Efficient quantum circuits are necessary for realizing quantum algorithms on noisy intermediate-scale quantum devices. Fermionic excitations entering unitary coupled-cluster (UCC) ansätze give rise to quantum circuits containing CNOT “staircases” whose number scales exponentially with the excitation rank. Recently, Yordanov et al. [ Phys. Rev. A 102, 062612 (2020); Commun. Phys. 4, 228 (2021)] constructed CNOT-efficient quantum circuits for both Fermionic- (FEB) and qubit-excitation-based (QEB) singles and doubles and illustrated their usefulness in adaptive derivative-assembled pseudo-Trotterized variational quantum eigensolver (ADAPT-VQE) simulations. In this work, we extend these CNOT-efficient quantum circuits to arbitrary excitation ranks. To illustrate the benefits of these compact FEB and QEB quantum circuits, we perform numerical simulations using the recently developed selected projective quantum eigensolver (SPQE) approach, which relies on an adaptive UCC ansatz built from arbitrary-order particle–hole excitation operators. We show that both FEB- and QEB-SPQE decrease the number of CNOT gates compared to traditional SPQE by factors as large as 15. At the same time, QEB-SPQE requires, in general, more ansatz parameters than FEB-SPQE, in particular those corresponding to higher-than-double excitations, resulting in quantum circuits with larger CNOT counts. Although ADAPT-VQE generates quantum circuits with fewer CNOTs than SPQE, SPQE requires orders of magnitude less residual element evaluations than gradient element evaluations in ADAPT-VQE.
Efficient quantum circuits are necessary for realizing quantum algorithms on noisy intermediate-scale quantum devices. Fermionic excitations entering unitary coupled-cluster (UCC) ansätze give rise to quantum circuits containing CNOT “staircases” whose number scales exponentially with the excitation rank. Recently, Yordanov et al. [ Phys. Rev. A 102, 062612 (2020); Commun. Phys. 4, 228 (2021)] constructed CNOT-efficient quantum circuits for both Fermionic- (FEB) and qubit-excitation-based (QEB) singles and doubles and illustrated their usefulness in adaptive derivative-assembled pseudo-Trotterized variational quantum eigensolver (ADAPT-VQE) simulations. In this work, we extend these CNOT-efficient quantum circuits to arbitrary excitation ranks. To illustrate the benefits of these compact FEB and QEB quantum circuits, we perform numerical simulations using the recently developed selected projective quantum eigensolver (SPQE) approach, which relies on an adaptive UCC ansatz built from arbitrary-order particle–hole excitation operators. We show that both FEB- and QEB-SPQE decrease the number of CNOT gates compared to traditional SPQE by factors as large as 15. At the same time, QEB-SPQE requires, in general, more ansatz parameters than FEB-SPQE, in particular those corresponding to higher-than-double excitations, resulting in quantum circuits with larger CNOT counts. Although ADAPT-VQE generates quantum circuits with fewer CNOTs than SPQE, SPQE requires orders of magnitude less residual element evaluations than gradient element evaluations in ADAPT-VQE.
The adaptive derivative-assembled pseudo-trotter (ADAPT) variational quantum eigensolver (VQE) is an appealing framework for iteratively constructing accurate representations of ground- and excited-state wave functions as products of exponentialized one- and two-body operators acting on a reference state. In this work, we propose a CNOT-efficient circuit for implementing exponentialized two-body qubit-excitation-based (QEB) operators, enabling the construction of the low-depth wave function Ansätze. Our proposed circuit architecture employs a 2-qubit-controlled rotation gate flanked by two layers of CNOT gates, requiring only 9 CNOT gates per two-body QEB operator while preserving essential symmetries, including particle number and the Z -component of spin. By integrating these optimized circuits into the ADAPT–VQE framework, we achieve a reduction in circuit depth of approximately 28% compared to the original QEB ADAPT–VQE method, without sacrificing accuracy in simulating ground- and excited-state properties of small molecules. Numerical simulations validate the improved performance of our approach, demonstrating its potential as an efficient tool for quantum simulations of electronic structures.
Molecular quantum simulations with the variational quantum eigensolver (VQE) rely on ansatz states that approximate the molecular ground states. These ansatz states are generally defined by parametrized fermionic excitation operators and an initial reference state. Efficient ways to perform fermionic excitations are vital for the realization of the VQE on noisy intermediate-scale quantum computers. Here, we address this issue by first demonstrating circuits that perform qubit excitations, excitations that do not account for fermionic anticommutation relations. We then extend the functionality of these circuits to perform fermionic excitations. Compared to circuits constructed with the standard use of ``CNOT staircases'', our circuits offer a linear reduction in the number of CNOT gates, by a factor of 2 (8) per single (double) qubit or fermionic excitation, respectively. Our results reduce the requirements for near-term realizations of quantum molecular simulations.
Abstract Due to their non-iterative nature, fixed unitary coupled cluster (UCC) ansätze are attractive for performing quantum chemistry variational quantum eigensolver (VQE) computations as they avoid pre-circuit measurements on a quantum computer. However, achieving chemical accuracy for strongly correlated systems with UCC requires further inclusion of higher-order fermionic excitations beyond triples increasing circuit depth. We introduce k -non-iterative disentangled unitary coupled cluster (NI-DUCC), a fixed and non-iterative disentangled UCC compact ansatz, based on specific ‘ k ’ sets of ‘qubit’ excitations, eliminating the needs for fermionic-type excitations. These elements scale linearly ( O ( n ) ) by leveraging Lie algebraic structures, with n being the number of qubits. The key excitations are screened through specific selection criteria, including the enforcement of all symmetries, to ensure the construction of a robust set of generators. NI-DUCC employs ‘ k ’ products of the exponential of O ( n ) - anti-Hermitian Pauli operators, where each single Pauli string has a length p . This results in a fewer two-qubit CNOT gates circuit scaling, O ( k n p ) , suitable for hardware implementations. Tested on LiH, H 6 and BeH 2 , NI-DUCC-VQE achieves both chemical accuracy and rapid convergence even for molecules deviating significantly from equilibrium. It is hardware-efficient, reaching the exact full configuration interaction energy solution at specific layers, while reducing significantly the VQE optimization steps. NI-DUCC-VQE effectively addresses the gradient measurement bottleneck of ADAPT-VQE-like iterative algorithms, yet the classical computational cost of constructing the O ( n ) set of excitations increases exponentially with the number of qubits. We provide a first implementation for constructing the generators’ set, able to handle up to 20 qubits and discuss the efficiency perspectives.
Abstract Molecular simulations with the variational quantum eigensolver (VQE) are a promising application for emerging noisy intermediate-scale quantum computers. Constructing accurate molecular ansatze that are easy to optimize and implemented by shallow quantum circuits is crucial for the successful implementation of such simulations. Ansatze are, generally, constructed as series of fermionic-excitation evolutions. Instead, we demonstrate the usefulness of constructing ansatze with ``qubit-excitation evolutions', which, contrary to fermionic excitation evolutions, obey ``qubit commutation relations'. We show that qubit excitation evolutions, despite the lack of some of the physical features of fermionic excitation evolutions, accurately construct ansatze, while requiring asymptotically fewer gates. Utilizing qubit excitation evolutions, we introduce the iterative qubit excitation based VQE (IQEB-VQE) algorithm. The IQEB-VQE performs molecular simulations using a problem-tailored ansatz, grown iteratively by appending evolutions of single and double qubit excitation operators. By performing numerical simulations for small molecules, we benchmark the IQEB-VQE, and compare it against other competitive VQE algorithms. In terms of circuit efficiency and time complexity, we find that the IQEB-VQE systematically outperforms the previously most circuit-efficient, practically scalable VQE algorithms.
In order to answer the problem of Quantum Phase Estimation Algorithm been not suitable for NISQ devices, and allows one to outperform classical computers, Variational Quantum Algorithms (VQAs) were designed. Our subject of interest is the so-called Variational Quantum Eigensolver (VQE) algorithm and was originally designed to simulate electronic structures and to compute the ground state of a given molecule. VQE is made of two main components : an ansatz and a classical optimizer. The ansatz runs on the quantum device and aims to simulate the wavefunction, the parameters of the ansatz will be optimized until the expectation value is minimum. The very first ansatz that has originally been used is called UCCSD and it is based on Coupled Cluster Theory. The main issue considering UCCSD is the large amount of parameters to optimize and this leads us to the introduction of Adaptive Derivative-Assembled Pseudo-Trotter ansatz VQE (ADAPT-VQE) which determines a quasi-optimal ansatz with a minimal number of parameters. The key point of ADAPT-VQE is to grow the ansatz at every step, by adding operators chosen from a pre-determined pool of operators one-at-a-time, assuring that the maximal amount of correlation energy is recovered at each step. There exists different kind of ADAPT-VQE depending on the starting pool of operators as the fermionic-ADAPT, the qubit-ADAPT or even the qubit excitation based (QEB). Our goal is to implement the different types of ADAPT-VQE mentioned before. After a quick review of the theoretical background under all of these concepts, we will implement each algorithm using quiskit. We will also compare all of these algorithms on different criterions such as the number of parameters, the accuracy or the number of CNOT gate used on H2 and LiH molecules. Then we will have a small discussion about the results we obtained.
High Resolution Image Download MS PowerPoint Slide We have recently constructed compact, CNOT-efficient, quantum circuits for Fermionic and qubit excitations of arbitrary many-body rank [Magoulas, I.; Evangelista, F. A. J. Chem. Theory Comput. 2023, 19, 822]. Here, we present approximations of these circuits that substantially reduce the CNOT counts even further. Our preliminary numerical data, using the selected projective quantum eigensolver approach, show up to a 4-fold reduction in CNOTs. At the same time, there is practically no loss of accuracy in the energies compared to the parent implementation, while the ensuing symmetry breaking is essentially negligible.