markovian and non-Markovian noise. As an application of our method, we perform a comparative theoretical and experimental analysis of silicon spin qubits. We first develop a detailed noise model that accounts for the dominant sources of noise and validate the model against experimental data. Applying our framework for time-correlated QPT, we find that the number of independent parameters needed to characterize one and two-qubit gates can be compressed by 10x and 100x, respectively, when compared to the fully generic case. These compressions reduce the amount of tomographic measurements needed in experiment, while also significantly speeding up numerical simulations of noisy quantum circuit dynamics compared to time-dependent Hamiltonian simulation. Using this compressed noise model, we find good agreement between our theoretically predicted process fidelities and two qubit interleaved randomized benchmarking fidelities of 99.8% measured in recent experiments on silicon spin qubits. More broadly, our formalism can be directly extended to develop efficient and scalable tuning protocols for high-fidelity control of large-arrays of quantum devices with non-Markovian noise.

We provide a non-unit disk framework to solve combinatorial optimization problems such as Maximum Cut (Max-Cut) and Maximum Independent Set (MIS) on a Rydberg quantum annealer. Our setup consists of a many-body interacting Rydberg system where locally controllable light shifts are applied to individual qubits in order to map the graph problem onto the Ising spin model. Exploiting the flexibility that optical tweezers offer in terms of spatial arrangement, our numerical simulations implement the local-detuning protocol while globally driving the Rydberg annealer to the desired many-body ground state, which is also the solution to the optimization problem. Using optimal control methods, these solutions are obtained for prototype graphs with varying sizes at time scales well within the system lifetime and with approximation ratios close to one. The non-blockade approach facilitates the encoding of graph problems with specific topologies that can be realized in two-dimensional Rydberg configurations and is applicable to both unweighted as well as weighted graphs. A comparative analysis with fast simulated annealing is provided which highlights the advantages of our scheme in terms of system size, hardness of the graph, and the number of iterations required to converge to the solution.

We propose an extended compass model that hosts subsystem symmetries and has potential experimental relevance with 3d transition metal compounds. The subsystem symmetries strongly constrain the mobility of spin excitations and lead to profound consequences. At the quantum critical point we find the presence of "critical Bose surface" along the entire $k_x$ and $k_y$ axis. Across which we find a nodal-line spin liquid that undergoes nematic instability at low temperatures. In the ferro-quadrupole phase, we find that one excitation is immobile individually analogous to "fractons".

We discuss the limitations imposed on entanglement distribution, quantum teleportation, and quantum communication by holographic bounds, such as the Bekenstein bound and Susskind's spherical entropy bound. For continuous-variable (CV) quantum information, we show how the naive application of holographic corrections disrupts well-established results. These corrections render perfect CV teleportation impossible, preclude uniform convergence in the teleportation simulation of lossy quantum channels, and impose a revised PLOB bound for quantum communication. While these mathematical corrections do not immediately impact practical quantum technologies, they are critical for a deeper theoretical understanding of quantum information theory.

We obtain a time-evolution operator for a forced optomechanical quantum system using Lie algebraic methods when the normalized coupling between the electromagnetic field and a mechanical oscillator, $G/\omega_m$, is not negligible compared to one. Due to the forcing term, the interaction picture Hamiltonian contains the number operator in the exponents, and in order to deal with it, we approximate these exponentials by their average values taken between initial coherent states. Our approximation is justified when we compare our results with the numerical solution of the number of photons, phonons, Mandel parameter, and the Wigner function, showing an excellent agreement.

It has long been postulated that within density-functional theory (DFT) the total energy of a finite electronic system is convex with respect to electron count, so that 2 E_v[N_0] <= E_v[N_0 - 1] + E_v[N_0 + 1]. Using the infinite-separation-limit technique, this article proves the convexity condition for any formulation of DFT that is (1) exact for all v-representable densities, (2) size-consistent, and (3) translationally invariant. An analogous result is also proven for one-body reduced density matrix functional theory. While there are known DFT formulations in which the ground state is not always accessible, indicating that convexity does not hold in such cases, this proof nonetheless confirms a stringent constraint on the exact exchange-correlation functional. We also provide sufficient conditions for convexity in approximate DFT, which could aid in the development of density-functional approximations. This result lifts a standing assumption in the proof of the piecewise linearity condition with respect to electron count, which has proven central to understanding the Kohn-Sham band-gap and the exchange-correlation derivative discontinuity of DFT.

In this paper, the spin transfer between two ferromagnetic insulators is studied. There is a narrow gap between the ferromagnetic insulators so that they are weakly interacting with each other. One of the ferromagnetic insulators is moving at a constant speed while the other is at rest; hence, the system is out of equilibrium. In the presence of the shearing motion, the interaction amplitude is periodically modulated at the Doppler frequency. A unitary transformation allows us to regard the periodic modulation of the interaction amplitude as an effective potential, which drives the spin transfer. The amount of the spin current is controlled by the spectral overlap and the carrier population difference between the two ferromagnetic media. If the spectra of the two ferromagnets are moderately broadened, the overlap in the spectral domain increases, enlarging the spin current. However, too much broadening spoils the spectral overlap and, hence, the spin current. This implies that there is an optimal condition for maximising the spin transfer.