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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Variational preparation of the thermofield double state of the Sachdev-Ye-Kitaev model

Here, we provide an algorithm for preparing the thermofield double (TFD) state of the Sachdev-Ye-Kitaev (SYK) model without the need for an auxiliary bath. Following previous work, the TFD can be cast as the approximate ground state of a Hamiltonian, H TFD . Using variational quantum circuits, we propose and implement a gradient-based algorithm for learning parameters that find this ground state, an application of the variational quantum eigensolver. Concretely, we find shallow quantum circuits that prepare the ground state of H TFD for the q = 4 SYK model for N = 8 Majoranas per side. For N = 12, we achieve a variational energy within 1% of the true ground-state energy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Probabilistic simulation of quantum circuits using a deep-learning architecture

The fundamental question of how to best simulate quantum systems using conventional computational resources lies at the forefront of condensed matter and quantum computation. It impacts both our understanding of quantum materials and our ability to emulate quantum circuits. Here we present an exact formulation of quantum dynamics via factorized generalized measurements which maps quantum states to probability distributions with the advantage that local unitary dynamics and quantum channels map to local quasistochastic matrices. This representation provides a general framework for using state-of-the-art probabilistic models in machine learning for the simulation of quantum many-body dynamics. Using this framework, we have developed a practical algorithm to simulate quantum circuits using an attention network based on a powerful neural network ansatz responsible for the most recent breakthroughs in natural language processing. We demonstrate our approach by simulating circuits that build Greenberger-Horne-Zeilinger and linear graph states of up to 60 qubits, as well as a variational quantum eigensolver circuit for preparing the ground state of the transverse field Ising model on several system sizes. Our methodology constitutes a modern machine learning approach to the simulation of quantum physics with applicability both to quantum circuits as well as other quantum many-body systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Decomposition of high-rank factorized unitary coupled-cluster operators using ancilla and multiqubit controlled low-rank counterparts

The factorized form of the unitary coupled-cluster (UCC) approximation is one of the most promising methodologies to prepare trial states for strongly correlated systems within the variational quantum eigensolver framework. The factorized form of the UCC Ansatz can be systematically applied to a reference state to generate the desired entanglement. The difficulty associated with such an approach is the requirement of simultaneously entangling a growing number of qubits, which quickly exceeds the hardware limitations of today's quantum machines. In particular, while circuits for singles and double excitations can be performed on current hardware, higher-rank excitations require too many gate operations. In this work, we propose a set of schemes that trade off using extra qubits for a reduced gate depth to decompose high-rank UCC excitation operators into significantly lower depth circuits. These results will remain useful even when fault-tolerant machines are available to reduce the overall state-preparation circuit depth.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Error mitigation, optimization, and extrapolation on a trapped-ion testbed

Current noisy intermediate-scale quantum (NISQ) trapped-ion devices are subject to errors which can significantly impact the accuracy of calculations if left unchecked. A form of error mitigation called zero noise extrapolation (ZNE) can decrease an algorithm’s sensitivity to these errors without increasing the number of required qubits. Here we explore different methods for integrating this error mitigation technique into the Variational Quantum Eigensolver (VQE) algorithm for calculating the ground state of the HeH + molecule at 0.8 Å in the presence of experimental noise. Using the Quantum Scientific Computing Open User Testbed (QSCOUT) trapped-ion device, we test three methods of scaling noise for extrapolation: time stretching the two-qubit gates, scaling the sideband detuning parameter, and inserting two-qubit gate identity operations into the ansatz circuit. We find that time stretching and sideband detuning scaling fail to scale the noise on our particular hardware in a way that can be extrapolated to zero noise. Scaling our noise with global gate identity insertions and extrapolating after variational optimization, we achieve error suppression of 96.8%, resulting in an energy estimate within –0.004 ± 0.04 hartree of the ground state energy. This is an improvement, but still outside the chemical accuracy threshold of 0.0016 hartree. Furthermore, our results show that the efficacy of this error mitigation technique depends on choosing the correct implementation for a given device architecture.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Cheaper and more noise-resilient quantum state preparation using eigenvector continuation

Subspace methods are powerful, noise-resilient methods that can effectively prepare ground states on quantum computers. The challenge is to get a subspace with a small condition number that spans the states of interest using minimal quantum resources. In this work, we will use eigenvector continuation to build a subspace from the low-lying states of a set of Hamiltonians. The basis vectors are prepared using truncated versions of standard state preparation methods such as imaginary-time evolution (ITE), adiabatic state preparation (ASP), and variational quantum eigensolver. By using these truncated methods combined with eigenvector continuation, we can directly improve upon them, obtaining more accurate ground-state energies at a reduced cost. We use several spin systems to demonstrate convergence even when methods like ITE and ASP fail, such as ASP in the presence of level crossings and ITE with vanishing energy gaps. We also showcase the noise resilience of this approach beyond the gains already made by having shallower quantum circuits. Furthermore, our findings suggest that eigenvector continuation can be used to improve existing state preparation methods in the near term.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Lipkin model on a quantum computer

Atomic nuclei are important laboratories for exploring and testing new insights into the universe, such as experiments to directly detect dark matter or explore properties of neutrinos. The targets of interest are often heavy, complex nuclei that challenge our ability to reliably model them (as well as quantify the uncertainty of those models) with classical computers. Hence there is great interest in applying quantum computation to nuclear structure for these applications. As an early step in this direction, especially with regards to the uncertainties in the relevant quantum calculations, we develop circuits to implement variational quantum eigensolver (VQE) algorithms for the Lipkin-Meshkov-Glick model, which is often used in the nuclear physics community as a testbed for many-body methods. Here, we present quantum circuits for VQE for two and three particles and discuss the construction of circuits for more particles. Implementing the VQE for a two-particle system on the IBM Quantum Experience, we identify initialization and two-qubit gates as the largest sources of error. We find that error mitigation procedures reduce the errors in the results significantly, but additional quantum hardware improvements are needed for quantum calculations to be sufficiently accurate to be competitive with the best current classical methods.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Solving nuclear structure problems with the adaptive variational quantum algorithm

Here we use the Lipkin-Meshkov-Glick (LMG) model and the valence-space nuclear shell model to examine the likely performance of variational quantum eigensolvers in nuclear-structure theory. The LMG model exhibits both a phase transition and spontaneous symmetry breaking at the mean-field level in one of the phases, features that characterize collective dynamics in medium-mass and heavy nuclei. We show that with appropriate modifications, the ADAPT-VQE algorithm, a particularly flexible and accurate variational approach, is not troubled by these complications. We treat up to 12 particles and show that the number of quantum operations needed to approach the ground-state energy scales linearly with the number of qubits. We find similar scaling when the algorithm is applied to the nuclear shell model with realistic interactions in the sd and pf shells. Although most of these simulations contain no noise, we use a noise model from real IBM hardware to show that for the LMG model with four particles, weak noise has no effect on the efficiency of the algorithm.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Scattering phase shifts from a quantum computer

We calculate two-body scattering phase shifts on a quantum computer using a leading order short-range effective field theory Hamiltonian. The algorithm combines the variational quantum eigensolver and the quantum subspace expansion. As an example, we consider scattering in the deuteron 3S1 partial wave. We calculate scattering phase shifts with a quantum simulator and on real hardware. Here, we also study how noise impacts these calculations and discuss noise mitigation required to extend our work to larger quantum processing units. With current hardware, up to five superconducting qubits can produce acceptable results, and larger calculations will require a significant noise reduction.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Quantum computing for heavy quarkonium spectroscopy

Here, we report a first demonstration for the application of quantum computing to heavy quarkonium spectroscopy study. Based on a Cornell-potential model for the heavy quark and antiquark system, we show how this Hamiltonian problem can be formulated and solved with the variational quantum eigensolver (VQE) approach on the IBM cloud quantum computing platform. Errors due to a global depolarizing noise channel are corrected with a zero-noise extrapolation method, resulting in good agreement with the expected value. We also generalize the VQE method for solving excited states by orthogonalization with respect to the ground state. This new approach is demonstrated to be successful for the quarkonium system on a noiseless quantum simulator and can easily be adapted for solving similar excited state problems in many other physical systems.

79 ASTRONOMY AND ASTROPHYSICS↗
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 OSTI2024

TETRIS-ADAPT-VQE: An adaptive algorithm that yields shallower, denser circuit Ansätze

Adaptive quantum variational algorithms are particularly promising for simulating strongly correlated systems on near-term quantum hardware, but they are not yet viable due, in large part, to the severe coherence time limitations on current devices. In this paper, we introduce an algorithm called TETRIS-ADAPT-VQE (tiling efficient trial circuits with rotations implemented simultaneously adaptive derivative-assembled problem-tailored variational quantum eigensolver), which iteratively builds up variational a few operators at a time in a way dictated by the problem being simulated. This algorithm is a modified version of the ADAPT-VQE algorithm, in which the one-operator-at-a-time rule is lifted to allow for the addition of multiple operators with disjoint supports in each iteration. TETRIS-ADAPT-VQE results in denser but significantly shallower circuits, without increasing the number of controlled- gates or variational parameters. Its advantage over the original algorithm in terms of circuit depths increases with the system size. Moreover, the expensive step of measuring the energy gradient with respect to each candidate unitary at each iteration is performed only a fraction of the time compared with ADAPT-VQE. These improvements bring us closer to the goal of demonstrating a practical quantum advantage on quantum hardware. Published by the American Physical Society 2024

Anastasiou, Panagiotis G. (ORCID:0000000256601791)↗
DOE OSTI2024

Noise robust detection of quantum phase transitions

Quantum computing allows for the manipulation of highly correlated states whose properties quickly go beyond the capacity of any classical method to calculate. Thus one natural problem which could lend itself to quantum advantage is the study of ground-states of condensed matter models, and the transitions between them. However, current levels of hardware noise can require extensive application of error-mitigation techniques to achieve reliable computations. In this work, we use several IBM devices to explore a finite-size spin model with multiple “phaselike” regions characterized by distinct ground-state configurations. Using preoptimized Variational Quantum Eigensolver (VQE) solutions, we demonstrate that in contrast to calculating the energy, where zero-noise extrapolation is required in order to obtain qualitatively accurate yet still unreliable results, calculations of the energy derivative, two-site spin correlation functions, and the fidelity susceptibility yield accurate behavior across multiple regions, even with minimal or no application of error-mitigation approaches. Taken together, these sets of observables could be used to identify level crossings in a simple, noise-robust manner which is agnostic to the method of ground state preparation. This work shows promising potential for near-term application to identifying quantum phase transitions, including avoided crossings and nonadiabatic conical intersections in electronic structure calculations. Published by the American Physical Society 2024

Lively, Kevin (ORCID:0000000320981494)↗
DOE OSTI2024

Scaling adaptive quantum simulation algorithms via operator pool tiling

Adaptive variational quantum simulation algorithms use information from a quantum computer to dynamically create optimal trial wave functions for a given problem Hamiltonian. A key ingredient in these algorithms is a predefined operator pool from which trial wave functions are constructed. Finding suitable pools is critical for the efficiency of the algorithm as the problem size increases. Here, we present a technique called operator pool tiling that facilitates the construction of problem-tailored pools for arbitrarily large problem instances. By first performing an Adaptive Derivative-Assembled Problem-Tailored Ansatz Variational Quantum Eigensolver (ADAPT-VQE) calculation on a smaller instance of the problem using a large, but computationally inefficient, operator pool, we extract the most relevant operators and use them to design more efficient pools for larger instances. We demonstrate the method here on strongly correlated quantum spin models in one and two dimensions, finding that ADAPT automatically finds a highly effective ansatz for these systems. Given that many problems, such as those arising in condensed matter physics, have a naturally repeating lattice structure, we expect the pool tiling method to be a widely applicable technique apt for such systems. Published by the American Physical Society 2024

Van Dyke, John S. (ORCID:0000000167815480)↗
DOE OSTI2025

Variational Simulation of the Lipkin-Meshkov-Glick Model on a Neutral Atom Quantum Computer

We simulate the Lipkin-Meshkov-Glick model using the variational-quantum-eigensolver algorithm on a neutral atom quantum computer. We test the ground-state energy of spin systems with up to 15 spins. Two different encoding schemes are used: an individual spin encoding where each spin is represented by one qubit, and an efficient Gray code encoding scheme that only requires a number of qubits that scales with the logarithm of the number of spins. This more efficient encoding, together with zero-noise extrapolation techniques, is shown to improve the fidelity of the simulated energies with respect to exact solutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Efficacious Qubit Mappings for Quantum Simulations of the 12 C Rotational Band

Solving atomic nuclei from first principles places enormous demands on computational resources, which grow exponentially with increasing number of particles and the size of the space they occupy. We present first quantum simulations based on the variational quantum eigensolver for the low-lying structure of the 12C nucleus that provide acceptable bound-state energies even in the presence of noise. Here, we achieve this by taking advantage of two critical developments. First, we utilize an almost perfect symmetry of atomic nuclei that, in a complete symmetry-adapted basis, drastically reduces the size of the model space. Second, we use the efficacious Gray encoding, for which it has been recently shown that it is resource efficient, especially when coupled with a near band-diagonal structure of the nuclear Hamiltonian.

Encoding↗
DOE OSTI2023

Prepare Ground States of Highly Frustrated Magnetic Clusters on Quantum Computers

Solving challenging problems in physical, chemical, and materials sciences is one of the most promising applications of quantum utility that can be realized on current noisy hardware, considering (i) the direct map (encoding) from the quantum particles and their interactions to the qubits and their entangling gates and (ii) the rapidly improved quantum hardware and advanced error-mitigation techniques. Understanding quantum spin liquid in frustrated magnetic materials is a longstanding challenge in condensed matter physics and the nature of the ground-state phases is highly debated among researchers. Using IBM quantum computers with superconducting qubits, we implemented a variational quantum eigensolver (VQE) algorithm to prepare the ground states of two 12-site cluster approximations of these highly frustrated magnetic materials. The interaction graphs of the two corresponding Hamiltonians are (a) the six-pointed star graph (a unit cell of the kagome lattice) and (b) the cuboctahedral graph (the kagome on a sphere). These are also two instances of Quantum Max Cut problem. With the VQE based on the Hamiltonian variational ansatz acting on a valence bond solid initial trial state, we prepared the ground states and obtained the exact ground energy on simulator and high accuracy on noisy hardware. The deep ansatz necessary to reach the ground state of the cuboctahedral graph indicates that it is a hard instance of Quantum Max Cut.

Wang, Yan↗
DOE OSTI2024

Distributionally Robust Variational Quantum Algorithms With Shifted Noise

Given their potential to demonstrate near-term quantum advantage, variational quantum algorithms (VQAs) have been extensively studied. Although numerous techniques have been developed for VQA parameter optimization, it remains a significant challenge. A practical issue is the high sensitivity of quantum noise to environmental changes, and its propensity to shift in real time. This presents a critical problem as an optimized VQA ansatz may not perform effectively under a different noise environment. For the first time, we explore how to optimize VQA parameters to be robust against unknown shifted noise. We model the noise level as a random variable with an unknown probability density function (PDF), and we assume that the PDF may shift within an uncertainty set. This assumption guides us to formulate a distributionally robust optimization problem, with the goal of finding parameters that maintain effectiveness under shifted noise. We utilize a distributionally robust Bayesian optimization solver for our proposed formulation. This provides numerical evidence in both the Quantum Approximate Optimization Algorithm (QAOA) and the Variational Quantum Eigensolver (VQE) with hardware-efficient ansatz, indicating that we can identify parameters that perform more robustly under shifted noise. We regard this work as the first step towards improving the reliability of VQAs influenced by real-time noise.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Description of reaction and vibrational energetics of CO 2 –NH 3 interaction using quantum computing algorithms

CO 2 capture is critical to solving global warming. Amine-based solvents are extensively used to chemically absorb CO 2 . Thus, it is crucial to study the chemical absorption of CO 2 by amine-based solvents to better understand and optimize CO 2 capture processes. Here, we use quantum computing algorithms to quantify molecular vibrational energies and reaction pathways between CO 2 and a simplified amine-based solvent model—NH 3 . Molecular vibrational properties are important to understanding kinetics of reactions. However, the molecule size correlates with the strength of anharmonicity effect on vibrational properties, which can be challenging to address using classical computing. Quantum computing can help enhance molecular vibrational calculations by including anharmonicity. We implement a variational quantum eigensolver (VQE) algorithm in a quantum simulator to calculate ground state vibrational energies of reactants and products of the CO 2 and NH 3 reaction. The VQE calculations yield ground vibrational energies of CO 2 and NH 3 with similar accuracy to classical computing. In the presence of hardware noise, Compact Heuristic for Chemistry (CHC) ansatz with shallower circuit depth performs better than Unitary Vibrational Coupled Cluster. The “Zero Noise Extrapolation” error-mitigation approach in combination with CHC ansatz improves the vibrational calculation accuracy. Excited vibrational states are accessed with quantum equation of motion method for CO 2 and NH 3 . Using quantum Hartree–Fock (HF) embedding algorithm to calculate electronic energies, the corresponding reaction profile compares favorably with Coupled Cluster Singles and Doubles while being more accurate than HF. Our research showcases quantum computing applications in the study of CO 2 capture reactions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗