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Suppressing Quantum Circuit Errors Due to System Variability

We present a quantum circuit optimization technique that takes into account the variability in error rates that is inherent across present-day noisy quantum computing platforms. This method can be run after qubit routing or postcompilation and consists of computing isomorphic subgraphs to input circuits and scoring each using heuristic cost functions derived from system calibration data. Using an independent standard algorithmic test suite, we show that it is possible to recover on average nearly 40% of missing fidelity using better qubit selection via efficient to compute cost functions. We demonstrate additional performance gains by considering qubit placement over multiple quantum processors. The overhead from these tools is minimal with respect to other compilation steps, such as qubit routing, as the number of qubits increases. As such, our method can be used to find qubit mappings for problems at the scale of quantum advantage and beyond.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

TurboRVB: A many-body toolkit for ab initio electronic simulations by quantum Monte Carlo

TurboRVB is a computational package for ab initio Quantum Monte Carlo (QMC) simulations of both molecular and bulk electronic systems. The code implements two types of well established QMC algorithms: Variational Monte Carlo (VMC) and diffusion Monte Carlo in its robust and efficient lattice regularized variant. A key feature of the code is the possibility of using strongly correlated many-body wave functions (WFs), capable of describing several materials with very high accuracy, even when standard mean-field approaches [e.g., density functional theory (DFT)] fail. The electronic WF is obtained by applying a Jastrow factor, which takes into account dynamical correlations, to the most general mean-field ground state, written either as an antisymmetrized geminal power with spin-singlet pairing or as a Pfaffian, including both singlet and triplet correlations. This WF can be viewed as an efficient implementation of the so-called resonating valence bond (RVB) Ansatz, first proposed by Pauling and Anderson in quantum chemistry [L. Pauling, The Nature of the Chemical Bond (Cornell University Press, 1960)] and condensed matter physics [P.W. Anderson, Mat. Res. Bull 8, 153 (1973)], respectively. The RVB Ansatz implemented in TurboRVB has a large variational freedom, including the Jastrow correlated Slater determinant as its simplest, but nontrivial case. Moreover, it has the remarkable advantage of remaining with an affordable computational cost, proportional to the one spent for the evaluation of a single Slater determinant. Therefore, its application to large systems is computationally feasible. The WF is expanded in a localized basis set. Several basis set functions are implemented, such as Gaussian, Slater, and mixed types, with no restriction on the choice of their contraction. The code implements the adjoint algorithmic differentiation that enables a very efficient evaluation of energy derivatives, comprising the ionic forces. Thus, one can perform structural optimizations and molecular dynamics in the canonical NVT ensemble at the VMC level. For the electronic part, a full WF optimization (Jastrow and antisymmetric parts together) is made possible, thanks to state-of-the-art stochastic algorithms for energy minimization. In the optimization procedure, the first guess can be obtained at the mean-field level by a built-in DFT driver. The code was efficiently parallelized by using a hybrid MPI-OpenMP protocol, which is also an ideal environment for exploiting the computational power of modern Graphics Processing Unit accelerators.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Reducing the complexity of finite-temperature auxiliary-field quantum Monte Carlo

The auxiliary-field quantum Monte Carlo (AFMC) method is a powerful and widely used technique for ground-state and finite-temperature simulations of quantum many-body systems. Here we introduce several algorithmic improvements for finite-temperature AFMC calculations of dilute fermionic systems that reduce the computational complexity of most parts of the algorithm. This is principally achieved by reducing the number of single-particle states that contribute at each configuration of the auxiliary fields to a number that is of the order of the number of fermions. Our methods are applicable for both the canonical and grand-canonical ensembles. We demonstrate the reduced computational complexity of the methods for the homogeneous unitary Fermi gas.

67.85.Lm↗

Characterizing quantum circuits with qubit functional configurations

Abstract We develop a systematic framework for characterizing all quantum circuits with qubit functional configurations. The qubit functional configuration is a mathematical structure that can classify the properties and behaviors of quantum circuits collectively. Major benefits of classifying quantum circuits in this way include: 1. All quantum circuits can be classified into corresponding types; 2. Each type characterizes important properties (such as circuit complexity) of the quantum circuits belonging to it; 3. Each type contains a huge collection of possible quantum circuits allowing systematic investigation of their common properties. We demonstrate the theory’s application to analyzing the hardware-efficient ansatzes of variational quantum algorithms. For potential applications, the functional configuration theory may allow systematic understanding and development of quantum algorithms based on their functional configuration types.

97 MATHEMATICS AND COMPUTING↗

Efficient use of quantum computers for collider physics

Most observables at particle colliders involve physics at a wide variety of distance scales. Due to asymptotic freedom of the strong interaction, the physics at short distances can be calculated reliably using perturbative techniques, while long distance physics is non-perturbative in nature. Factorization theorems separate the contributions from different scales, allowing to identify the pieces that can be determined perturbatively from those that require non-perturbative information, and if the non-perturbative pieces can be reliably determined, one can use experimental measurements to extract the short distance effects, sensitive to possible new physics. Without the ability to compute the non-perturbative ingredients from first principles one typically identifies observables for which the non-perturbative information is universal in the sense that it can be extracted from some experimental observables and then used to predict other observables. In this paper we argue that the future ability to use quantum computers to calculate non-perturbative matrix elements from first principles will allow to make predictions for observables with non-universal non-perturbative long-distance physics.

Algorithms and Theoretical Developments↗

Kato expansion in quantum canonical perturbation theory

This work establishes a connection between canonical perturbation series in quantum mechanics and a Kato expansion for the resolvent of the Liouville superoperator. Our approach leads to an explicit expression for a generator of a block-diagonalizing Dyson’s ordered exponential in arbitrary perturbation order. Unitary intertwining of perturbed and unperturbed averaging superprojectors allows for a description of ambiguities in the generator and block-diagonalized Hamiltonian. We compare the efficiency of the corresponding computational algorithm with the efficiencies of the Van Vleck and Magnus methods for high perturbative orders.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

SU-C-207-05: A Comparative Study of Noise-Reduction Algorithms for Low-Dose Cone-Beam Computed Tomography

Purpose: To study different noise-reduction algorithms and to improve the image quality of low dose cone beam CT for patient positioning in radiation therapy. Methods: In low-dose cone-beam CT, the reconstructed image is contaminated with excessive quantum noise. In this study, three well-developed noise reduction algorithms namely, a) penalized weighted least square (PWLS) method, b) split-Bregman total variation (TV) method, and c) compressed sensing (CS) method were studied and applied to the images of a computer–simulated “Shepp-Logan” phantom and a physical CATPHAN phantom. Up to 20% additive Gaussian noise was added to the Shepp-Logan phantom. The CATPHAN phantom was scanned by a Varian OBI system with 100 kVp, 4 ms and 20 mA. For comparing the performance of these algorithms, peak signal-to-noise ratio (PSNR) of the denoised images was computed. Results: The algorithms were shown to have the potential in reducing the noise level for low-dose CBCT images. For Shepp-Logan phantom, an improvement of PSNR of 2 dB, 3.1 dB and 4 dB was observed using PWLS, TV and CS respectively, while for CATPHAN, the improvement was 1.2 dB, 1.8 dB and 2.1 dB, respectively. Conclusion: Penalized weighted least square, total variation and compressed sensing methods were studied and compared for reducing the noise on a simulated phantom and a physical phantom scanned by low-dose CBCT. The techniques have shown promising results for noise reduction in terms of PSNR improvement. However, reducing the noise without compromising the smoothness and resolution of the image needs more extensive research.

60 APPLIED LIFE SCIENCES↗

A non-orthogonal variational quantum eigensolver

Variational algorithms for strongly correlated chemical and materials systems are one of the most promising applications of near-term quantum computers. We present an extension to the variational quantum eigensolver that approximates the ground state of a system by solving a generalized eigenvalue problem in a subspace spanned by a collection of parametrized quantum states. This allows for the systematic improvement of a logical wavefunction ansatz without a significant increase in circuit complexity. To minimize the circuit complexity of this approach, we propose a strategy for efficiently measuring the Hamiltonian and overlap matrix elements between states parametrized by circuits that commute with the total particle number operator. This strategy doubles the size of the state preparation circuits but not their depth, while adding a small number of additional two-qubit gates relative to standard variational quantum eigensolver. We also propose a classical Monte Carlo scheme to estimate the uncertainty in the ground state energy caused by a finite number of measurements of the matrix elements. We explain how this Monte Carlo procedure can be extended to adaptively schedule the required measurements, reducing the number of circuit executions necessary for a given accuracy. We apply these ideas to two model strongly correlated systems, a square configuration of H4 and the π-system of hexatriene (C6H8).

97 MATHEMATICS AND COMPUTING↗

Adaptive variational quantum eigensolvers for highly excited states

Highly excited states of quantum many-body systems are central objects in the study of quantum dynamics and thermalization that challenge classical computational methods due to their volume-law entanglement content. In this work, we explore the potential of variational quantum algorithms to approximate such states. We propose an adaptive variational quantum eigensolver (VQE) for excited states (X) that self-generates a variational ansatz for arbitrary eigenstates of a many-body Hamiltonian H by attempting to minimize the energy variance with respect to H. We benchmark the method by applying it to an Ising spin chain with integrable and nonintegrable regimes, where we calculate various quantities of interest, including the total energy, magnetization density, and entanglement entropy. We also compare the performance of adaptive VQE-X to an adaptive variant of the folded-spectrum method. For both methods, we find a strong dependence of the algorithm's performance on the choice of operator pool used for the adaptive construction of the ansatz. In particular, an operator pool including long-range two-body gates accelerates the convergence of both algorithms in the nonintegrable regime. Here, we also study the scaling of the number of variational parameters with system size, finding that an exponentially large number of parameters may be necessary to approximate individual highly excited states. Nevertheless, we argue that these methods lay a foundation for the use of quantum algorithms to study finite-energy-density properties of many-body systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Quantum Simulation for High-Energy Physics

It is for the first time that quantum simulation for high-energy physics (HEP) is studied in the U.S. decadal particle-physics community planning, and in fact until recently, this was not considered a mainstream topic in the community. This fact speaks of a remarkable rate of growth of this subfield over the past few years, stimulated by the impressive advancements in quantum information sciences (QIS) and associated technologies over the past decade, and the significant investment in this area by the government and private sectors in the U.S. and other countries. High-energy physicists have quickly identified problems of importance to our understanding of nature at the most fundamental level, from tiniest distances to cosmological extents, that are intractable with classical computers but may benefit from quantum advantage. They have initiated, and continue to carry out, a vigorous program in theory, algorithm, and hardware co-design for simulations of relevance to the HEP mission. This Roadmap is an attempt to bring this exciting and yet challenging area of research to the spotlight, and to elaborate on what the promises, requirements, challenges, and potential solutions are over the next decade and beyond.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

TensorFlow Quantum: A Software Framework for Quantum Machine Learning

We introduce TensorFlow Quantum (TFQ), an open source library for the rapid prototyping of hybrid quantum-classical models for classical or quantum data. This framework offers high-level abstractions for the design and training of both discriminative and generative quantum models under TensorFlow and supports high-performance quantum circuit simulators. We provide an overview of the software architecture and building blocks through several examples and review the theory of hybrid quantum-classical neural networks. We illustrate TFQ functionalities via several basic applications including supervised learning for quantum classification, quantum control, simulating noisy quantum circuits, and quantum approximate optimization. Moreover, we demonstrate how one can apply TFQ to tackle advanced quantum learning tasks including meta-learning, layerwise learning, Hamiltonian learning, sampling thermal states, variational quantum eigensolvers, classification of quantum phase transitions, generative adversarial networks, and reinforcement learning. We hope this framework provides the necessary tools for the quantum computing and machine learning research communities to explore models of both natural and artificial quantum systems, and ultimately discover new quantum algorithms which could potentially yield a quantum advantage.

Broughton, Michael↗

Assessment of Quantum ML Applicability for Climate Actions: Comparison of the Variational Quantum Classifier and the Quantum Support Vector Classifier with Classical ML Models

Climate change refers to significant and long-term alterations in the Earth’s climate patterns, typically resulting from human activities that increase greenhouse gas emissions. Addressing climate change is not merely an option but a necessity, demanding creative solutions and efforts from individuals, researchers, communities, and governments. Despite the capabilities of machine learning (ML) with data-driven solutions promising to combat climate change-related problems, they face challenges stemming from traditional computational methods and prolonged training times, impeding their practical utility. Recent strides in quantum computing have permeated diverse domains, spanning from manufacturing engineering and pharmaceutical discovery to the latest frontier of detecting climate anomalies. With the potential to substantially reduce time and computational complexity, quantum computing shows promise in addressing climate change impacts. Its distinctive features will enable the concurrent exploration of expansive solution spaces, making it well-suited for analyzing extensive climate datasets, simulating intricate climate models, optimizing resource allocation, and discerning patterns in climate data for mitigation and adaptation endeavors. This study explores the potential of using Quantum machine learning (QML) techniques on climate and weather data obtained from NASA Giovannis. We used two QML algorithms, the Quantum Support Vector Classifier (QSVC) and the Variational Quantum Classifier (VQC) models, using the IBM Qiskit ML 0.7.2 ecosystem. We used an actual 127-Qubit IBM Quantum Computer (IBM 127-qubit Eagle) in this study. The methodology and results sections describe the experiences gained from applying and evaluating quantum ML results on climate and weather data obtained from NASA satellites as a novel practical application of quantum computing.

Earth Observational Data↗

Fast and converged classical simulations of evidence for the utility of quantum computing before fault tolerance

A recent quantum simulation of observables of the kicked Ising model on 127 qubits implemented circuits that exceed the capabilities of exact classical simulation. We show that several approximate classical methods, based on sparse Pauli dynamics and tensor network algorithms, can simulate these observables orders of magnitude faster than the quantum experiment and can also be systematically converged beyond the experimental accuracy. Our most accurate technique combines a mixed Schrödinger and Heisenberg tensor network representation with the Bethe free entropy relation of belief propagation to compute expectation values with an effective wave function–operator sandwich bond dimension >16,000,000, achieving an absolute accuracy, without extrapolation, in the observables of <0.01, which is converged for many practical purposes. We thereby identify inaccuracies in the experimental extrapolations and suggest how future experiments can be implemented to increase the classical hardness.

Science & Technology - Other Topics↗

Unorthodox parallelization for Bayesian quantum state estimation

Quantum state tomography (QST) allows for the reconstruction of quantum states through measurements and some inference technique under the assumption of repeated state preparations. Bayesian inference provides a promising platform to achieve both efficient QST and accurate uncertainty quantification, yet is generally plagued by the computational limitations associated with long Markov chains. In this work, we present a novel Bayesian QST approach that leverages modern distributed parallel computer architectures to efficiently sample a D-dimensional Hilbert space. Using a parallelized preconditioned Crank–Nicholson Metropolis–Hastings algorithm, we demonstrate our approach on simulated data and experimental results from IBM Quantum systems up to four qubits, showing significant speedups through parallelization. Although highly unorthodox in pooling independent Markov chains, our method proves remarkably practical, with validation ex post facto via diagnostics like the intrachain autocorrelation time. We conclude by discussing scalability to higher-dimensional systems, offering a path toward efficient and accurate Bayesian characterization of large quantum systems.

Bayesian inference↗

Increased Reliability for Near-Term Quantum Computers via Low-Level Control (CRADA Final Report)

This project helped narrow the gap between near-term hardware and practical applications of quantum computing through the development and implementation of optimized compilation and error mitigation techniques. These advances were enabled by low-level control available on the Advanced Quantum Testbed, and led to methods that characterized and improved the platform’s performance on quantum algorithms. Results of this work were published in the scientific literature and used to inform internal software development of partner Super.tech.

97 MATHEMATICS AND COMPUTING↗

The black hole interior from non-isometric codes and complexity

Quantum error correction has given us a natural language for the emergence of spacetime, but the black hole interior poses a challenge for this framework: at late times the apparent number of interior degrees of freedom in effective field theory can vastly exceed the true number of fundamental degrees of freedom, so there can be no isometric (i.e. inner-product preserving) encoding of the former into the latter. In this paper we explain how quantum error correction nonetheless can be used to explain the emergence of the black hole interior, via the idea of “non-isometric codes protected by computational complexity”. We show that many previous ideas, such as the existence of a large number of “null states”, a breakdown of effective field theory for operations of exponential complexity, the quantum extremal surface calculation of the Page curve, post-selection, “state-dependent/state-specific” operator reconstruction, and the “simple entropy” approach to complexity coarse-graining, all fit naturally into this framework, and we illustrate all of these phenomena simultaneously in a soluble model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Discriminating Quantum States with Quantum Machine Learning

Quantum machine learning (QML) algorithms have obtained great relevance in the machine learning (ML) field due to the promise of quantum speedups when performing basic linear algebra subroutines (BLAS), a fundamental element in most ML algorithms. By making use of BLAS operations, we propose, implement and analyze a quantum k-means (qk-means) algorithm with a low time complexity of O(NKlog(D)I/C) to apply it to the fundamental problem of discriminating quantum states at readout. Discriminating quantum states allows the identification of quantum states |0⟩ and |1⟩ from low-level in-phase and quadrature signal (IQ) data, and can be done using custom ML models. In order to reduce dependency on a classical computer, we use the qk-means to perform state discrimination on the IBMQ Bogota device and managed to find assignment fidelities of up to 98.7% that were only marginally lower than that of the k-means algorithm. We also performed a cross-talk benchmark on the quantum device by applying both algorithms to perform state discrimination on a combination of quantum states and using Pearson Correlation coefficients and assignment fidelities of discrimination results to conclude on the presence of cross-talk on qubits. Evidence shows cross-talk in the (1, 2) and (2, 3) neighboring qubit couples for the analyzed device.

Quiroga, David↗

Long-time simulations for fixed input states on quantum hardware

Publicly accessible quantum computers open the exciting possibility of experimental dynamical quantum simulations. While rapidly improving, current devices have short coherence times, restricting the viable circuit depth. Despite these limitations, we demonstrate long-time, high fidelity simulations on current hardware. Specifically, we simulate an XY-model spin chain on Rigetti and IBM quantum computers, maintaining a fidelity over 0.9 for 150 times longer than is possible using the iterated Trotter method. Our simulations use an algorithm we call fixed state Variational Fast Forwarding (fsVFF). Recent work has shown an approximate diagonalization of a short time evolution unitary allows a fixed-depth simulation. fsVFF substantially reduces the required resources by only diagonalizing the energy subspace spanned by the initial state, rather than over the total Hilbert space. We further demonstrate the viability of fsVFF through large numerical simulations, and provide an analysis of the noise resilience and scaling of simulation errors.

97 MATHEMATICS AND COMPUTING↗