QUROPE Quantum Information Processing and Communication in Europe

We consider the problem of decoding corrupted error correcting codes with NC$^0[\oplus]$ circuits in the classical and quantum settings. We show that any such classical circuit can correctly recover only a vanishingly small fraction of messages, if the codewords are sent over a noisy channel with positive error rate. Previously this was known only for linear codes with large dual distance, whereas our result applies to any code. By contrast, we give a simple quantum circuit that correctly decodes the Hadamard code with probability $\Omega(\varepsilon^2)$ even if a $(1/2 - \varepsilon)$-fraction of a codeword is adversarially corrupted.

Our classical hardness result is based on an equidistribution phenomenon for multivariate polynomials over a finite field under biased input-distributions. This is proved using a structure-versus-randomness strategy based on a new notion of rank for high-dimensional polynomial maps that may be of independent interest.

Our quantum circuit is inspired by a non-local version of the Bernstein-Vazirani problem, a technique to generate ``poor man's cat states'' by Watts et al., and a constant-depth quantum circuit for the OR function by Takahashi and Tani.

An approach to modeling the dynamics of x-ray amplified spontaneous emission and superfluorescence -- the phenomenon of collective x-ray emission initiated by intense pulses of X-ray Free Electron Lasers -- is developed based on stochastic partial differential equations. The equations are derived from first principles, and the relevant approximations, derivation steps, and extensions specific to stimulated x-ray emission are presented. The resulting equations take the form of three-dimensional generalized Maxwell-Bloch equations augmented with noise terms for both field and atomic variables. The derived noise terms possess specific correlation properties that enable the correct reconstruction of spontaneous emission. Consequently, the developed theoretical formalism is universally suitable for describing all stages of stimulated x-ray emission: spontaneous emission, amplified spontaneous emission, and superfluorescence. We present numerical examples that illustrate various properties of the emitted field, including spatio-temporal coherence, spectral-angular and polarization characteristics. We anticipate that the proposed theoretical framework will establish a robust foundation for interpreting measurements in stimulated x-ray emission spectroscopy, modeling x-ray laser oscillators, and describing other experiments leveraging x-ray superfluorescence.

Superconducting diode effect (SDE) with nonreciprocal supercurrent transport has attracted intense attention recently, not only for its intriguing physics, but also for its great application potential in superconducting circuits. It is revealed in this work that planar Josephson junctions (JJs) based on type-II Weyl semimetal (WSM) MoTe$_2$ can exhibit a prominent SDE due to the emergence of asymmetric Josephson effect (AJE) in perpendicular magnetic fields. The AJE manifests itself in a very large asymmetry in the critical supercurrents with respect to the current direction. The sign of this asymmetry can also be effectively modulated by the external magnetic field. Considering the special noncentrosymmetric crystal symmetry of MoTe$_2$, this AJE is understood in terms of the Edelstein effect, which induces a nontrivial phase shift in the current phase relation of the junctions. Besides these, it is further demonstrated that the rectification of supercurrent in such MoTe$_2$ JJs with the rectification efficiency up to 50.4%, unveiling the great application potential of WSMs in superconducting electronics.

Quantum reference frames are needed in quantum theory for much the same reasons as reference frames are in classical relativity theories: to manifest invariance in line with fundamental relativity principles. Though around since the 1960s, and used in a wide range of applications, only recently has the means for transforming descriptions between different frames been tackled in detail. Such transformations are needed for an internally consistent theory of quantum reference frames. In this work, we provide a general, operationally motivated framework for quantum reference frames and their transformations, holding for locally compact groups. The work is built around the notion of operational equivalence, in which theoretical objects that cannot be physically distinguished are identified. For example, we describe the collection of observables relative to a given frame as a subspace of the algebra of invariants on the composite of system and frame, and from here the set of relative states can be constructed as a convex subset of the predual. Besides being invariant, the relative observables are also framed, meaning that they can be realized with the chosen frame observable. The frame transformations are then maps between equivalence classes of relative states that can be distinguished by both initial and final frames. We give an explicit realisation in the setting that the initial frame admits a highly localized state with respect to the frame observable. The transformations are invertible exactly when the final frame also has such a localizability property. The procedure we present is in operational agreement with other recent inequivalent constructions on the domain of common applicability, but extends them in a number of ways which we describe.

Many quantum algorithms demand a large number of repetitions to obtain reliable statistical results. Thus, at each repetition it is necessary to reset the qubits efficiently and precisely in the shortest possible time, so that quantum computers actually have advantages over classical ones. In this work, we perform a detailed analysis on three different models for information resetting in superconducting qubits. Our experimental setup consists of a main qubit coupled to different auxiliary dissipative systems, that are employed in order to perform the erasing of the information of the main qubit. Our analysis shows that it is not enough to increase the coupling and the dissipation rate associated with the auxiliary systems to decrease the resetting time of the main qubit, a fact that motivates us to find the optimal set of parameters for each studied approach, allowing a significant decrease in the reset time of the three models analyzed.

A set of classical or quantum states is equivalent to another one if there exists a pair of classical or quantum channels mapping either set to the other one. For dichotomies (pairs of states), this is closely connected to (classical or quantum) R\'enyi divergences (RD) and the data-processing inequality: If a RD remains unchanged when a channel is applied to the dichotomy, then there is a recovery channel mapping the image back to the initial dichotomy. Here, we prove for classical dichotomies that equality of the RDs alone is already sufficient for the existence of a channel in any of the two directions and discuss some applications. In the quantum case, all families of quantum RDs are seen to be insufficient because they cannot detect anti-unitary transformations. Thus, including anti-unitaries, we pose the problem of finding a sufficient family. It is shown that the Petz and maximal quantum RD are still insufficient in this more general sense and we provide evidence for sufficiency of the minimal quantum RD. As a side result of our techniques, we obtain an infinite list of inequalities fulfilled by the classical, the Petz quantum, and the maximal quantum RDs. These inequalities are not true for the minimal quantum RDs. Our results further imply that any sufficient set of conditions for state transitions in the resource theory of athermality must be able to detect time-reversal.

A dimerized chain of dipolar emitters strongly coupled to a multimode optical waveguide cavity is studied. By integrating out the photonic degrees of freedom of the cavity, the system is recast in a two-band model with an effective coupling, so that it mimics a variation of the paradigmatic Su-Schrieffer-Heeger model, which features a nontrivial topological phase and hosts topological edge states. In the strong-coupling regime, the cavity photons hybridize the bright dipolar bulk band into a polaritonic one, renormalizing the eigenspectrum and strongly breaking chiral symmetry. This leads to a formal loss of the in-gap edge states present in the topological phase while they merge into the polaritonic bulk band. Interestingly, however, we find that bulk polaritons entering in resonance with the edge states inherit part of their localization properties, so that multiple polaritonic edge states are observed. Although these states are not fully localized on the edges, they present unusual properties. In particular, due to their delocalized bulk part, owing from their polaritonic nature, such edge states exhibit efficient edge-to-edge transport characteristics. Instead of being degenerate, they occupy a large portion of the spectrum, allowing one to probe them in a wide driving frequency range. Moreover, being reminiscent of symmetry-protected topological edge states, they feature a strong tolerance to positional disorder.

We consider the problems of testing and learning quantum $k$-junta channels, which are $n$-qubit to $n$-qubit quantum channels acting non-trivially on at most $k$ out of $n$ qubits and leaving the rest of qubits unchanged. We show the following.

1. An $O\left(k\right)$-query algorithm to distinguish whether the given channel is $k$-junta channel or is far from any $k$-junta channels, and a lower bound $\Omega\left(\sqrt{k}\right)$ on the number of queries;

2. An $\widetilde{O}\left(4^k\right)$-query algorithm to learn a $k$-junta channel, and a lower bound $\Omega\left(4^k/k\right)$ on the number of queries.

This gives the first junta channel testing and learning results, and partially answers an open problem raised by Chen et al. (2023). In order to settle these problems, we develop a Fourier analysis framework over the space of superoperators and prove several fundamental properties, which extends the Fourier analysis over the space of operators introduced in Montanaro and Osborne (2010).

Besides, we introduce $\textit{Influence-Sample}$ to replace $\textit{Fourier-Sample}$ proposed in Atici and Servedio (2007). Our $\textit{Influence-Sample}$ includes only single-qubit operations and results in only constant-factor decrease in efficiency.

Collateral optimization refers to the systematic allocation of financial assets to satisfy obligations or secure transactions, while simultaneously minimizing costs and optimizing the usage of available resources. {This involves assessing number of characteristics, such as cost of funding and quality of the underlying assets to ascertain the optimal collateral quantity to be posted to cover exposure arising from a given transaction or a set of transactions. One of the common objectives is to minimise the cost of collateral required to mitigate the risk associated with a particular transaction or a portfolio of transactions while ensuring sufficient protection for the involved parties}. Often, this results in a large-scale combinatorial optimization problem. In this study, we initially present a Mixed Integer Linear Programming (MILP) formulation for the collateral optimization problem, followed by a Quadratic Unconstrained Binary optimization (QUBO) formulation in order to pave the way towards approaching the problem in a hybrid-quantum and NISQ-ready way. We conduct local computational small-scale tests using various Software Development Kits (SDKs) and discuss the behavior of our formulations as well as the potential for performance enhancements. We further survey the recent literature that proposes alternative ways to attack combinatorial optimization problems suitable for collateral optimization.

Within a strongly interacting Fermi liquid framework, we calculate the effects of the Zeeman energy $\omega_H$ for a finite magnetic field, in a metallic system with a van Hove peak in the density of states, located close to and below the Fermi surface. We find that the chemical potential increases with the square of $\omega_H$. We obtain a characteristic quasiparticle scattering rate linear in the maximum of $\omega_H$ and temperature, both in the normal and the d-wave superconducting state. We predict that ARPES experiments in copper oxides, and related compounds, should be able to elucidate this behavior of the scattering rate, and in particular, the difference between spin up and down electrons.

As a signal recovery algorithm, compressed sensing is particularly useful when the data has low-complexity and samples are rare, which matches perfectly with the task of quantum phase estimation (QPE). In this work we present a new Heisenberg-limited QPE algorithm for early quantum computers based on compressed sensing. More specifically, given many copies of a proper initial state and queries to some unitary operators, our algorithm is able to recover the frequency with a total runtime $\mathcal{O}(\epsilon^{-1}\text{poly}\log(\epsilon^{-1}))$, where $\epsilon$ is the accuracy. Moreover, the maximal runtime satisfies $T_{\max}\epsilon \ll \pi$, which is comparable to the state of art algorithms, and our algorithm is also robust against certain amount of noise from sampling. We also consider the more general quantum eigenvalue estimation problem (QEEP) and show numerically that the off-grid compressed sensing can be a strong candidate for solving the QEEP.

Quantum annealing (QA) is a type of analog quantum computation that is a relaxed form of adiabatic quantum computation and uses quantum fluctuations in order to search for ground state solutions of a programmable Ising model. Here we present extensive experimental random number results from a D-Wave 2000Q quantum annealer, totaling over 20 billion bits of QA measurements, which is significantly larger than previous D-Wave QA random number generator studies. Current quantum annealers are susceptible to noise from environmental sources and calibration errors, and are not in general unbiased samplers. Therefore, it is of interest to quantify whether noisy quantum annealers can effectively function as an unbiased QRNG. The amount of data that was collected from the quantum annealer allows a comprehensive analysis of the random bits to be performed using the NIST SP 800-22 Rev 1a testsuite, as well as min-entropy estimates from NIST SP 800-90B. The randomness tests show that the generated random bits from the D-Wave 2000Q are biased, and not unpredictable random bit sequences. With no server-side sampling post-processing, the $1$ microsecond annealing time measurements had a min-entropy of $0.824$.

Scalability presents a central platform challenge for the components of current quantum network implementations that can be addressed by microfabrication techniques. We demonstrate a high-bandwidth optical memory using a warm alkali atom ensemble in a microfabricated vapor cell compatible with wafer-scale fabrication. By applying an external tesla-order magnetic field, we explore a novel ground-state quantum memory scheme in the hyperfine Paschen-Back regime, where individual optical transitions can be addressed in a Doppler-broadened medium. Working on the $^{87}$Rb D$_2$ line, where deterministic quantum dot single-photon sources are available, we demonstrate bandwidth-matching with hundreds of megahertz broad light pulses keeping such sources in mind. For a storage time of 80 ns we measure an end-to-end efficiency of $\eta_{e2e}^{\text{80ns}} = 3.12(17)\%$, corresponding to an internal efficiency of $\eta_{\text{int}}^{\text{0ns}} = 24(3)\%$, while achieving a signal-to-noise ratio of $\text{SNR} = 7.9(8)$ with coherent pulses at the single-photon level.

We report spectroscopy experiments of rubidium vapor in a high magnetic field under conditions of electromagnetically induced transparency (EIT) and optical pumping. The 1.1 T static magnetic field decouples nuclear and electronic spins and shifts each magnetic state via the Zeeman effect, allowing us to resolve individual optical transitions of the D$_2$ line in a Doppler-broadened medium. By varying the control laser power driving one leg of a spectrally isolated $\Lambda$ system we tune the vapor from the EIT regime to conditions of Autler-Townes line splitting. The resulting spectra conform to simple three-level models demonstrating the effective simplification of the energetic structure. Further, we quantify the viability of state preparation via optical pumping on nuclear spin-forbidden transitions. We conclude that the ``cleanliness'' of this system greatly enhances the capabilities of quantum control in hot vapor, offering advantages in a broad variety of quantum applications plagued by spurious light-matter interaction processes, such as atomic quantum memories for light.

Quantum chaos, a phenomenon that began to be studied in the last century, still does not have a rigorous understanding. By virtue of the correspondence principle, the properties of the system that lead to chaotic dynamics at the classical level must also be present in the underlying quantum system. In the classical case, the exponential divergence of nearby trajectories in time is described in terms of the Lyapunov exponent. However, in the quantum case, a similar description of chaos is, strictly speaking, impossible due to absence of trajectories. There are different approaches to remedy this situation, but the universal criterion of quantum chaos is absent. We propose the quantum chaos definition in the manner similar to the classical one using decoherent histories as a quantum analogue of trajectories. For this purpose, we consider the model of an open quantum kicked top interacting with the environment, which is a bosonic bath, and illustrate this idea. Here, the environment plays the role of a trajectory recording device. For the kicked top model at the classical level, depending on the kick strength, crossover occurs between the integrable and chaotic regimes. We show that for such a model, the production of entropy of decoherent histories is radically different in integrable and chaotic regimes. Thus, the entropy of an ensemble of quantum trajectories can be used as a signature of quantum chaos.

We study $N$ qubits having infinite-range Ising interaction and subjected to periodic pulse of external magnetic field. We solve the cases of $N=5$ to $11$ qubits analytically, finding its eigensystem, the dynamics of the entanglement for various initial states, and the unitary evolution operator. These quantities shows signatures of quantum integrability. For the general case of $N>11$ qubits, we provide a conjecture on quantum integrability based on the numerical evidences like degenerate spectrum, and the exact periodic nature of the time-evolved unitary evolution operator and the entanglement dynamics. Using linear entropy we show that for class of initial unentangled state the entanglement displays periodically maximum and zero values.

We show how to achieve strong squeezing of a microwave output field by reservoir engineering a cavity magnomechanical system, consisting of a microwave cavity, a magnon mode, and a mechanical vibration mode. The magnon mode is simultaneously driven by two microwave fields at the blue and red sidebands associated with the vibration mode. The two-tone drive induces a squeezed magnonic reservoir for the intracavity field, leading to a squeezed cavity mode due to the cavity-magnon state swapping, which further yields a squeezed cavity output field. The squeezing of the output field is stationary and substantial using currently available parameters in cavity magnomechanics. The work indicates the potential of the cavity magnomechanical system in preparing squeezed microwave fields, and may find promising applications in quantum information science and quantum metrology.

Finding optimal pathways in chemical reaction networks is essential for elucidating and designing chemical processes, with significant applications such as synthesis planning and metabolic pathway analysis. Such a chemical pathway-finding problem can be formulated as a constrained combinatorial optimization problem, aiming to find an optimal combination of chemical reactions connecting starting materials to target materials in a given network. Due to combinatorial explosion, the computation time required to find an optimal pathway increases exponentially with the network size. Ising machines, including quantum and simulated annealing devices, are promising novel computers dedicated to such hard combinatorial optimization. However, to the best of our knowledge, there has yet to be an attempt to apply Ising machines to chemical pathway-finding problems. In this article, we present the first Ising/quantum computing application for chemical pathway-finding problems. The Ising model, translated from a chemical pathway-finding problem, involves several types of penalty terms for violating constraints. It is not obvious how to set appropriate penalty strengths of different types. To address this challenge, we employ Bayesian optimization for parameter tuning. Furthermore, we introduce a novel technique that enhances tuning performance by grouping penalty terms according to the underlying problem structure. The performance evaluation and analysis of the proposed algorithm were conducted using a D-Wave Advantage system and simulated annealing. The benchmark results reveal challenges in finding exact optimal pathways. Concurrently, the results indicate the feasibility of finding approximate optimal pathways, provided that a certain degree of relative error in cost value is acceptable.

Communication scenarios between two parties can be implemented by first encoding messages into some states of a physical system which acts as the physical medium of the communication and then decoding the messages by measuring the state of the system. We show that already in the simplest possible scenarios it is possible to detect a definite, unbounded advantage of quantum systems over classical systems. We do this by constructing a family of operationally meaningful communication tasks each of which on one hand can be implemented by using just a single qubit but which on the other hand require unboundedly larger classical system for classical implementation. Furthemore, we show that even though with the additional resource of shared randomness the proposed communication tasks can be implemented by both quantum and classical systems of the same size, the number of coordinated actions needed for the classical implementation also grows unboundedly. In particular, no finite storage can be used to store all the coordinated actions needed to implement all the possible quantum communication tasks with classical systems. As a consequence, shared randomness cannot be viewed as a free resource.

We propose a single-photon-by-single-photon all-optical switch concept based on interference-localized states on lattices and their delocalization by interaction. In its 'open' operation, the switch stops single photons while allows photon pairs to pass the switch. Alternatively, in the 'closed' operation, the switch geometrically separates single-photon and two-photon states. We demonstrate the concept using a three-site Stub unit cell and the diamond chain. The systems are modeled by Bose-Hubbard Hamiltonians, and the dynamics is solved by exact diagonalization with Lindblad master equation. We discuss realization of the switch using photonic lattices with nonlinearities, superconductive qubit arrays, and ultracold atoms. We show that the switch allows arbitrary 'ON'/'OFF' contrast while achieving picosecond switching time at the single-photon switching energy with contemporary photonic materials.