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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Composite Qdrift-product formulas for quantum and classical simulations in real and imaginary time

Recent study has shown that it can be advantageous to implement a composite channel that partitions the Hamiltonian H for a given simulation problem into subsets A and B such that H = A + B , where the terms in A are simulated with a Trotter-Suzuki channel and the B terms are randomly sampled via the Qdrift algorithm. Here we extend Qdrift and composite product formulas to imaginary time, formulating candidate classical algorithms for quantum Monte Carlo calculations. We upper bound the induced Schatten- 1 → 1 norm on both imaginary-time Qdrift and composite channels. Another recent result demonstrated that simulations of lattice Hamiltonians containing geometrically local interactions can be improved using a Lieb-Robinson argument to decompose H into subsets that contain only terms supported on that subset of the lattice. Here, we provide a quantum algorithm by unifying this result with the composite approach into “local composite channels” and we upper bound the diamond distance. We provide exact numerical simulations of algorithmic cost by counting the number of gates of the form e − i H j t and e − H j β to meet a certain error tolerance ε . In doing so, we optimize the partitioning into sets A and B using gradient boosted tree models from machine learning. These numerical studies are important given that product formulas have been historically known to outperform analytic upper bounds. We show constant factor advantages for a variety of interesting Hamiltonians, the maximum of which is a ≈ 20 -fold speedup that occurs in the simulation of Jellium. Published by the American Physical Society 2024

Pocrnic, Matthew (ORCID:0000000203089376)↗
DOE OSTI2025

Characterization and thermometry of dissipatively stabilized steady states

In this work we study the properties of dissipatively stabilized steady states of noisy quantum algorithms, exploring the extent to which they can be well approximated as thermal distributions, and proposing methods to extract the effective temperature T. We study an algorithm called the relaxational quantum eigensolver (RQE), which is one of a family of algorithms that attempt to find ground states and balance error in noisy quantum devices. In RQE, we weakly couple a second register of auxiliary ‘shadow’ qubits to the primary system in Trotterized evolution, thus engineering an approximate zero-temperature bath by periodically resetting the auxiliary qubits during the algorithm’s runtime. Balancing the infinite temperature bath of random gate error, RQE returns states with an average energy equal to a constant fraction of the ground state. We probe the steady states of this algorithm for a range of base error rates, using several methods for estimating both T and deviations from thermal behavior. In particular, we both confirm that the steady states of these systems are often well-approximated by thermal distributions, and show that the same resources used for cooling can be adopted for thermometry, yielding a fairly reliable measure of the temperature. These methods could be readily implemented in near-term quantum hardware, and for stabilizing and probing Hamiltonians where simulating approximate thermal states is hard for classical computers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Quantum simulation of QED in Coulomb gauge

A recent work considered quantum simulation of Quantum Electrodynamics on a lattice in the Coulomb gauge with gauge degrees of freedom represented in the occupation basis in momentum space. In this work, we consider the more efficient representation of the gauge degrees of freedom in field basis in position space and develop a quantum algorithm for real-time simulation. We show that the continuum Coulomb gauge Hamiltonian is equivalent to the temporal gauge Hamiltonian when acting on physical states consisting of fermion and transverse gauge fields. The Coulomb gauge Hamiltonian is discretized by using the Green’s function of the discrete Laplacian operator under the Dirichlet boundary conditions. Both the continuum Coulomb gauge Hamiltonian and the discretized one proposed here guarantee that the unphysical longitudinal gauge fields are decoupled and commute with the corresponding Hamiltonian. Thus there is no need to impose any constraint. The local gauge field basis and the canonically conjugate variable basis are swapped efficiently using the quantum Fourier transform. We prove that the qubit cost to represent physical states and the gate count for real-time simulation scale polynomially with the lattice size, energy, time, accuracy, and Hamiltonian parameters in lattice units. The gate cost here for implementing the time evolution of the gauge field is reduced at least by a factor on the order of 10 8 for modest lattice size and accuracy level compared with the previous work.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Polariton spectra under the collective coupling regime. I. Efficient simulation of linear spectra and quantum dynamics

We outline two general theoretical techniques to simulate polariton quantum dynamics and optical spectra under the collective coupling regimes described by a Holstein–Tavis–Cummings (HTC) model Hamiltonian. The first one takes advantage of sparsity of the HTC Hamiltonian, which allows one to reduce the cost of acting polariton Hamiltonian onto a state vector to the linear order of the number of states, instead of the quadratic order. The second one is applying the well-known Chebyshev series expansion approach for quantum dynamics propagation and to simulate the polariton dynamics in the HTC system; this approach allows us to use a much larger time step for propagation and only requires a few recursive operations of the polariton Hamiltonian acting on state vectors. These two theoretical approaches are general and can be applied to any trajectory-based non-adiabatic quantum dynamics methods. We apply these two techniques with our previously developed Lindblad-partially linearized density matrix approach to simulate the linear absorption spectra of the HTC model system, with both inhomogeneous site energy disorders and dipolar orientational disorders. Our numerical results agree well with the previous analytic and numerical work.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Parallelization techniques for quantum simulation of fermionic systems

Mapping fermionic operators to qubit operators is an essential step for simulating fermionic systems on a quantum computer. We investigate how the choice of such a mapping interacts with the underlying qubit connectivity of the quantum processor to enable (or impede) parallelization of the resulting Hamiltonian-simulation algorithm. It is shown that this problem can be mapped to a path coloring problem on a graph constructed from the particular choice of encoding fermions onto qubits and the fermionic interactions onto paths. The basic version of this problem is called the weak coloring problem. Taking into account the fine-grained details of the mapping yields what is called the strong coloring problem, which leads to improved parallelization performance. A variety of illustrative analytical and numerical examples are presented to demonstrate the amount of improvement for both weak and strong coloring-based parallelizations. Our results are particularly important for implementation on near-term quantum processors where minimizing circuit depth is necessary for algorithmic feasibility.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Characterizing non-Markovian and coherent errors in quantum simulation

Quantum simulation of many-body systems, particularly using ultracold atoms and trapped ions, presents a unique form of quantum control—it is a direct implementation of a multi-qubit gate generated by the Hamiltonian. As a consequence, it also faces a unique challenge in terms of benchmarking, because the well-established gate benchmarking techniques are unsuitable for this form of quantum control. Here we show that the symmetries of the target many-body Hamiltonian can be used not only to benchmark but to characterize experimental errors in the quantum simulation. We use our results to develop protocols to characterize these errors, which can be implemented using state-of-the-art technology. We consider two forms of errors: (i) unitary errors arising out of systematic errors in the applied Hamiltonian and (ii) canonical non-Markovian errors arising out of random shot-to-shot fluctuations in the applied Hamiltonian. We show that the dynamics of the expectation value of the target Hamiltonian itself, which is ideally constant in time, can be used to characterize these errors. In the presence of errors, the expectation value of the target Hamiltonian shows a characteristic thermalization dynamics, when it satisfies the operator thermalization hypothesis (OTH). That is, an oscillation in the short time followed by relaxation to a steady-state value in the long time limit. We show that while the steady-state value can be used to characterize the coherent errors, the amplitude of the oscillations can be used to estimate the non-Markovian errors. We prove a sandwich theorem to establish a linear relation between the amplitude of the oscillations and the magnitude of the non-Markovian errors. Moreover, by varying the initial state, we show that the steady state values can be used to completely construct the generator of the coherent errors. Using these results, we develop two experimental protocols to characterize the unitary errors based on these results, one of which requires single-qubit addressing and the other one doesn't. We also develop a protocol to characterize non-Markovian errors. Published by the American Physical Society 2024

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Towards string order melting of spin-1 particle chains in superconducting transmons using optimal control

Utilizing optimal control to simulate a model Hamiltonian is an emerging strategy that leverages the intrinsic physics of a device with digital quantum simulation methods. Here we evaluate optimal control for probing the nonequilibrium properties of symmetry-protected topological (SPT) states simulated with superconducting hardware. Assuming a tunable transmon architecture, we cast the evolution of these SPT states as a series of one- and two-site pulse optimization problems that are solved in the presence of leakage constraints. From the generated pulses, we classically simulate the time-dependent melting of the perturbed SPT string order across a six-site model with an average state infidelity of 10 -3 . The feasibility of these pulses as well as their efficient application indicate that high-fidelity simulations of string order melting are within reach of current quantum computing systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

QuTree: A tree tensor network package

Here we present QuTree, a C++ library for tree tensor network approaches. QuTree provides class structures for tensors, tensor trees, and related linear algebra functions that facilitate the fast development of tree tensor network approaches such as the multilayer multiconfigurational time-dependent Hartree approach or the density matrix renormalization group approach and its various extensions. We investigate the efficiency of relevant tensor and tensor network operations and show that the overhead for managing the network structure is negligible, even in cases with a million leaves and small tensors. QuTree focuses on providing simple, high-level routines while retaining easy access to the backend to facilitate novel developments. We demonstrate the capabilities of the package by computing the eigenstates of coupled harmonic oscillator Hamiltonians and performing random circuit simulations on a virtual quantum computer.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Linear embedding of nonlinear dynamical systems and prospects for efficient quantum algorithms

The simulation of large nonlinear dynamical systems, including systems generated by discretization of hyperbolic partial differential equations, can be computationally demanding. Such systems are important in both fluid and kinetic computational plasma physics. This motivates exploring whether a future error-corrected quantum computer could perform these simulations more efficiently than any classical computer. In this work, we describe a method for mapping any finite nonlinear dynamical system to an infinite linear dynamical system (embedding) and detail three specific cases of this method that correspond to previously studied mappings. Then we explore an approach for approximating the resulting infinite linear system with finite linear systems (truncation). Using a number of qubits only logarithmic in the number of variables of the nonlinear system, a quantum computer could simulate truncated systems to approximate output quantities if the nonlinearity is sufficiently weak. Other aspects of the computational efficiency of the three detailed embedding strategies are also discussed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Floating Block Method for Quantum Monte Carlo Simulations

Quantum Monte Carlo simulations are powerful and versatile tools for the quantum many-body problem. In addition to the usual calculations of energies and eigenstate observables, quantum Monte Carlo simulations can in principle be used to build fast and accurate many-body emulators using eigenvector continuation or design time-dependent Hamiltonians for adiabatic quantum computing. Furthermore, these new applications require something that is missing from the published literature, an efficient quantum Monte Carlo scheme for computing the inner product of ground state eigenvectors corresponding to different Hamiltonians. In this work, we introduce an algorithm called the floating block method, which solves the problem by performing Euclidean time evolution with two different Hamiltonians and interleaving the corresponding time blocks. We use the floating block method and nuclear lattice simulations to build eigenvector continuation emulators for energies of 4 He, 8 Be, 12 C, and 16 O nuclei over a range of local and nonlocal interaction couplings. From the emulator data, we identify the quantum phase transition line from a Bose gas of alpha particles to a nuclear liquid.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Fock-Space Schrieffer–Wolff Transformation: Classically-Assisted Rank-Reduced Quantum Phase Estimation Algorithm

We present an extension of many-body downfolding methods to reduce the resources required in the quantum phase estimation (QPE) algorithm. In this paper, we focus on the Schrieffer–Wolff (SW) transformation of the electronic Hamiltonians for molecular systems that provides significant simplifications of quantum circuits for simulations of quantum dynamics. We demonstrate that by employing Fock-space variants of the SW transformation (or rank-reducing similarity transformations (RRST)) one can significantly increase the locality of the qubit-mapped similarity-transformed Hamiltonians. The practical utilization of the SW-RRST formalism is associated with a series of approximations discussed in the manuscript. In particular, amplitudes that define RRST can be evaluated using conventional computers and then encoded on quantum computers. The SW-RRST QPE quantum algorithms can also be viewed as an extension of the standard state-specific coupled-cluster downfolding methods to provide a robust alternative to the traditional QPE algorithms to identify the ground and excited states for systems with various numbers of electrons using the same Fock-space representations of the downfolded Hamiltonian. The RRST formalism serves as a design principle for developing new classes of approximate schemes that reduce the complexity of quantum circuits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Benchmarking Quantum Simulators Using Ergodic Quantum Dynamics

Here we propose and analyze a sample-efficient protocol to estimate the fidelity between an experimentally prepared state and an ideal target state, applicable to a wide class of analog quantum simulators without advanced spatiotemporal control. Our protocol relies on universal fluctuations emerging from generic Hamiltonian dynamics, which we discover in the present work. It does not require fine-tuned control over state preparation, quantum evolution, or readout capability, while achieving near optimal sample complexity: a percent-level precision is obtained with ~103 measurements, independent of system size. Furthermore, the accuracy of our fidelity estimation improves exponentially with increasing system size. We numerically demonstrate our protocol in a variety of quantum simulator platforms, including quantum gas microscopes, trapped ions, and Rydberg atom arrays. We discuss applications of our method for tasks such as multiparameter estimation of quantum states and processes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Scalar QED with Rydberg atoms

We review recent suggestions to quantum simulate scalar electrodynamics (the lattice Abelian Higgs model) in $1+1$ dimensions with rectangular arrays of Rydberg atoms. We show that platforms made publicly available recently allow empirical explorations of the critical behavior of quantum simulators. We discuss recent progress regarding the phase diagram of two-leg ladders, effective Hamiltonian approaches and the construction of hybrid quantum algorithms targeting hadronization in collider physics event generators.

Meurice, Yannick↗
DOE OSTI2019

Mapping Arbitrarily Sparse Two-body Interactions on One-dimensional Quantum Circuits

We consider an assignment problem arising in Fermionic-swap based mapping of the one-body and two-body interaction terms in simulating time evolution of a sparse second-quantized electronic structure Hamiltonian on a quantum computer. Relative efficiency of different swap networks depends on the relative costs of performing a swap layer and computing a Hamiltonian interaction term. Under the assumption that the interaction term cost dominates the computation, we develop an iterative algorithm that uses hypergraph optimal linear arrangement (HOLA) and partial distance-2 coloring to exploit arbitrary sparsity in the Hamiltonian for efficient computation using swap networks. Using a set of 122 problems from computational chemistry, we demonstrate performance improvements up to 100% relative to the state-of-the-art approaches for one-body terms and up to 86% utilization for two-body terms relative to a theoretical peak utilization. To the best of our knowledge, this is the first study to exploit arbitrary sparsity in orbital interactions for efficient computation on one-dimensional qubit connectivity layouts. The proposed algorithms form the basis for extension to map general k-body interactions that arise in other domains onto generalized qubit connectivity layouts.

quantum computing, Combinatorial Optimization, hyp↗
DOE OSTI2020

Effective Gaps Are Not Effective: Quasipolynomial Classical Simulation of Obstructed Stoquastic Hamiltonians

All known examples suggesting an exponential separation between classical simulation algorithms and stoquastic adiabatic quantum computing (StoqAQC) exploit symmetries that constrain adiabatic dynamics to effective, symmetric subspaces. The symmetries produce large effective eigenvalue gaps, which in turn make adiabatic computation efficient. We present a classical algorithm to subexponentially sample from an effective subspace of any k -local stoquastic Hamiltonian H , without a priori knowledge of its symmetries (or near symmetries). Our algorithm maps any k -local Hamiltonian to a graph G = ( V , E ) with | V | = O (poly (n)) , where n is the number of qubits. Given the well-known result of Babai [Graph isomorphism in quasipolynomial time, in Proceedings of the Forty-Eighth Annual ACM Symposium on Theory of Computing (2016), pp. 684–697], we exploit graph isomorphism to study the automorphisms of G and arrive at an algorithm quasipolynomial in | V | for producing samples from effective subspace eigenstates of H . Our results rule out exponential separations between StoqAQC and classical computation that arise from hidden symmetries in k -local Hamiltonians. Our graph representation of H is not limited to stoquastic Hamiltonians and may rule out corresponding obstructions in nonstoquastic cases, or be useful in studying additional properties of k -local Hamiltonians.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Optimal Control for the Quantum Simulation of Nuclear Dynamics

We propose a method for enacting the unitary time propagation of two interacting neutrons at leading order of chiral effective-field theory by efficiently encoding the nuclear dynamics into a single multilevel quantum device. The emulated output of the quantum simulation shows that, by applying a single gate that draws on the underlying characteristics of the device, it is possible to observe multiple cycles of the nuclear dynamics before the onset of decoherence. Owing to the signal's longevity, we can then extract spectroscopic properties of the simulated nuclear system. This allows us to validate the encoding of the nuclear Hamiltonian and the robustness of the simulation in the presence of quantum-hardware noise by comparing the extracted spectroscopic information to exact calculations. This work paves the way for transformative calculations of the dynamical properties of nuclei on near-term quantum devices.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Lowering tomography costs in quantum simulation with a symmetry projected operator basis

Measurement in quantum simulations provides a means for extracting meaningful information from a complex quantum state, and for quantum computing, reducing the complexity of measurement will be vital for near-term applications. For most quantum simulations, the targeted state will obey several symmetries inherent to the system Hamiltonian. Here, we obtain an alternative symmetry projected basis of measurement that reduces the number of measurements needed by a constant factor. Our scheme can be implemented at no additional cost on a quantum computer, can be implemented under various measurement or tomography schemes, and is reasonably resilient under noise.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

From trivial to topological paramagnets: The case of Z 2 and Z 2 3 symmetries in two dimensions

Using quantum Monte Carlo simulations, we map out the phase diagram of Hamiltonians interpolating between trivial and nontrivial bosonic symmetry-protected topological phases, protected by Z 2 and Z 2 3 symmetries, in two dimensions. In all cases, we find that the trivial and the topological phases are separated by an intermediate phase in which the protecting symmetry is spontaneously broken. Depending on the model, we identify a variety of magnetic orders on the triangular lattice, including ferromagnetism, 3 × 3 order, and stripe orders (both commensurate and incommensurate). Critical properties are determined through a finite-size scaling analysis. Possible scenarios regarding the nature of the phase transitions are discussed.

2-dimensional systems↗