skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


Title: Toward efficient quantum computation of molecular ground‐state energies
Abstract Variational quantum eigensolvers (VQEs) represent a promising approach to computing molecular ground states and energies on modern quantum computers. These approaches use a classical computer to optimize the parameters of a trial wave function, while the quantum computer simulates the energy by preparing and measuring a set of bitstring observations, referred to as shots, over which an expected value is computed. Although more shots improve the accuracy of the expected ground state, it also increases the simulation cost. Hence, we propose modifications to the standard Bayesian optimization algorithm to leverage few‐shot circuit observations to solve VQEs with fewer quantum resources. We demonstrate the effectiveness of our proposed approach, Bayesian optimization with priors on surface topology (BOPT), by comparing optimizers for molecular systems and demonstrate how current quantum hardware can aid in finding ground‐state energies.  more » « less
Award ID(s):
2237616
PAR ID:
10640343
Author(s) / Creator(s):
 ;  ;  ;  ;  ;  ;  ;  ;  
Publisher / Repository:
Wiley Blackwell (John Wiley & Sons)
Date Published:
Journal Name:
AIChE Journal
Volume:
71
Issue:
12
ISSN:
0001-1541
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Generative modeling is a flavor of machine learning with applications ranging from computer vision to chemical design. It is expected to be one of the techniques most suited to take advantage of the additional resources provided by near-term quantum computers. Here, we implement a data-driven quantum circuit training algorithm on the canonical Bars-and-Stripes dataset using a quantum-classical hybrid machine. The training proceeds by running parameterized circuits on a trapped ion quantum computer and feeding the results to a classical optimizer. We apply two separate strategies, Particle Swarm and Bayesian optimization to this task. We show that the convergence of the quantum circuit to the target distribution depends critically on both the quantum hardware and classical optimization strategy. Our study represents the first successful training of a high-dimensional universal quantum circuit and highlights the promise and challenges associated with hybrid learning schemes. 
    more » « less
  2. Experimental demonstrations of modified chemical structure and reactivity under strong light–matter coupling have spurred theoretical and computational efforts to uncover underlying mechanisms. Ab initio cavity quantum electrodynamics (QED) combines quantum chemistry with cavity QED to investigate these phenomena in detail. Unitary transformations of ab initio cavity QED Hamiltonians have been used to make them more computationally tractable. We analyze one such transformation, the coherent state transformation, using perturbation theory. Applying perturbation theory up to third order for ground state energies and potential energy surfaces of several molecular systems under electronic strong coupling, we show that the coherent state transformation yields better agreement with exact ground state energies. We examine one specific case using perturbation theory up to ninth order and find that coherent state transformation performs better up to fifth order but converges more slowly to the exact ground state energy at higher orders. In addition, we apply perturbation theory up to second order for cavity mode states under bilinear coupling, elucidating how the coherent state transformation accelerates the convergence of the photonic subspace toward the complete basis limit and renders molecular ion energies origin invariant. These findings contribute valuable insights into computational advantages of the coherent state transformation in the context of ab initio cavity quantum electrodynamics methods. 
    more » « less
  3. Classical computing plays a critical role in the advancement of quantum frontiers in the NISQ era. In this spirit, this work uses classical simulation to bootstrap Variational Quantum Algorithms (VQAs). VQAs rely upon the iterative optimization of a parameterized unitary circuit (ansatz) with respect to an objective function. Since quantum machines are noisy and expensive resources, it is imperative to classically choose the VQA ansatz initial parameters to be as close to optimal as possible to improve VQA accuracy and accelerate their convergence on today’s devices. This work tackles the problem of finding a good ansatz initialization, by proposing CAFQA, a Clifford Ansatz For Quantum Accuracy. The CAFQA ansatz is a hardware-efficient circuit built with only Clifford gates. In this ansatz, the parameters for the tunable gates are chosen by searching efficiently through the Clifford parameter space via classical simulation. The resulting initial states always equal or outperform traditional classical initialization (e.g., Hartree-Fock), and enable high-accuracy VQA estimations. CAFQA is well-suited to classical computation because: a) Clifford-only quantum circuits can be exactly simulated classically in polynomial time, and b) the discrete Clifford space is searched efficiently via Bayesian Optimization. For the Variational Quantum Eigensolver (VQE) task of molecular ground state energy estimation (up to 18 qubits), CAFQA’s Clifford Ansatz achieves a mean accuracy of nearly 99% and recovers as much as 99.99% of the molecular correlation energy that is lost in Hartree-Fock initialization. CAFQA achieves mean accuracy improvements of 6.4x and 56.8x, over the state-of-the-art, on different metrics. The scalability of the approach allows for preliminary ground state energy estimation of the challenging chromium dimer (Cr2) molecule. With CAFQA’s high-accuracy initialization, the convergence of VQAs is shown to accelerate by 2.5x, even for small molecules. Furthermore, preliminary exploration of allowing a limited number of non-Clifford (T) gates in the CAFQA framework, shows that as much as 99.9% of the correlation energy can be recovered at bond lengths for which Clifford-only CAFQA accuracy is relatively limited, while remaining classically simulable. 
    more » « less
  4. This paper introduces the Quadratic Quantum Variational Monte Carlo (Q2 VMC) algorithm, an innovative algorithm in quantum chemistry that significantly enhances the efficiency and accuracy of solving the Schrödinger equation. Inspired by the discretization of imaginary-time Schrödinger evolution, Q2 VMC employs a novel quadratic update mechanism that integrates seamlessly with neural network-based ansatzes. Our extensive experiments showcase Q2 VMC's superior performance, achieving faster convergence and lower ground state energies in wavefunction optimization across various molecular systems, without additional computational cost. This study not only advances the field of computational quantum chemistry but also highlights the important role of discretized evolution in variational quantum algorithms, offering a scalable and robust framework for future quantum research. 
    more » « less
  5. Abstract We introduce a family of variational quantum algorithms, which we coin as quantum iterative power algorithms (QIPAs), and demonstrate their capabilities as applied to global-optimization numerical experiments. Specifically, we demonstrate the QIPA based on a double exponential oracle as applied to ground state optimization of theH2molecule, search for the transmon qubit ground-state, and biprime factorization. Our results indicate that QIPA outperforms quantum imaginary time evolution (QITE) and requires a polynomial number of queries to reach convergence even with exponentially small overlap between an initial quantum state and the final desired quantum state, under some circumstances. We analytically show that there exists an exponential amplitude amplification at every step of the variational quantum algorithm, provided the initial wavefunction has non-vanishing probability with the desired state and that the unique maximum of the oracle is given by λ 1 > 0 , while all other values are given by the same value 0 < λ 2 < λ 1 (hereλcan be taken as eigenvalues of the problem Hamiltonian). The generality of the global-optimization method presented here invites further application to other problems that currently have not been explored with QITE-based near-term quantum computing algorithms. Such approaches could facilitate identification of reaction pathways and transition states in chemical physics, as well as optimization in a broad range of machine learning applications. The method also provides a general framework for adaptation of a class of classical optimization algorithms to quantum computers to further broaden the range of algorithms amenable to implementation on current noisy intermediate-scale quantum computers. 
    more » « less