Search

Classical shadow (CS) has opened the door to predicting the characteristics of quantum systems using very few measurements. As quantum systems grow in size, new ways to characterize them are needed to show the quality of their qubits, gates, and how noise affects them. In this work, we explore the capabilities of CS for reconstructing density state operators of sections of quantum devices to make a diagnostic of their qubits quality. We introduce zero-entropy classical shadow (ZECS), a methodology that focuses on reconstructing a positive semidefinite and unit trace density state operator using the CS information. This procedure makes a reliable reconstruction of the density state operator removing partially the errors associated with a limited sampling and quantum device noise. It gives a threshold of the maximum coherent information that qubits on a quantum device have. We test ZECS on ibm_lagos and ibm_brisbane using up to 10,000 shots. We show that with only 6,000 shots, we can make a diagnostic of the properties of groups of 2, 3, and 4 qubits on the 127-qubits ibm_brisbane device. We show two applications of ZECS: as a routing technique and as a detector for non-local noisy correlations. In the routing technique, an optimal set of 20 ibm_brisbane qubits is selected based on the ZECS procedure and used for a quantum optimization application. This method improves the solution quality by 10% and extends the quantum algorithm's lifetime by 33% when compared to the qubits chosen by the best transpilation procedure in Qiskit. Additionally, with the detector of non-local correlations, we identify regions of ibm\_brisbane that are not directly connected but have a strong correlation that maintains in time, suggesting some non-local crosstalk that can come, for example, at the multiplexing readout stage., Comment: 13 pages, 10 figures

Graph partitioning has many applications in powersystems from decentralized state estimation to parallel simulation. Focusing on parallel simulation, optimal grid partitioning minimizes the idle time caused by different simulation times for the sub-networks and their components and reduces the overhead required to simulate the cuts. Partitioning a graph into two parts such that, for example, the cut is minimal and the subgraphs have equal size is an NP-hard problem. In this paper we show how optimal partitioning of a graph can be obtained using quantum annealing (QA). We show how to map the requirements for optimal splitting to a quadratic unconstrained binary optimization (QUBO) formulation and test the proposed formulation using a current D-Wave QPU. We show that the necessity to find an embedding of the QUBO on current D-Wave QPUs limits the problem size to under 200 buses and notably affects the time-to-solution. We finally discuss the implications on near-term implementation of QA in combination to traditional CPU or GPU based simulation., Comment: 10 pages, 5 figures

The analysis of empirical data through model-free inequalities leads to the conclusion that violations of Bell-type inequalities by empirical data cannot have any significance unless one believes that the universe operates according to the rules of a mathematical model., Comment: Expanded version of the paper published in Annals of Physics 469 (2024) 169742. arXiv admin note: text overlap with arXiv:2304.03962

False vacuum decay is a potential mechanism governing the evolution of the early Universe, with profound connections to non-equilibrium quantum physics, including quenched dynamics, the Kibble-Zurek mechanism, and dynamical metastability. The non-perturbative character of the false vacuum decay and the scarcity of its experimental probes make the effect notoriously difficult to study, with many basic open questions, such as how the bubbles of true vacuum form, move and interact with each other. Here we utilize a quantum annealer with 5564 superconducting flux qubits to directly observe quantized bubble formation in real time -- the hallmark of false vacuum decay dynamics. Moreover, we develop an effective model that describes the initial bubble creation and subsequent interaction effects. We demonstrate that the effective model remains accurate in the presence of dissipation, showing that our annealer can access coherent scaling laws in driven many-body dynamics of 5564 qubits for over $1\mu$s, i.e., more than 1000 intrinsic qubit time units. This work sets the stage for exploring late-time dynamics of the false vacuum at computationally intractable system sizes, dimensionality, and topology in quantum annealer platforms., Comment: 12 pages, 5 figures

Asteroseismology, the study of stellar pulsations, offers insights into the internal structures and evolution of stars. Analysing the variations in a star's brightness allows the determination of fundamental properties such as mass, radius, age, and chemical composition. Asteroseismology heavily relies on computational tools, but a significant number of them are closed-source, thus inaccessible to the broader astronomic community. This manuscript presents Foam, a Python package designed to perform forward asteroseismic modelling of stars exhibiting gravity modes. It automates and streamlines a considerable fraction of the modelling process, comparing grids of theoretical stellar models and their oscillation frequencies to observed frequency sets in stars. Foam offers the flexibility to employ diverse modelling approaches, allowing users to choose different methodologies for matching theoretically predicted oscillations to observations. It provides options to utilise various sets of observables for comparison with their theoretical counterparts, employ different merit functions for assessing goodness of fit, and to incorporate nested subgrids in a statistically rigorous manner. For applications of these methodologies in modelling observed gravity modes, refer to Michielsen et al. (2021) and Michielsen et al. (2023)., Comment: 8 pages, 1 figure

PLATO (PLAnetary Transits and Oscillations of stars) is ESA's M3 mission designed to detect and characterise extrasolar planets and perform asteroseismic monitoring of a large number of stars. PLATO will detect small planets (down to <2 R_(Earth)) around bright stars (<11 mag), including terrestrial planets in the habitable zone of solar-like stars. With the complement of radial velocity observations from the ground, planets will be characterised for their radius, mass, and age with high accuracy (5 %, 10 %, 10 % for an Earth-Sun combination respectively). PLATO will provide us with a large-scale catalogue of well-characterised small planets up to intermediate orbital periods, relevant for a meaningful comparison to planet formation theories and to better understand planet evolution. It will make possible comparative exoplanetology to place our Solar System planets in a broader context. In parallel, PLATO will study (host) stars using asteroseismology, allowing us to determine the stellar properties with high accuracy, substantially enhancing our knowledge of stellar structure and evolution. The payload instrument consists of 26 cameras with 12cm aperture each. For at least four years, the mission will perform high-precision photometric measurements. Here we review the science objectives, present PLATO's target samples and fields, provide an overview of expected core science performance as well as a description of the instrument and the mission profile at the beginning of the serial production of the flight cameras. PLATO is scheduled for a launch date end 2026. This overview therefore provides a summary of the mission to the community in preparation of the upcoming operational phases.

Asteroseismology gives us the opportunity to look inside stars and determine their internal properties. Based on these observations, estimations can be made for the amount of the convective boundary mixing and envelope mixing of such stars, and the shape of the mixing profile in the envelope. However, these results are not typically included in stellar evolution models. We aim to investigate the impact of varying convective boundary mixing and envelope mixing in a range based on asteroseismic modelling in stellar models, both for the stellar structure and for the nucleosynthetic yields. In this first study, we focus on the pre-explosive evolution of a 20Msun star and evolve the models to the final phases of carbon burning. We vary the convective boundary mixing, implemented as step-overshoot, with the overshoot parameter in the range 0.05-0.4 and the amount of envelope mixing in the range 1-10$^{6}$ with a mixing profile based on internal gravity waves. We use a large nuclear network of 212 isotopes to study the nucleosynthesis. We find that enhanced mixing according to asteroseismology of main-sequence stars, both at the convective core boundary and in the envelope, has significant effects on the nucleosynthetic wind yields. Our evolutionary models beyond the main sequence diverge in yields from models based on rotational mixing, having longer helium burning lifetimes and lighter helium-depleted cores. We find that the asteroseismic ranges of internal mixing calibrated from core hydrogen burning stars lead to similar wind yields as those resulting from the theory of rotational mixing. Adopting the seismic mixing levels beyond the main sequence, we find earlier transitions to radiative carbon burning compared to models based on rotational mixing. This influences the compactness and the occurrence of shell-mergers, which may affect the supernova properties and explosive nucleosynthesis., Comment: 18 pages, 14 figures, 2 tables

The quantum approximate optimization algorithm (QAOA) is a promising algorithm for solving combinatorial optimization problems (COPs). In this algorithm, there are alternating layers consisting of a mixer and a problem Hamiltonian. Each layer $i=0,\ldots,p-1$ is parameterized by $\beta_i$ and $\gamma_i$. How to find these parameters has been an open question with the majority of the research focused on finding them using classical algorithms. In this work, we present evidence that fixed linear ramp schedules constitute a universal set of QAOA parameters, i.e., a set of $\gamma$ and $\beta$ parameters that rapidly approximate the optimal solution, $x^*$, independently of the COP selected, and that the success probability of finding it, $probability(x^*)$, increases with the number of QAOA layers $p$. We simulate linear ramp QAOA protocols (LR-QAOA) involving up to $N_q=42$ qubits and $p = 400$ layers on random instances of 9 different COPs. The results suggest that $probability(x^*) \approx 1/2^{(\eta N_q / p)}$ for a constant $\eta$. For example, when implementing LR-QAOA with $p=42$, the $probability(x^*)$ for 42-qubit Weighted MaxCut problems (W-MaxCut) increases from $2/2^{42}\approx 10^{-13}$ to an average of 0.13. We compare LR-QAOA, simulated annealing (SA), and branch-and-bound (B\&B) finding a scaling improvement in LR-QAOA. We test LR-QAOA on real hardware using IonQ Aria, Quantinuum H2-1, IBM Brisbane, IBM Kyoto, and IBM Osaka, encoding random weighted MaxCut (W-MaxCut) problems from 5 to 109 qubits and $p=3$ to $100$. Even for the largest case, $N_q=109$ qubits and $p=100$, information about the LR-QAOA optimization protocol is present. The circuit involved requires 21200 CNOT gates. These results show that LR-QAOA effectively finds high-quality solutions for a large variety of COPs and suggest a scaling advantage of quantum computation for combinatorial optimization.

Numerical computations of stellar oscillations for models representative of B-type stars predict fewer modes to be excited than observations reveal from modern space-based photometric data. One shortcoming of state-of-the-art evolution models of B-type stars that may cause a lack of excited modes is the absence of microscopic diffusion in most such models. We investigate whether the inclusion of microscopic diffusion in stellar models of B-type stars, notably radiative levitation experienced by isotopes, leads to extra mode driving by the opacity mechanism compared to the case of models that do not include microscopic diffusion. We consider the case of slowly to moderately rotating stars and use non-rotating equilibrium models, while we account for (uniform) rotation in the computations of the pulsation frequencies. We calculate 1D stellar models with and without microscopic diffusion and examine the effect of radiative levitation on mode excitation, for both low-radial order pressure and gravity modes and for high-radial order gravity modes. We find systematically more modes to be excited for the stellar models including microscopic diffusion compared to those without it, in agreement with observational findings of pulsating B-type dwarfs. Furthermore, the models with microscopic diffusion predict that excited modes occur earlier on in the evolution compared to modes without it. In order to maintain realistic surface abundances during the main sequence, we include macroscopic envelope mixing by internal gravity waves. While radiative levitation has so far largely been neglected in stellar evolution computations of B-type stars for computational convenience, it impacts mode excitation predictions for stellar models of such stars. We conclude that the process of radiative levitation is able to reduce the discrepancy between predicted and observed excited pulsation modes in B-type stars., Comment: Paper accepted for publication in Astronomy & Astrophysics (10 pages, 11 figures). Full abstract in PDF

We investigate the Lindblad equation in the context of boundary-driven magnetization transport in spin-$1/2$ chains. Our central question is whether the nonequilibrium steady state of the open system, including its buildup in time, can be described on the basis of the dynamics in the closed system. To this end, we rely on a previous work [Phys. Rev. B 108, L201119 (2023)], where a description in terms of spatio-temporal correlation functions has been suggested in the case of weak driving and small system-bath coupling. Because this work has focused on integrable systems and periodic boundary conditions, we here extend the analysis in three directions: We (i) consider nonintegrable systems, (ii) take into account open boundary conditions and other bath-coupling geometries, and (iii) provide a comparison to time-evolving block decimation. While we find that nonintegrability plays a minor role, the choice of the specific boundary conditions can be crucial, due to potentially nondecaying edge modes. Our large-scale numerical simulations suggest that a description based on closed-system correlation functions is an useful alternative to already existing state-of-the-art approaches., Comment: 12 pages, 12 figures

Solving combinatorial optimization problems (COPs) is a promising application of quantum computation, with the Quantum Approximate Optimization Algorithm (QAOA) being one of the most studied quantum algorithms for solving them. However, multiple factors make the parameter search of the QAOA a hard optimization problem. In this work, we study transfer learning (TL), a methodology to reuse pre-trained QAOA parameters of one problem instance into different COP instances. To this end, we select small cases of the traveling salesman problem (TSP), the bin packing problem (BPP), the knapsack problem (KP), the weighted maximum cut (MaxCut) problem, the maximal independent set (MIS) problem, and portfolio optimization (PO), and find optimal $\beta$ and $\gamma$ parameters for $p$ layers. We compare how well the parameters found for one problem adapt to the others. Among the different problems, BPP is the one that produces the best transferable parameters, maintaining the probability of finding the optimal solution above a quadratic speedup for problem sizes up to 42 qubits and p = 10 layers. Using the BPP parameters, we perform experiments on IonQ Harmony and Aria, Rigetti Aspen-M-3, and IBM Brisbane of MIS instances for up to 18 qubits. The results indicate IonQ Aria yields the best overlap with the ideal probability distribution. Additionally, we show that cross-platform TL is possible using the D-Wave Advantage quantum annealer with the parameters found for BPP. We show an improvement in performance compared to the default protocols for MIS with up to 170 qubits. Our results suggest that there are QAOA parameters that generalize well for different COPs and annealing protocols., Comment: 11 pages, 8 figures

Computational models are an essential tool for the design, characterization, and discovery of novel materials. Hard computational tasks in materials science stretch the limits of existing high-performance supercomputing centers, consuming much of their simulation, analysis, and data resources. Quantum computing, on the other hand, is an emerging technology with the potential to accelerate many of the computational tasks needed for materials science. In order to do that, the quantum technology must interact with conventional high-performance computing in several ways: approximate results validation, identification of hard problems, and synergies in quantum-centric supercomputing. In this paper, we provide a perspective on how quantum-centric supercomputing can help address critical computational problems in materials science, the challenges to face in order to solve representative use cases, and new suggested directions., Comment: 65 pages, 15 figures; comments welcome

1D stellar evolution calculations produce uncertain predictions for quantities like the age, core mass, core compactness, and nucleo-synthetic yields; a key source of uncertainty is the modeling of interfaces between regions that are convectively stable and those that are not. Theoretical and numerical work has demonstrated that there should be numerous processes adjacent to the convective boundary that induce chemical and angular momentum transport, as well as modify the thermal structure of the star. One such process is called convective penetration, wherein vigorous convection extends beyond the nominal convective boundary and alters both the composition and thermal structure. In this work, we incorporate the process of convective penetration in stellar evolution calculations using the stellar evolution software instrument mesa. We implement convective penetration according to the description presented by Anders et al. (2022a) to calculate a grid of models from the pre main sequence to He core depletion. The extent of the convective penetration zone is self-consistently calculated at each time step without introducing new free parameters. We find both a substantial penetration zone in all models with a convective core and observable differences to global stellar properties such as the luminosity and radius. We preset how the predicted radial extent of the penetration zone scales with the total stellar mass, age and the metallicity of the star. We discuss our results in the context of existing numerical and observational studies., Comment: Accepted for publication in The Astrophysical Journal, 16 pages, 8 figures, accompanying repository (https://github.com/mathren/dbconvpen)

At the Paul Scherrer Institut (PSI), we are currently working on the development of a high-precision apparatus with the aim of searching for the muon electric dipole moment (EDM) with unprecedented sensitivity. The underpinning principle of this experiment is the frozen-spin technique, a method that suppresses the spin precession due to the anomalous magnetic moment, thereby enhancing the signal-to-noise ratio for EDM signals. This increased sensitivity facilitates measurements that would be difficult to achieve with conventional $g - 2$ muon storage rings. Given the availability of the $p = 125$ MeV/$c$ muon beam at PSI, the anticipated statistical sensitivity for the EDM after a year of data collection is $6\times 10^{-23}e\cdot$cm. To achieve this goal, it is imperative to meticulously analyse and mitigate any potential spurious effects that could mimic EDM signals. In this study, we present a quantitative methodology to evaluate the systematic effects that might arise in the context of employing the frozen-spin technique within a compact storage ring. Our approach entails the analytical derivation of equations governing the motion of the muon spin in the electromagnetic (EM) fields intrinsic to the experimental setup, validated through subsequent numerical simulations. We also illustrate a method to calculate the cumulative geometric (Berry's) phase. This work complements ongoing experimental efforts to detect a muon EDM at PSI and contributes to a broader understanding of spin-precession systematic effects., Comment: submitted to The European Physical Journal C

Stellar evolution models of B-type stars are still uncertain in terms of internal mixing properties, notably in the area between the convective core and the radiative envelope. This impacts age determination of such stars in addition to the computation of chemical yields produced at the end of their life. We investigated the thermal and chemical structure and rotation rate in the near-core boundary layer of the double-lined B-type binary KIC4930889 from its four-year Kepler light curve, ground-based spectroscopy, and Gaia astrometry. We computed grids of 1D stellar structure and evolution models for different mixing profiles and prescriptions of the temperature gradient in the near-core region. We examined the preferred prescription and the near-core rotation rate using 22 prograde dipole modes detected by Kepler photometry. We employed a Mahalanobis distance merit function and considered various nested stellar model grids, rewarding goodness of fit but penalising model complexity. Furthermore, we found a preference for either an exponentially decaying mixing profile in the near-core region or absence of additional near-core mixing, but found no preference for the temperature gradient in this region. The frequency (co)variances of our theoretical predictions are much larger than the errors on the observed frequencies. This forms the main limitation on further constraining the individual parameters of our models. Additionally, non-adiabatic pulsation computations of our best models indicate a need for opacity enhancements to accurately reproduce the observed mode excitation. The eccentric close binary system KIC4930889 proves to be a promising target to investigate additional physics in close binaries by developing new modelling methods with the capacity to include the effect of tidal interactions for full exploitation of all detected oscillation modes., Comment: Accepted for publication in A&A, 20 pages, 14 figures, 10 tables

We utilize the theory of local amplitude transfers (LAT) to gain insights into quantum walks (QWs) and quantum annealing (QA) beyond the adiabatic theorem. By representing the eigenspace of the problem Hamiltonian as a hypercube graph, we demonstrate that probability amplitude traverses the search space through a series of local Rabi oscillations. We argue that the amplitude movement can be systematically guided towards the ground state using a time-dependent hopping rate based solely on the problem's energy spectrum. Building upon these insights, we extend the concept of multi-stage QW by introducing the guided quantum walk (GQW) as a bridge between QW-like and QA-like procedures. We assess the performance of the GQW on exact cover, traveling salesperson and garden optimization problems with 9 to 30 qubits. Our results provide evidence for the existence of optimal annealing schedules, beyond the requirement of adiabatic time evolutions. These schedules might be capable of solving large-scale combinatorial optimization problems within evolution times that scale linearly in the problem size.

Shor's factoring algorithm is one of the most anticipated applications of quantum computing. However, the limited capabilities of today's quantum computers only permit a study of Shor's algorithm for very small numbers. Here we show how large GPU-based supercomputers can be used to assess the performance of Shor's algorithm for numbers that are out of reach for current and near-term quantum hardware. First, we study Shor's original factoring algorithm. While theoretical bounds suggest success probabilities of only 3-4 %, we find average success probabilities above 50 %, due to a high frequency of "lucky" cases, defined as successful factorizations despite unmet sufficient conditions. Second, we investigate a powerful post-processing procedure, by which the success probability can be brought arbitrarily close to one, with only a single run of Shor's quantum algorithm. Finally, we study the effectiveness of this post-processing procedure in the presence of typical errors in quantum processing hardware. We find that the quantum factoring algorithm exhibits a particular form of universality and resilience against the different types of errors. The largest semiprime that we have factored by executing Shor's algorithm on a GPU-based supercomputer, without exploiting prior knowledge of the solution, is 549755813701 = 712321 * 771781. We put forward the challenge of factoring, without oversimplification, a non-trivial semiprime larger than this number on any quantum computing device., Comment: differs from the published version in formatting and style; open source code available at https://jugit.fz-juelich.de/qip/shorgpu

Massive stars are progenitors of supernovae, neutron stars and black holes. During the hydrogen-core burning phase their convective cores are the prime drivers of their evolution, but inferences of core masses are subject to unconstrained boundary mixing processes. Moreover, uncalibrated transport mechanisms can lead to strong envelope mixing and differential radial rotation. Ascertaining the efficiency of the transport mechanisms is challenging because of a lack of observational constraints. Here we deduce the convective core mass and robustly demonstrate non-rigid radial rotation in a supernova progenitor, the $12.0^{+1.5}_{-1.5}$ solar-mass hydrogen-burning star HD 192575, using asteroseismology, TESS photometry, high-resolution spectroscopy, and Gaia astrometry. We infer a convective core mass ($M_{\rm cc} = 2.9^{+0.5}_{-0.8}$ solar masses), and find the core to be rotating between 1.4 and 6.3 times faster than the stellar envelope depending on the location of the rotational shear layer. Our results deliver a robust inferred core mass of a massive star using asteroseismology from space-based photometry. HD 192575 is a unique anchor point for studying interior rotation and mixing processes, and thus also angular momentum transport mechanisms inside massive stars., Comment: 41 pages, 5 figures, 1 table. Version comment: updated erroneous affiliation

Combinatorial optimization problems are one of the target applications of current quantum technology, mainly because of their industrial relevance, the difficulty of solving large instances of them classically, and their equivalence to Ising Hamiltonians using the quadratic unconstrained binary optimization (QUBO) formulation. Many of these applications have inequality constraints, usually encoded as penalization terms in the QUBO formulation using additional variables known as slack variables. The slack variables have two disadvantages: (i) these variables extend the search space of optimal and suboptimal solutions, and (ii) the variables add extra qubits and connections to the quantum algorithm. Recently, a new method known as unbalanced penalization has been presented to avoid using slack variables. This method offers a trade-off between additional slack variables to ensure that the optimal solution is given by the ground state of the Ising Hamiltonian, and using an unbalanced heuristic function to penalize the region where the inequality constraint is violated with the only certainty that the optimal solution will be in the vicinity of the ground state. This work tests the unbalanced penalization method using real quantum hardware on D-Wave Advantage for the traveling salesman problem (TSP). The results show that the unbalanced penalization method outperforms the solutions found using slack variables and sets a new record for the largest TSP solved with quantum technology., Comment: 8 pages, 7 figures, conference

We take the point of view that building a one-way bridge from experimental data to mathematical models instead of the other way around avoids running into controversies resulting from attaching meaning to the symbols used in the latter. In particular, we show that adopting this view offers new perspectives for constructing mathematical models for and interpreting the results of Einstein-Podolsky-Rosen-Bohm experiments. We first prove new Bell-type inequalities constraining the values of the four correlations obtained by performing Einstein-Podolsky-Rosen-Bohm experiments under four different conditions. The proof is ``model-free'' in the sense that it does not refer to any mathematical model that one imagines to have produced the data. The constraints only depend on the number of quadruples obtained by reshuffling the data in the four data sets without changing the values of the correlations. These new inequalities reduce to model-free versions of the well-known Bell-type inequalities if the maximum fraction of quadruples is equal to one. Being model-free, a violation of the latter by experimental data implies that not all the data in the four data sets can be reshuffled to form quadruples. Furthermore, being model-free inequalities, a violation of the latter by experimental data only implies that any mathematical model assumed to produce this data does not apply. Starting from the data obtained by performing Einstein-Podolsky-Rosen-Bohm experiments, we construct instead of postulate mathematical models that describe the main features of these data. The mathematical framework of plausible reasoning is applied to reproducible and robust data, yielding without using any concept of quantum theory, the expression of the correlation for a system of two spin-1/2 objects in the singlet state. (truncated here), Comment: Corrected typo's, minor corrections in appendix B.3, major correction in section 11.4.2

In recent years, the development of quantum annealers has enabled experimental demonstrations and has increased research interest in applications of quantum annealing, such as in quantum machine learning and in particular for the popular quantum SVM. Several versions of the quantum SVM have been proposed, and quantum annealing has been shown to be effective in them. Extensions to multiclass problems have also been made, which consist of an ensemble of multiple binary classifiers. This work proposes a novel quantum SVM formulation for direct multiclass classification based on quantum annealing, called Quantum Multiclass SVM (QMSVM). The multiclass classification problem is formulated as a single Quadratic Unconstrained Binary Optimization (QUBO) problem solved with quantum annealing. The main objective of this work is to evaluate the feasibility, accuracy, and time performance of this approach. Experiments have been performed on the D-Wave Advantage quantum annealer for a classification problem on remote sensing data. The results indicate that, despite the memory demands of the quantum annealer, QMSVM can achieve accuracy that is comparable to standard SVM methods and, more importantly, it scales much more efficiently with the number of training examples, resulting in nearly constant time. This work shows an approach for bringing together classical and quantum computation, solving practical problems in remote sensing with current hardware., Comment: 12 pages, 10 figures, 3 tables. Submitted to IEEE JSTARS

State-of-the-art approaches to extract transport coefficients of many-body quantum systems broadly fall into two categories: (i) they target the linear-response regime in terms of equilibrium correlation functions of the closed system; or (ii) they consider an open-system situation typically modeled by a Lindblad equation, where a nonequilibrium steady state emerges from driving the system at its boundaries. While quantitative agreement between (i) and (ii) has been found for selected model and parameter choices, also disagreement has been pointed out in the literature. Studying magnetization transport in the spin-1/2 XXZ chain, we here demonstrate that at weak driving, the nonequilibrium steady state in an open system, including its buildup in time, can remarkably be constructed just on the basis of correlation functions in the closed system. We numerically illustrate this direct correspondence of closed-system and open-system dynamics, and show that it allows the treatment of comparatively large open systems, usually only accessible to matrix product state simulations. We also point out potential pitfalls when extracting transport coefficients from nonequilibrium steady states in finite systems., Comment: 7 pages, 4 figures (+ 4 pages, 4 figures), v2: updated manuscript and author list

Superconducting quantum processors have a long road ahead to reach fault-tolerant quantum computing. One of the most daunting challenges is taming the numerous microscopic degrees of freedom ubiquitous in solid-state devices. State-of-the-art technologies, including the world's largest quantum processors, employ aluminum oxide (AlO$_x$) tunnel Josephson junctions (JJs) as sources of nonlinearity, assuming an idealized pure $\sin\varphi$ current-phase relation (C$\varphi$R). However, this celebrated $\sin\varphi$ C$\varphi$R is only expected to occur in the limit of vanishingly low-transparency channels in the AlO$_x$ barrier. Here we show that the standard C$\varphi$R fails to accurately describe the energy spectra of transmon artificial atoms across various samples and laboratories. Instead, a mesoscopic model of tunneling through an inhomogeneous AlO$_x$ barrier predicts %-level contributions from higher Josephson harmonics. By including these in the transmon Hamiltonian, we obtain orders of magnitude better agreement between the computed and measured energy spectra. The reality of Josephson harmonics transforms qubit design and prompts a reevaluation of models for quantum gates and readout, parametric amplification and mixing, Floquet qubits, protected Josephson qubits, etc. As an example, we show that engineered Josephson harmonics can reduce the charge dispersion and the associated errors in transmon qubits by an order of magnitude, while preserving anharmonicity.

We present a new inequality constraining correlations obtained when performing Einstein-Podolsky-Rosen-Bohm experiments. The proof does not rely on mathematical models that are imagined to have produced the data and is therefore ``model-free''. The new inequality contains the model-free version of the well-known Bell-CHSH inequality as a special case. A violation of the latter implies that not all the data pairs in four data sets can be reshuffled to create quadruples. This conclusion provides a new perspective on the implications of the violation of Bell-type inequalities by experimental data., Comment: Extended version of Annals of Physics, Volume 453, 169314, 2023 (https://doi.org/10.1016/j.aop.2023.169314)

Solving combinatorial optimization problems of the kind that can be codified by quadratic unconstrained binary optimization (QUBO) is a promising application of quantum computation. Some problems of this class suitable for practical applications such as the traveling salesman problem (TSP), the bin packing problem (BPP), or the knapsack problem (KP) have inequality constraints that require a particular cost function encoding. The common approach is the use of slack variables to represent the inequality constraints in the cost function. However, the use of slack variables considerably increases the number of qubits and operations required to solve these problems using quantum devices. In this work, we present an alternative method that does not require extra slack variables and consists of using an unbalanced penalization function to represent the inequality constraints in the QUBO. This function is characterized by larger penalization when the inequality constraint is not achieved than when it is. We evaluate our approach on the TSP, BPP, and KP, successfully encoding the optimal solution of the original optimization problem near the ground state cost Hamiltonian. Additionally, we employ D-Wave Advantage and D-Wave hybrid solvers to solve the BPP, surpassing the performance of the slack variables approach by achieving solutions for up to 29 items, whereas the slack variables approach only handles up to 11 items. This new approach can be used to solve combinatorial problems with inequality constraints with a reduced number of resources compared to the slack variables approach using quantum annealing or variational quantum algorithms., Comment: 14 pages, 16 figures

Constructing a quantum computer requires immensely precise control over a quantum system. A lack of precision is often quantified by gate-error metrics, such as the average infidelity or the diamond distance. However, usually such gate-error metrics are only considered for individual gates, and not the errors that accumulate over consecutive gates. Furthermore, it is not well known how susceptible the metrics are to the assumptions which make up the model. Here, we investigate these issues using realistic simulation models of quantum computers with flux-tunable transmons and coupling resonators. Our main findings reveal that (1) gate-error metrics are indeed affected by the many assumptions of the model, (2) consecutive gate errors do not accumulate linearly, and (3) gate-error metrics are poor predictors for the performance of consecutive gates. Additionally, we discuss a potential limitation in the scalability of the studied device architecture., Comment: 28 pages, 13 figures and 25 tables

We report on two major hybrid applications of quantum computing, namely, the quantum approximate optimisation algorithm (QAOA) and the variational quantum eigensolver (VQE). Both are hybrid quantum classical algorithms as they require incremental communication between a classical central processing unit and a quantum processing unit to solve a problem. We find that the QAOA scales much better to larger problems than random guessing, but requires significant computational resources. In contrast, a coarsely discretised version of quantum annealing called approximate quantum annealing (AQA) can reach the same promising scaling behaviour using much less computational resources. For the VQE, we find reasonable results in approximating the ground state energy of the Heisenberg model when suitable choices of initial states and parameters are used. Our design and implementation of a general quasi-dynamical evolution further improves these results., Comment: This article is a book contribution. The book is freely available at http://hdl.handle.net/2128/31840

We present a comprehensive simulation study of the Newtonian and quantum model of a Stern-Gerlach experiment with cold neutrons.By solving Newton's equation of motion and the time-dependent Pauli equation, for a wide range of uniform magnetic field strengths, we scrutinize the role of the latter for drawing the conclusion that the magnetic moment of the neutron is quantized. We then demonstrate that a marginal modification of the Newtonian model suffices to construct, without invoking any concept of quantum theory, an event-based subquantum model that eliminates the shortcomings of the classical model and yields results that are in qualitative agreement with experiment and quantum theory. In this event-by-event model, the intrinsic angular momentum can take any value on the sphere, yet, for a sufficiently strong uniform magnetic field, the particle beam splits in two, exactly as in experiment and in concert with quantum theory.

We provide a detailed comparison between the dynamics of high-temperature spatiotemporal correlation functions in quantum and classical spin models. In the quantum case, our large-scale numerics are based on the concept of quantum typicality, which exploits the fact that random pure quantum states can faithfully approximate ensemble averages, allowing the simulation of spin-$1/2$ systems with up to $40$ lattice sites. Due to the exponentially growing Hilbert space, we find that for such system sizes even a single random state is sufficient to yield results with extremely low noise that is negligible for most practical purposes. In contrast, a classical analog of typicality is missing. In particular, we demonstrate that, in order to obtain data with a similar level of noise in the classical case, extensive averaging over classical trajectories is required, no matter how large the system size. Focusing on (quasi-)one-dimensional spin chains and ladders, we find a remarkably good agreement between quantum and classical dynamics. This applies not only to cases where both the quantum and classical model are nonintegrable, but also to cases where the quantum spin-$1/2$ model is integrable and the corresponding classical $s\to\infty$ model is not. Our analysis is based on the comparison of space-time profiles of the spin and energy correlation functions, where the agreement is found to hold not only in the bulk but also in the tails of the resulting density distribution. The mean-squared displacement of the density profiles reflects the nature of emerging hydrodynamics and is found to exhibit similar scaling for quantum and classical models., Comment: 14 pages, 9 figures

We use exact enumeration to characterize the solutions of quadratic unconstrained binary optimization problems of less than 21 variables in terms of their distributions of Hamming distances to close-by solutions. We also perform experiments with the D-Wave Advantage 5.1 quantum annealer, solving many instances of up to 170-variable, quadratic unconstrained binary optimization problems. Our results demonstrate that the exponents characterizing the success probability of a D-Wave annealer to solve a QUBO correlate very well with the predictions based on the Hamming distance distributions computed for small problem instances., Comment: 6 pages, 6 figures

Recent electron spin resonance experiments on CaWO$_4$:Gd$^{3+}$ and on other magnetic impurities have demonstrated that sustained Rabi oscillations can be created by driving a magnetic moment with a microwave field frequency slightly larger than the Larmor frequency and tuned to the Floquet resonance together with another microwave field (image drive). These observations are confirmed by the new experimental results reported in this paper. We investigate several mechanisms of decoherence and dissipation by using a combination of numerical and analytical techniques. The first microscopic model describes a magnetic moment in external magnetic fields, interacting with a bath of two-level systems acting as a source of decoherence and dissipation. The second model describes a collection of the identical, interacting magnetics moments, all subject to the same magnetic fields. In this case, the many-body interactions causes a decay of the Rabi oscillations. In addition, we also study the effect of the inhomogeneity of the microwave radiation on the decay of the Rabi oscillations. Our simulation results show that the dynamics of a magnetic moment subject to the two microwave fields with different frequencies and in contact with an environment is highly nontrivial. We show that under appropriate conditions, and in particular at the Floquet resonance, the magnetization exhibits sustained Rabi oscillations, in some cases with additional beatings. Although these two microscopic models separately describe the experimental data well, a simulation study that simultaneously accounts for both types of interactions is currently prohibitively costly. To gain further insight into the microscopic dynamics of these two different models, we study the time dependence of the bath and system energy and of the correlations of the spins, data that is not readily accessible experimentally.

The variational quantum eigensolver (VQE) is a hybrid quantum-classical algorithm designed for current and near-term quantum devices. Despite its initial success, there is a lack of understanding involving several of its key aspects. There are problems with VQE that forbid a favourable scaling towards quantum advantage. In order to alleviate the problems, we propose and extensively test a quantum annealing inspired heuristic that supplements VQE. The improved VQE enables an efficient initial state preparation mechanism, in a recursive manner, for a quasi-dynamical unitary evolution. We conduct an in-depth scaling analysis of finding the ground state energies with increasing lattice sizes of the Heisenberg model, employing simulations of up to $40$ qubits that manipulate the complete state vector. For the current devices, we further propose a benchmarking toolkit using a mean-field model and test it on IBM Q devices. The improved VQE avoids barren plateaus, exits local minima, and works with low-depth circuits. Realistic gate execution times estimate a longer computational time to complete the same computation on a fully functional error-free quantum computer than on a quantum computer emulator implemented on a classical computer. However, our proposal can be expected to help accurate estimations of the ground state energies beyond $50$ qubits when the complete state vector can no longer be stored on a classical computer, thus enabling quantum advantage.

In recent years, quantum annealing has gained the status of being a promising candidate for solving various optimization problems. Using a set of hard 2-satisfiabilty (2-SAT) problems, consisting of upto 18-variables problems, we analyze the scaling complexity of the quantum annealing algorithm and study the distributions of the minimum energy gap and the success probability. We extend the analysis of the standard quantum annealing Hamiltonian by introducing an additional term, the trigger Hamiltonian, which can be of two types : ferromagnetic and antiferromagnetic. We use these trigger Hamiltonians to study their influence on the success probability for solving the selected 2-SAT problems. We found that although the scaling of the run-time is exponential for the standard and modified quantum annealing Hamiltonians, the scaling constant in case of adding the trigger Hamiltonians can be significantly smaller. Furthermore, certain choices for the trigger Hamiltonian and annealing times can result in a better scaling than that for simulated annealing. Lastly, we also use the quantum annealers of D-Wave Systems Inc. to study their performance in solving the 2-SAT problems and compare it with the simulation results., Comment: 17 pages, 14 figures