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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

EQC: Ensembled Quantum Computing for Variational Quantum Algorithms

Variational quantum algorithms (VQA), which are comprised of a classical optimizer and a parameterized quantum circuit, emerges as one of the most promising approaches of harvesting quantum power in the noisy-intermediate-scale-quantum (NISQ) era. However, the deployment of VQAs on today's NISQ devices often faces considerable system noise and prohibitively slow training speeds. On the other hand, the expensive supporting sources and infrastructure make quantum computers extremely keen on high utilization. In this paper, we propose a novel way of thinking about a quantum backend: rather than relying on one physical device which tends to introduce platform-specific noise and bias, a quantum ensemble, which distributes quantum tasks across parallel devices, can serve as a virtualized quantum computer for offering reduced noise levels through an adaptive mixture and also provide significantly improved training speeds through parallelization. With this idea, we build a distributive VQA optimization framework called DVQA, serving as the first effort in adopting parallel quantum devices for cooperative VQA training. To further constraint noise and speed-up convergence, we design a model for individual NISQ devices concerning their properties and running conditions, and propose a weighting mechanism for regularizing the returned gradients. Extensive evaluations on 10 IBM-Q quantum devices using the VQE example show that the distributive VQA training framework can substantially boost the training speed by 10.5x on average (up to 86x and at least 5.2x) with improved training accuracy.

Stein, Samuel A.↗
DOE OSTI2025

Efficient Simulation of Open Quantum Systems on NISQ Trapped‐Ion Hardware

Abstract Simulating open quantum systems, which interact with external environments, presents significant challenges on noisy intermediate‐scale quantum (NISQ) devices due to limited qubit resources and noise. In this study, an efficient framework is proposed for simulating open quantum systems on NISQ hardware by leveraging a time‐perturbative Kraus operator representation of the system's dynamics. This approach avoids the computationally expensive Trotterization method and exploits the Lindblad master equation to represent time evolution in a compact form, particularly for systems satisfying specific commutation relations. The efficiency of this method is demonstrated by simulating quantum channels, such as the continuous‐time Pauli channel and damped harmonic oscillators, on NISQ trapped‐ion hardware, including IonQ Harmony and Quantinuum H1‐1. Additionally, hardware‐agnostic error mitigation techniques are introduced, including Pauli channel fitting and quantum depolarizing channel inversion, to enhance the fidelity of quantum simulations. These results show strong agreement between the simulations on real quantum hardware and exact solutions, highlighting the potential of Kraus‐based methods for scalable and accurate simulation of open quantum systems on NISQ devices. This framework opens pathways for simulating more complex systems under realistic conditions in the near term.

Burdine, Colin [Department of Electrical and Compu↗
DOE OSTI2021

Many-Body Physics in the NISQ Era: Quantum Programming a Discrete Time Crystal

Recent progress in the realm of noisy intermediate-scale quantum (NISQ) devices represents an exciting opportunity for many-body physics by introducing new laboratory platforms with unprecedented control and measurement capabilities. We explore the implications of NISQ platforms for many-body physics in a practical sense: we ask which physical phenomena, in the domain of quantum statistical mechanics, they may realize more readily than traditional experimental platforms. While a universal quantum computer can simulate any system, the eponymous noise inherent to NISQ devices practically favors certain simulation tasks over others in the near term. As a particularly well-suited target, we identify discrete time crystals (DTCs), novel nonequilibrium states of matter that break time translation symmetry. These can only be realized in the intrinsically out-of-equilibrium setting of periodically driven quantum systems stabilized by disorder-induced many-body localization. While promising precursors of the DTC have been observed across a variety of experimental platforms—ranging from trapped ions to nitrogen-vacancy centers to NMR crystals—none have all the necessary ingredients for realizing a fully fledged incarnation of this phase, and for detecting its signature long-range spatiotemporal order. We show that a new generation of quantum simulators can be programmed to realize the DTC phase and to experimentally detect its dynamical properties, a task requiring extensive capabilities for programmability, initialization, and readout. Specifically, the architecture of Google’s Sycamore processor is a remarkably close match for the task at hand. We also discuss the effects of environmental decoherence, and how they can be distinguished from ‘internal’ decoherence coming from closed-system thermalization dynamics. Already with existing technology and noise levels, we find that DTC spatiotemporal order would be observable over hundreds of periods, with parametric improvements to come as the hardware advances.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

QASMBench: A Low-Level Quantum Benchmark Suite for NISQ Evaluation and Simulation

The rapid development of quantum computing (QC) in the NISQ era urgently demands a low-level benchmark suite and insightful evaluation metrics for characterizing the properties of prototype NISQ devices, the efficiency of QC programming compilers, schedulers and assemblers, and the capability of quantum system simulators in a classical computer. In this work, we fill this gap by proposing a low-level, easy-to-use benchmark suite called QASMBench based on the OpenQASM assembly representation. It consolidates commonly used quantum routines and kernels from a variety of domains including chemistry, simulation, linear algebra, searching, optimization, arithmetic, machine learning, fault tolerance, cryptography, and so on, trading-off between generality and usability. To analyze these kernels in terms of NISQ device execution, in addition to circuit width and depth, we propose four circuit metrics including gate density, retention lifespan, measurement density, and entanglement variance, to extract more insights about the execution efficiency, the susceptibility to NISQ error, and the potential gain from machine-specific optimizations. Applications in QASMBench can be launched and verified on several NISQ platforms, including IBM-Q, Rigetti, IonQ and Quantinuum. For evaluation, we measure the execution fidelity of a subset of QASMBench applications on 12 IBM-Q machines through density matrix state tomography, comprising 25K circuit evaluations. In addition we also compare the fidelity of executions among the IBM-Q machines, the IonQ QPU and the Rigetti Aspen M-1 system.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Resource-Efficient Chemistry on Quantum Computers with the Variational Quantum Eigensolver and The Double Unitary Coupled-Cluster approach

Applications of quantum simulation algorithms to obtain electronic energies of molecules on noisy intermediate-scale quantum (NISQ) devices require careful consideration of resources describing the complex electron correlation effects. In modeling second-quantized problems, the biggest challenge confronted is that the number of qubits scales linearly with the size of molecular basis. This poses a significant limitation on the size of the basis sets and the number of correlated electrons included in quantum simulations of chemical processes. To address this issue and to enable more realistic simulations on NISQ computers, we employ the double unitary coupled-cluster (DUCC) method to effectively downfold correlation effects into the reduced-size orbital space, commonly referred to as the active space. Using downfolding techniques, we demonstrate that properly constructed effective Hamiltonians can capture the effect of the whole orbital space in small-size active spaces. Combining the downfolding pre-processing technique with the Variational Quantum Eigensolver, we solve for the ground-state energy of H2 and Li2 in the cc-pVTZ basis using the DUCC-reduced active spaces. We compare these results to full configuration-interaction and high-level coupled-cluster reference calculations.

quantum computing, variational quantum solver, cou↗
DOE OSTI2025

Quantum simulations of nuclear resonances with variational methods

Background: The many-body nature of nuclear physics problems poses significant computational challenges. These challenges become even more pronounced when studying the resonance states of nuclear systems, which are governed by the non-Hermitian Hamiltonian. Quantum computing, particularly for quantum many-body systems, offers a promising alternative, especially within the constraints of current noisy intermediate-scale quantum (NISQ) devices. Purpose: This work aims to simulate nuclear resonances using quantum algorithms by developing a variational framework compatible with non-Hermitian Hamiltonians and implementing it fully on a quantum simulator. Methods: We employ the complex scaling technique to extract resonance positions classically and adapt it for quantum simulations using a two-step algorithm. First, we transform the non-Hermitian Hamiltonian into a Hermitian form by using the energy variance as a cost function within a variational framework. Second, we perform 𝜃-trajectory calculations to determine optimal resonance positions in the complex energy plane. To address resource constraints on NISQ devices, we utilize Gray code (GC) encoding to reduce qubit requirements. Results: We first validate our approach using a schematic potential model that mimics a nuclear potential, successfully reproducing known resonance energies with high fidelity. We then extend the method to a more realistic 𝛼−𝛼 nuclear potential and compute the 𝐷- and 𝐺-wave resonance energies with a basis size of 𝑁=16, using only four qubits. The quantum simulation results closely match the classical values, demonstrating the feasibility of our approach. Conclusions: This study demonstrates, for the first time, that the complete 𝜃-trajectory method can be implemented on a quantum computer without relying on any classical input beyond the Hamiltonian. The results establish a scalable and efficient quantum framework for simulating resonance phenomena in nuclear systems. This work represents a significant step toward quantum simulations of open quantum systems and lays the foundation for future investigations into resonance structures in nuclear, atomic, and molecular physics.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Qubit-efficient entanglement spectroscopy using qubit resets

One strategy to fit larger problems on NISQ devices is to exploit a tradeoff between circuit width and circuit depth. Unfortunately, this tradeoff still limits the size of tractable problems since the increased depth is often not realizable before noise dominates. Here, we develop qubit-efficient quantum algorithms for entanglement spectroscopy which avoid this tradeoff. In particular, we develop algorithms for computing the trace of the n -th power of the density operator of a quantum system, T r ( ρ n ) , (related to the Rényi entropy of order n ) that use fewer qubits than any previous efficient algorithm while achieving similar performance in the presence of noise, thus enabling spectroscopy of larger quantum systems on NISQ devices. Our algorithms, which require a number of qubits independent of n , are variants of previous algorithms with width proportional to n , an asymptotic difference. The crucial ingredient in these new algorithms is the ability to measure and reinitialize subsets of qubits in the course of the computation, allowing us to reuse qubits and increase the circuit depth without suffering the usual noisy consequences. We also introduce the notion of effective circuit depth as a generalization of standard circuit depth suitable for circuits with qubit resets. This tool helps explain the noise-resilience of our qubit-efficient algorithms and should aid in designing future algorithms. We perform numerical simulations to compare our algorithms to the original variants and show they perform similarly when subjected to noise. Additionally, we experimentally implement one of our qubit-efficient algorithms on the Honeywell System Model H0, estimating T r ( ρ n ) for larger n than possible with previous algorithms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Advancing quantum simulations of the nuclear shell model with Gray-code–based resource-efficient protocols

Background: Some of the computational limitations in solving the nuclear many-body problem could be overcome by utilizing quantum computers. The nuclear shell-model calculations providing deeper insights into the properties of atomic nuclei are one such case with high demand for resources, as the size of the Hilbert space grows exponentially with the number of particles involved. Quantum algorithms are being developed to overcome these challenges and advance such calculations. Purpose: To develop quantum circuits for the nuclear shell-model, leveraging the capabilities of noisy intermediate-scale quantum (NISQ) devices. Here, we aim to minimize resource requirements (specifically in terms of qubits and gates) and strive to reduce the impact of noise by employing relevant mitigation techniques. Methods: We achieve noise resilience by designing an optimized Ansatz for the variational quantum eigensolver (VQE) based on Givens rotations and incorporating qubit-ADAPT-VQE in combination with variational quantum deflation (VQD) to compute ground and excited states, incorporating the zero-noise extrapolation mitigation technique. Furthermore, the qubit requirements are significantly reduced by mapping the basis states to qubits using Gray-code encoding and generalizing transformations of fermionic operators to efficiently represent many-body states. Results: By employing the resource-efficient protocols, we achieve the ground and excited state energy levels of 38 Ar and 6 Li with better accuracy. These energy levels are presented for noiseless simulations, noisy conditions, and after applying noise mitigation techniques. Results are compared for Jordan-Wigner and Gray-code encoding using VQE, qubit-ADAPT-VQE, and VQD. Conclusions: Our work highlights the potential of resource-efficient protocols to leverage the full potential of NISQ devices in scaling the nuclear shell model calculations, offering a pathway toward more complex quantum simulations in nuclear physics. This approach establishes a framework for studying other nuclear systems with improved quantum resource efficiency, marking a significant advancement in applying quantum computing to realistic nuclear physics applications.

Physics - Nuclear physics and radiation physics↗
DOE OSTI2023

Erasure conversion in a high-fidelity Rydberg quantum simulator

Minimizing and understanding errors is critical for quantum science, both in noisy intermediate scale quantum (NISQ) devices and for the quest towards fault-tolerant quantum computation. Rydberg arrays have emerged as a prominent platform in this context with impressive system sizes and proposals suggesting how error-correction thresholds could be significantly improved by detecting leakage errors with single-atom resolution, a form of erasure error conversion. However, two-qubit entanglement fidelities in Rydberg atom arrays have lagged behind competitors and this type of erasure conversion is yet to be realized for matter-based qubits in general. Here we demonstrate both erasure conversion and high-fidelity Bell state generation using a Rydberg quantum simulator. When excising data with erasure errors observed via fast imaging of alkaline-earth atoms, we achieve a Bell state fidelity of $\ge 0.997{1}_{-13}^{+10}$ , which improves to $\ge 0.998{5}_{-12}^{+7}$ when correcting for remaining state-preparation errors. We further apply erasure conversion in a quantum simulation experiment for quasi-adiabatic preparation of long-range order across a quantum phase transition, and reveal the otherwise hidden impact of these errors on the simulation outcome. Our work demonstrates the capability for Rydberg-based entanglement to reach fidelities in the 0.999 regime, with higher fidelities a question of technical improvements, and shows how erasure conversion can be utilized in NISQ devices. These techniques could be translated directly to quantum-error-correction codes with the addition of long-lived qubits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Quantum Simulation of Molecular Electronic States with a Transcorrelated Hamiltonian: Higher Accuracy with Fewer Qubits

Simulation of electronic structure is one of the most promising applications on noisy intermediate-scale quantum (NISQ) era devices. However, NISQ devices suffer from a number of challenges like limited qubit connectivity, short coherence times, and sizable gate error rates. Thus, desired quantum algorithms should require shallow circuit depths and low qubit counts to take advantage of these devices. Here, we attempt to reduce quantum resource requirements for molecular simulations on a quantum computer while maintaining the desired accuracy with the help of classical quantum chemical theories of canonical transformation and explicit correlation. In this work, compact ab initio Hamiltonians are generated classically, in the second quantized form, through an approximate similarity transformation of the Hamiltonian with (a) an explicitly correlated two-body unitary operator with generalized pair excitations that remove the Coulombic electron–electron singularities from the Hamiltonian and (b) a unitary one-body operator to efficiently capture the orbital relaxation effects required for accurate description of the excited states. The resulting transcorrelated Hamiltonians are able to describe both the ground and the excited states of molecular systems in a balanced manner. Using the variational quantum eigensolver (VQE) method based on the unitary coupled cluster with singles and doubles (UCCSD) ansatz and only a minimal basis set (ANO-RCC-MB), we demonstrate that the transcorrelated Hamiltonians can produce ground state energies comparable to the reference CCSD energies with the much larger cc-pVTZ basis set. This leads to a reduction in the number of required CNOT gates by more than 3 orders of magnitude for the chemical species studied in this work. Furthermore, using the quantum equation of motion (qEOM) formalism in conjunction with the transcorrelated Hamiltonian, we are able to reduce the deviations in the excitation energies from the reference EOM-CCSD/cc-pVTZ values by an order of magnitude. In conclusion, the transcorrelated Hamiltonians developed here are Hermitian and contain only one- and two-body interaction terms and thus can be easily combined with any quantum algorithm for accurate electronic structure simulations.

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

Gutzwiller hybrid quantum-classical computing approach for correlated materials

Rapid progress in noisy intermediate-scale quantum (NISQ) computing technology has led to the development of novel resource-efficient hybrid quantum-classical algorithms, such as the variational quantum eigensolver (VQE), that can address open challenges in quantum chemistry, physics, and material science. Proof-of-principle quantum chemistry simulations for small molecules have been demonstrated on NISQ devices. While several approaches have been theoretically proposed for correlated materials, NISQ simulations of interacting periodic models on current quantum devices have not yet been demonstrated. Here, we develop a hybrid quantum-classical simulation framework for correlated electron systems based on the Gutzwiller variational embedding approach. We implement this framework on Rigetti quantum processing units (QPUs) and apply it to the periodic Anderson model, which describes a correlated heavy electron band hybridizing with noninteracting conduction electrons. Our simulation results quantitatively reproduce the known ground state quantum phase diagram including metallic, Kondo and Mott insulating phases. This is the first fully self-consistent hybrid quantum-classical simulation of an infinite correlated lattice model executed on QPUs, demonstrating that the Gutzwiller hybrid quantum-classical embedding framework is a powerful approach to simulate correlated materials on NISQ hardware. This benchmark study also puts forth a concrete pathway towards practical quantum advantage on NISQ devices.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Classical Optimizers for Noisy Intermediate-Scale Quantum Devices

We present a collection of optimizers tuned for usage on Noisy Inter-mediate-Scale Quantum (NISQ) devices. Optimizers have a range of applications in quantum computing, including the Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization (QAOA) algorithms. They have further uses in calibration, hyperparameter tuning, machine learning, etc. We employ the VQE algorithm as a case study. VQE is a hybrid algorithm, with a classical minimizer step driving the next evaluation on the quantum processor. While most results to date concentrated on tuning the quantum VQE circuit, our study indicates that in the presence of quantum noise the classical minimizer step is a weak link and a careful choice combined with tuning is required for correct results. We explore state-of-the-art gradient-free optimizers capable of handling noisy, black-box, cost functions and stress-test them using a quantum circuit simulation environment with noise injection capabilities on individual gates. Our results indicate that specifically tuned optimizers are crucial to obtaining valid science results on NISQ hardware, as well as projecting forward on fault tolerant circuits.

Lavrijsen, Wim↗
DOE OSTI2020

Establishing the quantum supremacy frontier with a 281 Pflop/s simulation

Noisy intermediate-scale quantum (NISQ) computers are entering an era in which they can perform computational tasks beyond the capabilities of the most powerful classical computers, thereby achieving 'quantum supremacy', a major milestone in quantum computing. NISQ supremacy requires comparison with a state-of-the-art classical simulator. In this paper, we report HPC simulations of hard random quantum circuits (RQC), which have been recently used as a benchmark for the first experimental demonstration of quantum supremacy, sustaining an average performance of 281 Pflop/s (true single precision) on Summit, currently the fastest supercomputer in the world. These simulations were carried out using qFlex, a tensor-network-based classical high-performance simulator of RQCs. Our results show an advantage of many orders of magnitude in energy consumption of NISQ devices over classical supercomputers. In addition, we propose a standard benchmark for NISQ computers based on qFlex.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Digital-analog quantum computation

Digital quantum computing paradigm offers highly desirable features such as universality, scalability, and quantum error correction. However, physical resource requirements to implement useful error-corrected quantum algorithms are prohibitive in the current era of NISQ devices. As an alternative path to performing universal quantum computation, within the NISQ era limitations, we propose to merge digital single-qubit operations with analog multiqubit entangling blocks in an approach we call digital-analog quantum computing (DAQC). Along these lines, although the techniques may be extended to any resource, we propose to use unitaries generated by the ubiquitous Ising Hamiltonian for the analog entangling block and we prove its universal character. Here, we construct explicit DAQC protocols for efficient simulations of arbitrary inhomogeneous Ising, two-body, and M-body spin Hamiltonian dynamics by means of single-qubit gates and a fixed homogeneous Ising Hamiltonian. Additionally, we compare a sequential approach where the interactions are switched on and off (stepwise DAQC) with an always-on multiqubit interaction interspersed by fast single-qubit pulses (banged DAQC). Finally, we perform numerical tests comparing purely digital schemes with DAQC protocols, showing a remarkably better performance of the latter. The proposed DAQC approach combines the robustness of analog quantum computing with the flexibility of digital methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Benchmarking near-term quantum devices with the variational quantum eigensolver and the Lipkin-Meshkov-Glick model

The variational quantum eigensolver is a promising algorithm for noisy intermediate scale quantum (NISQ) computation. Verification and validation of NISQ algorithms' performance on NISQ devices is an important task. Here, we consider the exactly diagonalizable Lipkin-Meshkov-Glick (LMG) model as a candidate for benchmarking NISQ computers. We use the Bethe Ansatz to construct eigenstates of the trigonometric LMG model using quantum circuits inspired by the LMG's underlying algebraic structure. We construct circuits with depth $\mathcal{O}$(N) and $\mathcal{O}$(log 2 N) that can prepare any trigonometric LMG eigenstate of N particles. The number of gates required for both circuits is $\mathcal{O}$(N). The energies of the eigenstates can then be measured and compared to the exactly known answers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Fundamental Algorithmic Research for Quantum Computing (FAR-QC) (Final Technical Report)

Anticipation of the noisy intermediate‐scale quantum (NISQ) era has sparked unprecedented interest in quantum computing, yet we still lack a clear understanding of how NISQ‐era applications will perform relative to the best classical algorithms solving the same problems. The goals of this project include: (1) Developing better tools for characterizing the performance of NISQ devices and for assessing whether such devices can achieve a quantum advantage. (2) Conceiving and analyzing potential applications of quantum computing technology in the NISQ era and beyond.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Towards quantum simulations in particle physics and beyond on noisy intermediate-scale quantum devices

We review two algorithmic advances that bring us closer to reliable quantum simulations of model systems in high-energy physics and beyond on noisy intermediate-scale quantum (NISQ) devices. The first method is the dimensional expressivity analysis of quantum circuits, which allows for constructing minimal but maximally expressive quantum circuits. The second method is an efficient mitigation of readout errors on quantum devices. Both methods can lead to significant improvements in quantum simulations, e.g. when variational quantum eigensolvers are used. This article is part of the theme issue ‘Quantum technologies in particle physics’.

Science & Technology - Other Topics↗
DOE OSTI2022

Quantum simulations of hydrodynamics via the Madelung transformation

Developing numerical methods to simulate efficiently nonlinear fluid dynamics on universal quantum computers is a challenging problem. In this paper, a generalization of the Madelung transform is defined to solve quantum relativistic charged fluid equations interacting with external electromagnetic forces via the Dirac equation. The Dirac equation is discretized into discrete-time quantum walks which can be efficiently implemented on universal quantum computers. A variant of this algorithm is proposed to implement simulations using current noisy intermediate scale quantum (NISQ) devices in the case of homogeneous external forces. High resolution (up to N=2 17 grid points) numerical simulations of relativistic and nonrelativistic hydrodynamical shocks on current IBM NISQs are performed with this algorithm. Here, this paper demonstrates that fluid dynamics can be simulated on NISQs, and opens the door to simulating other fluids, including plasmas, with more general quantum walks and quantum automata.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗