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arXiv:2408.16523

Multi-Reference UCCSD Variational Quantum Algorithm for Molecular Ground State Energies

Di Wu, C. L. Bai, Hiroyuki Sagawa, H. Q. Zhang

Published Aug 29, 2024• 2 citations
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Abstract

We implement the Multi-Reference Unitary Coupled Cluster Singles and Doubles (MR-UCCSD) model with a quantum circuit that conserves the particle number to study the ground state energies of LiH, BeH$_2$, and H$_6$. This approach simplifies the MR-UCCSD computation by integrating quantum computing techniques, and reduces its complexity. As a profit of the better MR states, our MR-UCCSD approach satisfies systematically the predefined errors below 10$^{-5}$ Hartree,which is the highest precision of single reference UCCSD approach, along the whole bond length with only hundreds of CNOT gates, and meets satisfactory the requirements of both computational precision and quantum resource reduction.

DOI
10.48550/arxiv.2408.16523

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We implement the Multi-Reference Unitary Coupled Cluster Singles and Doubles (MR-UCCSD) model with a quantum circuit that conserves the particle number to study the ground state energies of LiH, BeH2_22​, and H6_66​. This approach simplifies the MR-UCCSD computation by integrating quantum computing techniques, and reduces its complexity. As a profit of the better MR states, our MR-UCCSD approach satisfies systematically the predefined errors below 10−5^{-5}−5 Hartree,which is the highest precision of single reference UCCSD approach, along the whole bond length with only hundreds of CNOT gates, and meets satisfactory the requirements of both computational precision and quantum resource reduction.
We present an efficient algorithm for the MultiReference Unitary Coupled-Cluster (MR-UCC) approach that integrates quantum computing techniques with particle number conserved (PNC) gates. This algorithm makes it possible to use sophisticated MR wave functions with minimal use of computer resources to calculate the ground-state energies of LiH, BeH2{\mathrm{BeH}}_{2}BeH2​, and H6{\mathrm{H}}_{6}H6​. The higher-order correlations in the subsequent UCC calculations can be included requiring only Single and Double excitations of the wave operator. This algorithm achieves a higher accuracy compared with other available sophisticated quantum computational models, using a single quantum circuit across the entire bond length including the dissociation length region.
Quantum chemistry calculations of large, strongly correlated systems are typically limited by the computation cost that scales exponentially with the size of the system. Quantum algorithms, designed specifically for quantum computers, can alleviate this, but the resources required are still too large for today's quantum devices. Here we present a quantum algorithm that combines a localization of multireference wave functions of chemical systems with quantum phase estimation (QPE) and variational unitary coupled cluster singles and doubles (UCCSD) to compute their ground state energy. Our algorithm, termed "local active space unitary coupled cluster" (LAS-UCC), scales linearly with system size for certain geometries, providing a polynomial reduction in the total number of gates compared with QPE, while providing accuracy above that of the variational quantum eigensolver using the UCCSD ansatz and also above that of the classical local active space self-consistent field. The accuracy of LAS-UCC is demonstrated by dissociating (H2_22​)2_22​ into two H2_22​ molecules and by breaking the two double bonds in trans-butadiene and resources estimates are provided for linear chains of up to 20 H2_22​ molecules.
Quantum chemistry calculations of large, strongly correlated systems are typically limited by the computation cost that scales exponentially with the size of the system. Quantum algorithms, designed specifically for quantum computers, can alleviate this, but the resources required are still too large for today's quantum devices. Here, we present a quantum algorithm that combines a localization of multireference wave functions of chemical systems with quantum phase estimation (QPE) and variational unitary coupled cluster singles and doubles (UCCSD) to compute their ground-state energy. Our algorithm, termed "local active space unitary coupled cluster" (LAS-UCC), scales linearly with the system size for certain geometries, providing a polynomial reduction in the total number of gates compared with QPE, while providing accuracy above that of the variational quantum eigensolver using the UCCSD ansatz and also above that of the classical local active space self-consistent field. The accuracy of LAS-UCC is demonstrated by dissociating (H2)2 into two H2 molecules and by breaking the two double bonds in trans-butadiene, and resource estimates are provided for linear chains of up to 20 H2 molecules.
Quantum chemistry calculations of large, strongly correlated systems are typically limited by the computation cost that scales exponentially with the size of the system. Quantum algorithms, designed specifically for quantum computers, can alleviate this, but the resources required are still too large for today’s quantum devices. Here we present a quantum algorithm that combines a localization of multireference wave functions of chemical systems with quantum phase estimation (QPE) and variational unitary coupled cluster singles and doubles (UCCSD) to compute their ground state energy. Our algorithm, termed “local active space unitary coupled cluster” (LAS-UCC), scales linearly with system size for certain geometries, providing a polynomial reduction in the total number of gates compared with QPE, while providing accuracy above that of the variational quantum eigensolver using the UCCSD ansatz and also above that of the classical local active space self-consistent field. The accuracy of LAS-UCC is demonstrated by dissociating (H2)2 into two H2 molecules and by breaking the two double bonds in trans-butadiene and resources estimates are provided for linear chains of up to 20 H2 molecules.
We present a large-scale experimental study of quantum-computing-based molecular simulation carried out on IQM's Sirius 24-qubit superconducting processor, utilizing up to 16 operational qubits. The work employs Sample-based Quantum Diagonalization (SQD) together with the Local Unitary Cluster Jastrow (LUCJ) ansatz to estimate ground-state energies for a set of benchmark molecules, including H2_22​, LiH, BeH2_22​, H2_22​O, and NH3_33​. In addition, we introduce a Linear-CNOT variant of the Unitary Coupled-Cluster Singles and Doubles (LCNot-UCCSD) ansatz within the SQD workflow, trading higher circuit depth for reduced classical preprocessing. A comparison between these ansätze is provided, clarifying their respective strengths, limitations, and suitability for near-term quantum hardware. We further explore potential energy landscapes through 1D scans for H2_22​ and HeH+^++ using both STO-3G and 6-31G basis sets, and for LiH and BeH2_22​ in STO-3G. Extending beyond this, we demonstrate the experimental construction of a full 2D potential energy surface for the water molecule on quantum hardware, mapped over a 32 ×\times× 32 grid in bond length and bond angle. To move beyond small benchmark systems, we combine SQD(LUCJ) with Density Matrix Embedding Theory (DMET) to compute active-space energies for a set of ligand-like molecules, as well as the pharmacologically relevant amantadine system. Across all studies, the majority of quantum-computed energies agree with reference FCI results, as well as with DMET-CASCI energies for embedded systems, to within chemical accuracy for the chosen basis sets. These results demonstrate the reliability of sample-based diagonalization approaches and underscore the potential of hybrid embedding strategies for extending quantum simulations to increasingly complex molecular systems, while also highlighting their practicality on current IQM quantum hardware.
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. 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.