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DOE OSTI2026

Optimization performance, fidelity, and cost: SIAM VQE

This dataset contains files storing results from classically-simulated quantum subroutines within a dynamical mean-field theory workflow, and jupyter notebooks processing the data in these files to generate plots. The files store: (1) Results from variational quantum eigensolver (VQE) simulations searching for optimal parameters allowing parametrized quantum circuits to prepare approximations to ground states of different Anderson impurity models (AIMs) (2) Results from simulations of a quantum Lanczos algorithm (QLA) estimating the Lanczos coefficients defining the continued-fraction representation of an (AIM) Green’s function Description: Any file named vqe_gs_results* stores approximations to the ground state and energy of a given AIM estimated using three different methods: (1) Numerical diagonalization (2) Ideal VQE simulation (3) VQE simulation with sampling noise For each VQE simulations metadata about the optimization (optimization results plus number of quantum circuits that would have been executed on real hardware) is also stored. Any file named qla_dos_results* estimations for the Lanczos coefficients defining the Green’s function of an AIM. The stored estimations are achieved using different methods: (1) Numerical Lanczos algorithm from initial states obtained from numerical diagonalization (2) Simulated quantum Lanczos algorithm from initial states prepared from parametrized quantum circuits yielded by corresponding ideal and noisy VQE subroutines. The dataset is used and described in M. Karabin et al., "Quantum solver for single-impurity Anderson models with particle-hole symmetry", Phys. Rev. Research 8, 033066 (2026). DOI: https://doi.org/10.1103/7ys3-tl4l

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Porting Classical Approaches for Quantum Simulations to Quantum Computers

Simulating quantum many-body systems is one of the most promising problems in which we might anticipate that quantum computers should show quantum advantage. Unfortunately, there is still a gap between this promise and actual practice. New quantum algorithms need to be developed and the current quantum algorithms have various difficulties - e.g efficient state preparation - which must be overcome and improved upon. In many cases, classical approaches need to be ported over to quantum devices. In this project we have developed a suite of new quantum algorithms which makes progress in this regard. We developed a new optimization scheme for variational quantum eigensolvers, UBOS, which mitigates problems with local minimas and barren plateaus while improving convergence to the ground state by an order of magnitude. We developed a new way to utilize qubitization to find ground states of nearly frustration-free Hamiltonians faster than all previous methods. We developed a series of state preparation techniques which helps initialize parameterized quantum circuits into reasonable starting points on which quantum algorithms are then applied. In addition to the development of novel algorithms, it is critical to have classical simulation techniques for approximately simulating quantum circuits which can be used to benchmark and understand quantum algorithms. Toward that end, we developed a novel POVM formalism to simulate quantum circuits as well as exemplify the massive parallelization of tensor network methodologies. Finally, we developed physical understanding of entanglement phase transitions such as many-body localization and random tensor networks.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Quantum Computing for Energy-Related Applications

Growing interest in quantum computing and simulations have created opportunities for its deployment to improve processes pertaining to energy production, distribution, and consumption. While quantum computing is considered as a paradigm shift in our basic understanding of physical computation, effective implementation of quantum computing in energy applications also depends on progress and development in the dimensions of both quantum computing hardware and quantum computing algorithms. To fully address the status and future challenges of quantum information science (QIS) applied within the energy sector, in this presentation, we firstly summarize recent advancements on the applications of quantum computing to energy infrastructure and materials, complex energy system processes, advanced manufacturing, and energy system security. Then, we will demonstrate the results of quantum computing both on a simulator and a quantum device accessing from OLCF. Our first example is to use the variational quantum eigensolver (VQE) with a unitary coupled cluster with singles and doubles (UCCSD) ansatz to simulate a series of LixHyq molecules (q=-1, 0, +1). The obtained results showed that the quantum computing VQE-UCCSD is comparable to classical CCSD for small systems like LiH with respect to full configuration interaction (FCI). Targeting on CO2 capture application, our second example is to use VQE to quantify molecular vibrational energies and reaction pathways between CO2 and a simplified amine-based solvent model—NH3 to form H2NCOOH. This research showcases quantum computing applications in the study of CO2 capture reactions.

Duan, Yuhua↗

DOE OSTI2024

Assessing Ground State Energy of Molecules and Energy Profile of the NH3 Capturing CO2 System Using the Quantum Computing Algorithms

Molecule size correlates with the number of electrons on electronic energies and strength of anharmonicity on vibrational properties, however, it is challenging to address using classical computing. In this study, variational quantum eigensolver (VQE) algorithm was implemented on a quantum simulator to quantify electronic and vibrational energies and reaction pathways of CO2 + NH3 = NH2COOH. The VQE-based Hartree-Fock-Embedding algorithm was adopted to benchmark electronic energies for a series of molecules (doi.org/10.1063/5.0188249) and quantify the reaction energy profile of the CO2 capture reaction (doi.org/10.1116/5.0137750). The generated reaction profile is in good agreement with the classical high-level Coupled-Cluster-Singles-and-Doubles (CCSD) results. The quantum computing algorithm also helps enhance the calculation of vibrational ground-state energies by considering the many-body coupling using the Vibrational Self-Consistent Field method, providing results for CO2 and NH3 molecules with accuracy comparable to the direct diagonalization method. Our approach indicates quantum computing can be applied to solve practical problems.

Lee, Yueh-Lin↗

DOE OSTI2024

Towards a Description of the Ground State Properties of LiHm Complexes and Reaction Energetics of Hydrogenation of Small Li Clusters using VQE-based Quantum Chemical Calculations

This presentation describes the utilization of the variational quantum eigensolver (VQE) using a unitary coupled cluster with singles and doubles (UCCSD) ansatz to simulate a series of LiHn molecules (n=1-3), including their singly charged ions. The performance is considered using a simulator by systematically increasing system size, providing data to compare against future VQE calculations. The predicted energy profiles are in semi-quantitative agreement with highly accurate CCSD/FCI methods.

quantum computing↗

DOE OSTI2022

Unitary Selective Coupled-Cluster Method

Simulating molecules using the Variational Quantum Eigensolver method is one of the promising applications for NISQ-era quantum computers. Designing an efficient ansatz to represent the electronic wave function is crucial in such simulations. Standard unitary coupled-cluster with singles and doubles (UCCSD) ansatz tends to have a large number of insignificant terms that do not lower the energy of the system. In this work, we present a unitary selective coupled-cluster method, a way to construct a unitary coupled-cluster ansatz iteratively using a selection procedure with excitations up to fourth order. This approach uses the electronic Hamiltonian matrix elements and the amplitudes for excitations already present in the ansatz to find the important excitations of higher order and to add them to the ansatz. The important feature of the method is that it systematically reduces the energy error with increasing ansatz size for a set of test molecules. {The main advantage of the proposed method is that the effort to increase the ansatz does not require any additional measurements on a quantum computer.}

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Robust measurement of wave function topology on NISQ quantum computers

Topological quantum phases of quantum materials are defined through their topological invariants. These topological invariants are quantities that characterize the global geometrical properties of the quantum wave functions and thus are immune to local noise. Here, we present a strategy to measure topological invariants on quantum computers. We show that our strategy can be easily integrated with the variational quantum eigensolver (VQE) so that the topological properties of generic quantum many-body states can be characterized on current quantum hardware. We demonstrate the robust nature of the method by measuring topological invariants for both non-interacting and interacting models, and map out interacting quantum phase diagrams on quantum simulators and IBM quantum hardware.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Scattering wave packets of hadrons in gauge theories: Preparation on a quantum computer

Quantum simulation holds promise of enabling a complete description of high-energy scattering processes rooted in gauge theories of the Standard Model. A first step in such simulations is preparation of interacting hadronic wave packets. To create the wave packets, one typically resorts to adiabatic evolution to bridge between wave packets in the free theory and those in the interacting theory, rendering the simulation resource intensive. In this work, we construct a wave-packet creation operator directly in the interacting theory to circumvent adiabatic evolution, taking advantage of resource-efficient schemes for ground-state preparation, such as variational quantum eigensolvers. By means of an ansatz for bound mesonic excitations in confining gauge theories, which is subsequently optimized using classical or quantum methods, we show that interacting mesonic wave packets can be created efficiently and accurately using digital quantum algorithms that we develop. Specifically, we obtain high-fidelity mesonic wave packets in the Z 2 and U(1) lattice gauge theories coupled to fermionic matter in 1+1 dimensions. Our method is applicable to both perturbative and non-perturbative regimes of couplings. The wave-packet creation circuit for the case of the Z 2 lattice gauge theory is built and implemented on the Quantinuum H1-1 trapped-ion quantum computer using 13 qubits and up to 308 entangling gates. The fidelities agree well with classical benchmark calculations after employing a simple symmetry-based noise-mitigation technique. This work serves as a step toward quantum computing scattering processes in quantum chromodynamics.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Light-Front Field Theory on Current Quantum Computers

We present a quantum algorithm for simulation of quantum field theory in the light-front formulation and demonstrate how existing quantum devices can be used to study the structure of bound states in relativistic nuclear physics. Specifically, we apply the Variational Quantum Eigensolver algorithm to find the ground state of the light-front Hamiltonian obtained within the Basis Light-Front Quantization (BLFQ) framework. The BLFQ formulation of quantum field theory allows one to readily import techniques developed for digital quantum simulation of quantum chemistry. This provides a method that can be scaled up to simulation of full, relativistic quantum field theories in the quantum advantage regime. As an illustration, we calculate the mass, mass radius, decay constant, electromagnetic form factor, and charge radius of the pion on the IBM Vigo chip. This is the first time that the light-front approach to quantum field theory has been used to enable simulation of a real physical system on a quantum computer.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Variational Quantum Chemistry Programs in JaqalPaq

We present example quantum chemistry programs written with JaqalPaq, a python meta-programming language used to code in Jaqal (Just Another Quantum Assembly Language). These JaqalPaq algorithms are intended to be run on the Quantum Scientific Computing Open User Testbed (QSCOUT) platform at Sandia National Laboratories. Our exemplars use the variational quantum eigensolver (VQE) quantum algorithm to compute the ground state energies of the H2, HeH+, and LiH molecules. Since the exemplars focus on how to program in JaqalPaq, the calculations of the second-quantized Hamiltonians are performed with the PySCF python package, and the mappings of the fermions to qubits are obtained from the OpenFermion python package. Using the emulator functionality of JaqalPaq, we emulate how these exemplars would be executed on an error-free QSCOUT platform and compare the emulated computation of the bond-dissociation curves for these molecules with their exact forms within the relevant basis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Simulating Quantum Systems with NWQ-Sim on HPC

NWQ-Sim is a cutting-edge quantum system simulation environment designed to run on classical multi-node, multi-CPU/GPU heterogeneous HPC systems. In this work, we provide a brief overview of NWQ-Sim and its implementation in simulating quantum circuit applications, such as the transverse field Ising model. We also demonstrate how NWQ-Sim can be used to examine the effects of errors that occur on real quantum devices, using a combined device noise model. Moreover, NWQ-Sim is particularly well-suited for implementing variational quantum algorithms where circuits are dynamically generated. Therefore, we also illustrate this with the variational quantum eigensolver (VQE) for the Ising model. In both cases, NWQ-Sim's performance is comparable to or better than alternative simulators. We conclude that NWQ-Sim is a useful and flexible tool for simulating quantum circuits and algorithms, with performance advantages and noise-aware simulation capabilities.

Suh, In-Saeng↗

DOE OSTI2024

Noise-induced transition in optimal solutions of variational quantum algorithms

Variational quantum algorithms are promising candidates for delivering practical quantum advantage on noisy intermediate-scale quantum (NISQ) hardware. However, optimizing the noisy cost functions associated with these algorithms is challenging for system sizes relevant to quantum advantage. In this work, we investigate the effect of noise on optimization by studying a variational quantum eigensolver (VQE) algorithm calculating the ground state of a spin chain model, and we observe an abrupt transition induced by noise to the optimal solutions. We will present numerical simulations, a demonstration using an IBM quantum processor unit (QPU), and a theoretical analysis indicating the origin of this transition. Our findings suggest that careful analysis is crucial to avoid misinterpreting the noise-induced features as genuine algorithm results.

Li, Andy C.Y.↗

DOE OSTI2021

Quantum Alternating Operator Ansatz (QAOA) Phase Diagrams and Applications for Quantum Chemistry

Determining Hamiltonian ground states and energies is a challenging task with many possible approaches on quantum computers. While variational quantum eigensolvers are popular approaches for near term hardware, adiabatic state preparation is an alternative that does not require noisy optimization of parameters. Beyond adiabatic schedules, QAOA is an important method for optimization problems. In this work we modify QAOA to apply to finding ground states of molecules and empirically evaluate the modified algorithm on several molecules. This modification applies physical insights used in classical approximations to construct suitable QAOA operators and initial state. We find robust qualitative behavior for QAOA as a function of the number of steps and size of the parameters, and demonstrate this behavior also occurs in standard QAOA applied to combinatorial search. To this end we introduce QAOA phase diagrams that capture its performance and properties in various limits. In particular we show a region in which non-adiabatic schedules perform better than the adiabatic limit while employing lower quantum circuit depth. We further provide evidence our results and insights also apply to QAOA applications beyond chemistry.

Kremenetski, Vladimir↗

DOE OSTI2021

Hybrid Quantum-Classical Eigensolver without Variation or Parametric Gates

The use of near-term quantum devices that lack quantum error correction, for addressing quantum chemistry and physics problems, requires hybrid quantum-classical algorithms and techniques. Here, we present a process for obtaining the eigenenergy spectrum of electronic quantum systems. This is achieved by projecting the Hamiltonian of a quantum system onto a limited effective Hilbert space specified by a set of computational bases. From this projection, an effective Hamiltonian is obtained. Furthermore, a process for preparing short depth quantum circuits to measure the corresponding diagonal and off-diagonal terms of the effective Hamiltonian is given, whereby quantum entanglement and ancilla qubits are used. The effective Hamiltonian is then diagonalized on a classical computer using numerical algorithms to obtain the eigenvalues. The use case of this approach is demonstrated for ground state and excited states of BeH2 and LiH molecules, and the density of states, which agrees well with exact solutions. Additionally, hardware demonstration is presented using IBM quantum devices for H2 molecule.

Jouzdani, Pejman (ORCID:0000000256470381)↗

DOE OSTI2022

AGP-based unitary coupled cluster theory for quantum computers

Electronic structure methods typically benefit from symmetry breaking and restoration, specially in the strong correlation regime. Here, the same goes for ansätze on a quantum computer. We develop a unitary coupled cluster method based on the antisymmetrized geminal power (AGP)—a state formally equivalent to the number-projected Bardeen–Cooper–Schrieffer wavefunction. We demonstrate our method for the single-band Fermi–Hubbard Hamiltonian in one and two dimensions. We also explore post-selection as a state preparation step to obtain correlated AGP and prove that it scales no worse than O(√M) in the number of measurements, thereby making it a less expensive alternative to gauge integration to restore particle number symmetry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Hidden Rotation Symmetry of the Jordan–Wigner Transformation and Its Application to Measurement in Quantum Computation

Using a global rotation by 𝜃 about the z-axis in the spin sector of the Jordan–Wigner transformation rotates Pauli matrices 𝑋̂ and 𝑌̂ in the 𝑥−𝑦 -plane, while it adds a global complex phase to fermionic quantum states that have a fixed number of particles. With the right choice of angles, this relates expectation values of Pauli strings containing products of 𝑋̂ and 𝑌̂ to different products, which can be employed to reduce the number of measurements needed when simulating fermionic systems on a quantum computer. Here, we derive this symmetry and show how it can be applied to systems in Physics and Chemistry that involve Hamiltonians with only single-particle (hopping) and two-particle (interaction) terms. We also discuss the consequences of this for finding efficient measurement circuits in variational ground state preparation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

QForte: An Efficient State-Vector Emulator and Quantum Algorithms Library for Molecular Electronic Structure

Here, we introduce a novel open-source software package QForte, a comprehensive development tool for new quantum simulation algorithms. QForte incorporates functionality for handling molecular Hamiltonians, fermionic encoding, ansatz construction, time evolution, and state-vector emulation, requiring only a classical electronic structure package as a dependency. QForte also contains black-box implementations of a wide variety of quantum algorithms, including variational and projective quantum eigensolvers, adaptive eigensolvers, quantum imaginary time evolution, and quantum Krylov methods. We highlight two features of QForte: (i) how the Python class structure of QForte enables the facile implementation of new algorithms, and (ii) how existing algorithms can be executed in just a few lines of code.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Benchmarking Quantum Chemistry Computations with Variational, Imaginary Time Evolution, and Krylov Space Solver Algorithms

Quantum chemistry is a key application area for noisy-intermediate scale quantum (NISQ) devices, and therefore serves as an important benchmark for current and future quantum computer performance. Previous benchmarks in this field have focused on variational methods for computing ground and excited states of various molecules, including a benchmarking suite focused on the performance of computing ground states for alkali-hydrides under an array of error mitigation methods. State-of-the-art methods to reach chemical accuracy in hybrid quantum-classical electronic structure calculations of alkali hydride molecules on NISQ devices from IBM are outlined here. Here it is demonstrated how to extend the reach of variational eigensolvers with symmetry preserving Ansätze. Next, it is outlined how to use quantum imaginary time evolution and Lanczos as a complementary method to variational techniques, highlighting the advantages of each approach. Finally, a new error mitigation method is demonstrated which uses systematic error cancellation via hidden inverse gate constructions, improving the performance of typical variational algorithms. These results show that electronic structure calculations have advanced rapidly, to routine chemical accuracy for simple molecules, from their inception on quantum computers a few short years ago, and they point to further rapid progress to larger molecules as the power of NISQ devices grows.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗