Quantum Physics (quant-ph)

Abstract: Mitigating measurement errors in quantum systems without relying on quantum error correction is of critical importance for the practical development of quantum technology. Deep learning-based quantum measurement error mitigation has exhibited advantages over the linear inversion method due to its capability to correct non-linear noise. However, scalability remains a challenge for both methods. In this study, we propose a scalable quantum measurement error mitigation method that leverages the conditional independence of distant qubits and incorporates transfer learning techniques. By leveraging the conditional independence assumption, we achieve an exponential reduction in the size of neural networks used for error mitigation. This enhancement also offers the benefit of reducing the number of training data needed for the machine learning model to successfully converge. Additionally, incorporating transfer learning provides a constant speedup. We validate the effectiveness of our approach through experiments conducted on IBM quantum devices with 7 and 13 qubits, demonstrating excellent error mitigation performance and highlighting the efficiency of our method.

Abstract: Efficient decoding to estimate error locations from outcomes of syndrome measurement is the prerequisite for quantum error correction. Decoding in presence of circuit-level noise including measurement errors should be considered in case of actual quantum computing devices. In this work, we develop a decoder for circuit-level noise that solves the error estimation problems as Ising-type optimization problems. We confirm that the threshold theorem in the surface code under the circuitlevel noise is reproduced with an error threshold of approximately 0.4%. We also demonstrate the advantage of the decoder through which the Y error detection rate can be improved compared with other matching-based decoders. Our results reveal that a lower logical error rate can be obtained using our algorithm compared with that of the minimum-weight perfect matching algorithm.

Abstract: The quantum three-box paradox considers a ball prepared in a superposition of being in one of three Boxes. Bob makes measurements by opening either Box 1 or Box 2. After performing some unitary operations (shuffling), Alice can infer with certainty that the ball was detected by Bob, regardless of which box he opened, if she detects the ball after opening Box 3. The paradox is that the ball would have been found with certainty in either box, if that box had been opened. Resolutions of the paradox include that Bob's measurement cannot be made non-invasively, or else that realism cannot be assumed at the quantum level. Here, we strengthen the case for the former argument, by constructing macroscopic versions of the paradox. Macroscopic realism implies that the ball is in one of the boxes, prior to Bob or Alice opening any boxes. We demonstrate consistency of the paradox with macroscopic realism, if carefully defined (as weak macroscopic realism, wMR) to apply to the system at the times prior to Alice or Bob opening any Boxes, but after the unitary operations associated with preparation or shuffling. By solving for the dynamics of the unitary operations, and comparing with mixed states, we demonstrate agreement between the predictions of wMR and quantum mechanics: The paradox only manifests if Alice's shuffling combines both local operations (on Box 3) and nonlocal operations, on the other Boxes. Following previous work, the macroscopic paradox is shown to correspond to a violation of a Leggett-Garg inequality, which implies non-invasive measurability, if wMR holds.

Abstract: We propose active steering protocols for quantum state preparation in quantum circuits where each ancilla qubit (detector) is connected to a single system qubit, employing a simple coupling selected from a small set of steering operators. The decision is made such that the expected cost function gain in one time step is maximized. We apply these protocols to several many-qubit models. Our results are underlined by three remarkable insights. First, we show that the standard fidelity does not give a useful cost function; instead, successful steering is achieved by including local fidelity terms. Second, although the steering dynamics acts on each system qubit separately, entanglement in the generated target state is introduced, and can be tuned at will, by performing Bell measurements on ancilla qubit pairs after every time step. This implements a weak-measurement variant of entanglement swapping. Third, numerical simulations suggest that the active steering protocol can reach arbitrarily designated target states, including passively unsteerable states such as the $N$-qubit W state.

Abstract: We experimentally demonstrate a recently proposed single-junction quantum-circuit refrigerator (QCR) as an in-situ-tunable low-temperature environment for a superconducting 4.7-GHz resonator. With the help of a transmon qubit, we measure the populations of the different resonator Fock states, thus providing reliable access to the temperature of the engineered electromagnetic environment and its effect on the resonator. We demonstrate coherent and thermal resonator states and that the on-demand dissipation provided by the QCR can drive these to a small fraction of a photon on average, even if starting above 1 K. We observe that the QCR can be operated either with a dc bias voltage or a gigahertz rf drive, or a combination of these. The bandwidth of the rf drive is not limited by the circuit itself and consequently, we show that 2.9-GHz continuous and 10-ns-pulsed drives lead to identical desired refrigeration of the resonator. These observations answer to the shortcomings of previous works where the Fock states were not resolvable and the QCR exhibited slow charging dynamics. Thus this work introduces a versatile tool to study open quantum systems, quantum thermodynamics, and to quickly reset superconducting qubits.

Abstract: Recent efforts have demonstrated the first prototypes of compact and programmable photonic quantum computers~(PQCs). Utilization of time-bin encoding in loop-like architectures enabled a programmable generation of quantum states and execution of different~(programmable) logic gates on a single circuit. Actually, there is still space for better compactness and complexity of available quantum states: photonic circuits~(PCs) can function at different frequencies. This necessitates an optical component, which can make different frequencies talk with each other. This component should be integrable into PCs and be controlled -- preferably -- by voltage for programmable generation of multifrequency quantum states and PQCs. Here, we propose a device that controls a four-wave mixing process, essential for frequency combs. We utilize nonlinear Fano resonances. Entanglement generated by the device can be tuned continuously by the applied voltage which can be delivered to the device via nm-thick wires. The device is integrable, CMOS-compatible, and operates within a timescale of hundreds of femtoseconds.

Abstract: With the rapid development of quantum computing, automatic verification of quantum circuits becomes more and more important. While several decision diagrams (DDs) have been introduced in quantum circuit simulation and verification, none of them supports symbolic computation. Algorithmic manipulations of symbolic objects, however, have been identified as crucial, if not indispensable, for several verification tasks. This paper proposes the first decision-diagram approach for operating symbolic objects and verifying quantum circuits with symbolic terms. As a notable example, our symbolic tensor decision diagrams (symbolic TDD) could verify the functionality of the 160-qubit quantum Fourier transform circuit within three minutes. Moreover, as demonstrated on Bernstein-Vazirani algorithm, Grover's algorithm, and the bit-flip error correction code, the symbolic TDD enables efficient verification of quantum circuits with user-supplied oracles and/or classical controls.

Abstract: Three major misconceptions concerning quantized tachyon fields: the energy spectrum unbounded from below, the frame-dependent and unstable vacuum state, and the non-covariant commutation rules, are shown to be a result of misrepresenting the Lorentz group in a too small Hilbert space. By doubling this space we establish an explicitly covariant framework that allows for the proper quantization of the tachyon fields eliminating all of these issues. Our scheme that is derived to maintain the relativistic covariance also singles out the two-state formalism developed by Aharonov et al. [1] as a preferred interpretation of the quantum theory.

Abstract: The local oscillator in practical continuous-variable quantum key distribution system fluctuates at any time during the key distribution process, which may open security loopholes for the eavesdropper to hide her eavesdropping behaviors. Based on this, we investigate a more stealthy quantum attack where the eavesdroppers simulates random fluctuations of local oscillator intensity in a practical discrete-modulated continuous-variable quantum key distribution system. Theoretical simulations show that both communicating parties will misestimate channel parameters and overestimate the secret key rate due to the modified attack model, even though they have monitored the mean local oscillator intensity and shot-noise as commonly used. Specifically, the eavesdropper's manipulation of random fluctuations in LO intensity disturbs the parameter estimation in realistic discrete-modulated continuous-variable quantum key distribution system, where the experimental parameters are always used for constraints of the semidefinite program modeling. The modified attack introduced by random fluctuations of local oscillator can only be eliminated by monitoring the local oscillator intensity in real time which places a higher demand on the accuracy of monitoring technology. Moreover, similar quantum hacking will also occur in practical local local oscillator system by manipulating the random fluctuations in pilot intensity, which shows the strong adaptability and the important role of the proposed attack.

Abstract: Open Markovian quantum systems with fast and full Hamiltonian control can be reduced to an equivalent control system on the standard simplex modelling the dynamics of the eigenvalues of the density matrix describing the quantum state. We explore this reduced control system for answering questions on reachability and stabilizability with immediate applications to the cooling of Markovian quantum systems. We show that for certain tasks of interest, the control Hamiltonian can be chosen time-independent. -- The reduction picture is an example of dissipative interconversion between equivalence classes of states, where the classes are induced by fast controls.

Abstract: Anomaly detection (AD) involves identifying observations or events that deviate in some way from the rest of the data. Machine learning techniques have shown success in automating this process by detecting hidden patterns and deviations in large-scale data. The potential of quantum computing for machine learning has been widely recognized, leading to extensive research efforts to develop suitable quantum machine learning (QML) algorithms. In particular, the search for QML algorithms for near-term NISQ devices is in full swing. However, NISQ devices pose additional challenges due to their limited qubit coherence times, low number of qubits, and high error rates. Kernel methods based on quantum kernel estimation have emerged as a promising approach to QML on NISQ devices, offering theoretical guarantees, versatility, and compatibility with NISQ constraints. Especially support vector machines (SVM) utilizing quantum kernel estimation have shown success in various supervised learning tasks. However, in the context of AD, semisupervised learning is of great relevance, and yet there is limited research published in this area. This paper introduces an approach to semisupervised AD based on the reconstruction loss of a support vector regression (SVR) with quantum kernel. This novel model is an alternative to the variational quantum and quantum kernel one-class classifiers, and is compared to a quantum autoencoder as quantum baseline and a SVR with radial-basis-function (RBF) kernel as well as a classical autoencoder as classical baselines. The models are benchmarked extensively on 10 real-world AD data sets and one toy data set, and it is shown that our SVR model with quantum kernel performs better than the SVR with RBF kernel as well as all other models, achieving highest mean AUC over all data sets. In addition, our QSVR outperforms the quantum autoencoder on 9 out of 11 data sets.

Abstract: Operator controllability refers to the ability to implement an arbitrary unitary in SU(N) and is a prerequisite for universal quantum computing. Controllability tests can be used in the design of quantum devices to reduce the number of external controls. Their practical use is hampered, however, by the exponential scaling of their numerical effort with the number of qubits. Here, we devise a hybrid quantum-classical algorithm based on a parametrized quantum circuit. We show that controllability is linked to the number of independent parameters, which can be obtained by dimensional expressivity analysis. We exemplify the application of the algorithm to qubit arrays with nearest-neighbour couplings and local controls. Our work provides a systematic approach to the resource-efficient design of quantum chips.

Abstract: High-energy physics is facing increasingly computational challenges in real-time event reconstruction for the near-future high-luminosity era. Using the LHCb vertex detector as a use-case, we explore a new algorithm for particle track reconstruction based on the minimisation of an Ising-like Hamiltonian with a linear algebra approach. The use of a classical matrix inversion technique results in tracking performance similar to the current state-of-the-art but with worse scaling complexity in time. To solve this problem, we also present an implementation as quantum algorithm, using the Harrow-Hassadim-Lloyd (HHL) algorithm: this approach can potentially provide an exponential speedup as a function of the number of input hits over its classical counterpart, in spite of limitations due to the well-known HHL Hamiltonian simulation and readout problems. The findings presented in this paper shed light on the potential of leveraging quantum computing for real-time particle track reconstruction in high-energy physics.

Abstract: We analyse time evolution of spread complexity (SC) in an isolated interacting quantum many-body system when it is subjected to a sudden quench. The differences in characteristics of the time evolution of the SC for different time scales is analysed, both in integrable and chaotic models. For a short time after the quench, the SC shows universal quadratic growth, irrespective of the initial state or the nature of the Hamiltonian, with the time scale of this growth being determined by the local density of states. The characteristics of the SC in the next phase depend upon the nature of the system, and we show that depending upon whether the survival probability of an initial state is Gaussian or exponential, the SC can continue to grow quadratically, or it can show linear growth. To understand the behaviour of the SC at late times, we consider sudden quenches in two models, a full random matrix in the Gaussian orthogonal ensemble, and a spin-1/2 system with disorder. We observe that for the full random matrix model and the chaotic phase of the spin-1/2 system, the complexity shows linear growth at early times and saturation at late times. The full random matrix case shows a peak in the intermediate time region, whereas this feature is less prominent in the spin-1/2 system, as we explain.

Abstract: Quantum simulators were originally proposed for simulating one partial differential equation (PDE) in particular - Schrodinger's equation. Can quantum simulators also efficiently simulate other PDEs? While most computational methods for PDEs - both classical and quantum - are digital (PDEs must be discretised first), PDEs have continuous degrees of freedom. This suggests that an analog representation can be more natural. While digital quantum degrees of freedom are usually described by qubits, the analog or continuous quantum degrees of freedom can be captured by qumodes. Based on a method called Schrodingerisation, we show how to directly map D-dimensional linear PDEs onto a (D+1)-qumode quantum system where analog or continuous-variable Hamiltonian simulation on D+1 qumodes can be used. This very simple methodology does not require one to discretise PDEs first, and it is not only applicable to linear PDEs but also to some nonlinear PDEs and systems of nonlinear ODEs. We show some examples using this method, including the Liouville equation, heat equation, Fokker-Planck equation, Black-Scholes equations, wave equation and Maxwell's equations. We also devise new protocols for linear PDEs with random coefficients, important in uncertainty quantification, where it is clear how the analog or continuous-variable framework is most natural. This also raises the possibility that some PDEs may be simulated directly on analog quantum systems by using Hamiltonians natural for those quantum systems.

Abstract: Understanding complex chemical systems -- such as biomolecules, catalysts, and novel materials -- is a central goal of quantum simulations. Near-term strategies hinge on the use of variational quantum eigensolver (VQE) algorithms combined with a suitable ansatz. However, straightforward application of many chemically-inspired ansatze yields prohibitively deep circuits. In this work, we employ several circuit optimization methods tailored for trapped-ion quantum devices to enhance the feasibility of intricate chemical simulations. The techniques aim to lessen the depth of the unitary coupled cluster with singles and doubles (uCCSD) ansatz's circuit compilation, a considerable challenge on current noisy quantum devices. Furthermore, we use symmetry-inspired classical post-selection methods to further refine the outcomes and minimize errors in energy measurements, without adding quantum overhead. Our strategies encompass optimal mapping from orbital to qubit, term reordering to minimize entangling gates, and the exploitation of molecular spin and point group symmetry to eliminate redundant parameters. The inclusion of error mitigation via post-selection based on known molecular symmetries improves the results to near milli-Hartree accuracy. These methods, when applied to a benzene molecule simulation, enabled the construction of an 8-qubit circuit with 69 two-qubit entangling operations, pushing the limits for variational quantum eigensolver (VQE) circuits executed on quantum hardware to date.

Abstract: The purpose of this paper is to discuss the existence of a nontrivial tradeoff relation for estimating two unitary-shift parameters in a relativistic spin-1/2 system. It is shown that any moving observer cannot estimate two parameters simultaneously, even though a parametric model is classical in the rest frame. This transition from the classical model to a genuine quantum model is investigated analytically using a one-parameter family of quantum Fisher information matrices. This paper proposes to use an indicator that can not only detect the existence of a tradeoff relation but can also evaluate its strength. Based on the proposed indicator, this paper investigates the nature of the tradeoff relation in detail.

Abstract: A criterion of local continuity of the relative entropy of resource -- the relative entropy distance to the set of free states -- is obtained. Several basic corollaries of this criterion are presented. Applications to the relative entropy of entanglement in multipartite quantum systems are considered. It is shown, in particular, that local continuity of any relative entropy of multipartite entanglement follows from local continuity of the quantum mutual information.

Abstract: The paper discusses Daniel Jafferis et al.'s "Nature" publication on "Traversable wormhole dynamics on a quantum processor." The experiment utilized Google's Sycamore quantum processor to simulate a sparse SYK model with a learned Hamiltonian. A debate ensued when Bryce Kobrin, Thomas Schuster, and Norman Yao raised concerns about the learned Hamiltonian's reliability, which Jafferis and the team addressed. Recently, there has been an update in the wormhole experiment saga. In an attempt to rescue the commuting Hamiltonian from its inevitable fate of being invalidated, a recent paper by Ping Gao proposed a creative solution to reinvigorate the concept within the context of teleportation through wormholes. This paper delves into the ongoing debate and the recent endeavor to address the comments made by Kobrin et al. I remain skeptical about the efforts to address Kobrin et al.'s challenges. By its nature, a commuting Hamiltonian does not exhibit chaotic behavior like non-commuting Hamiltonians. Moreover, it's always essential to assess the sensitivity of the Hamiltonian to noise to understand its practical feasibility for the real-world Sycamore processor.

Abstract: We present QCAM, a quantum analogue of Content-Addressable Memory (CAM), useful for finding matches in two sequences of bit-strings. Our QCAM implementation takes advantage of Grover's search algorithm and proposes a highly-optimized quantum circuit implementation of the QCAM oracle. Our circuit construction uses the parallel uniformly controlled rotation gates, which were used in previous work to generate QBArt encodings. These circuits have a high degree of quantum parallelism which reduces their critical depth. The optimal number of repetitions of the Grover iterator used in QCAM depends on the number of true matches and hence is input dependent. We additionally propose a hardware-efficient implementation of the quantum counting algorithm (HEQC) that can infer the optimal number of Grover iterations from the measurement of a single observable. We demonstrate the QCAM application for computing the Jaccard similarity between two sets of k-mers obtained from two DNA sequences.