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IEEE International Conference on Computer Design: VLSI in Computers and Processors (ICCD)

MOSQ: Accelerating Classical Simulation of UCCSD Ansatz Circuits using Merged Operation

Seungwoo Choi, Enhyeok Jang, Youngmin Kim, Won Woo Ro

Published Nov 18, 2024• 0 citations
Publisher

Abstract

The Variational Quantum Eigensolver (VQE) is considered one of the most effective algorithms for near-term quantum processors due to its potential to produce meaningful results and its relatively small number of required qubits. However, the Unitary Coupled Cluster Singles and Doubles (UCCSD) circuit, used as the ansatz circuit for VQE, requires an excessive number of gate operations. This consequently causes long simulation delay when we simulate any VQE algorithm on classical computers. In order to enhance this long simulation delay of VQE, we develop and demonstrate that each Pauli string composing the UCCSD circuit can be merged into a single operation and executed efficiently in a classical simulator. We propose MOSQ, Merged Operation in Sub Quantum circuits for Pauli strings, which operates in a coupled manner in the circuit compiler stage and the execution stage to utilize merged operations. MOSQ passes the Pauli string information from the compiler stage to the execution stage, where each Pauli string is computed in the execution stage as a merged operation that functions similarly to a l-qubit gate operation except for the memory access pattern. MOSQ shows$12.2\times$and$8.67\times$speedup in UCCSD simulation time and total VQE execution time, respectively, compared to the baseline qiskit-aer simulator. Additionally, it is$4.88\times$and$3.11\times$faster than qiskit-aer simulator with fusion optimization enabled.

DOI
10.1109/iccd63220.2024.00090

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The Variational Quantum Eigensolver (VQE) is considered one of the most effective algorithms for near-term quantum processors due to its potential to produce meaningful results and its relatively small number of required qubits. However, the Unitary Coupled Cluster Singles and Doubles (UCCSD) circuit, used as the ansatz circuit for VQE, requires an excessive number of gate operations. This consequently causes long simulation delay when we simulate any VQE algorithm on classical computers. In order to enhance this long simulation delay of VQE, we develop and demonstrate that each Pauli string composing the UCCSD circuit can be merged into a single operation and executed efficiently in a classical simulator. We propose MOSQ, Merged Operation in Sub Quantum circuits for Pauli strings, which operates in a coupled manner in the circuit compiler stage and the execution stage to utilize merged operations. MOSQ passes the Pauli string information from the compiler stage to the execution stage, where each Pauli string is computed in the execution stage as a merged operation that functions similarly to a l-qubit gate operation except for the memory access pattern. MOSQ shows12.2×12.2\times12.2×and8.67×8.67\times8.67×speedup in UCCSD simulation time and total VQE execution time, respectively, compared to the baseline qiskit-aer simulator. Additionally, it is4.88×4.88\times4.88×and3.11×3.11\times3.11×faster than qiskit-aer simulator with fusion optimization enabled.
The Unitary Coupled Cluster with Singles and Doubles (UCCSD) ansatz is a widely used kernel in quantum chemistry and variational quantum eigensolver (VQE) algorithms, but its execution on near-term superconducting quantum processors is hindered by high gate costs and limited qubit connectivity. Existing compilation approaches either adopt simultaneous synthesis, which efficiently diagonalizes excitations but ignores connectivity, or individual synthesis, which enforces connectivity-awareness but sacrifices optimization opportunities. In this work, we propose a connectivity-aware compiler framework for UCCSD kernels that combines the efficiency of simultaneous synthesis with the practicality of connectivity constraints. First, we introduce blockwise qubit mapping, which groups program qubits into excitation-specific blocks and maps them to internally connected regions of the hardware graph. Second, we design connectivity-aware synthesis rules that diagonalize excitations directly on the mapped hardware graph, reducing the number of SWAP gates. We implement our framework and evaluate it on molecular and random UCCSD kernels using Google Sycamore’s and IBMQ Manhattan’s connectivity. Compared with state-of-the-art compilers, our approach reduces CNOT count by up to 34% and circuit depth by 49%, while improving VQE accuracy under noise.
In recent years, the Variational Quantum Eigensolver (VQE) has emerged as one of the most popular algorithms for solving the electronic structure problem on near-term quantum computers. The utility of VQE is often hindered by the limitations of current quantum hardware, including, but not limited to, short qubit coherence times and low gate fidelities. These limitations become particularly pronounced when VQE is used along with deep quantum circuits, such as those required by the ”Unitary Coupled Cluster Singles and Doubles” (UCCSD) ansatz, often resulting in significant errors. To address these issues, we propose a low-depth ansatz based on parallelized Givens rotations, which can recover substantial correlation energy while drastically reducing circuit depth and two-qubit gate counts for an arbitrary active space (AS). Also, considering the current hardware architectures with low qubit counts, we introduce a systematic way to select molecular orbitals to define active spaces (ASs) that retain significant electron correlation. We validate our approach by computing bond dissociation profiles of water and strongly correlated systems, such as molecular nitrogen and oxygen, across various ASs. Noiseless simulations using the new ansatz yield ground-state energies comparable to those from the UCCSD ansatz while reducing circuit depth by 50–70%. Moreover, in noisy simulations, our approach achieves energy error rates an order of magnitude lower than that of UCCSD. Considering the efficiency and practical usage of our ansatz, we hope that it becomes a potential choice for performing quantum chemistry calculations on near-term quantum devices.
High Resolution Image Download MS PowerPoint Slide Quantum computers have the potential to efficiently solve the electronic structure problem but are currently limited by noise and shallow circuits. We present an enhanced Variational Quantum Eigensolver (VQE) ansatz based on the Qubit Coupled Cluster (QCC) approach that requires optimization of only n parameters, where n is the number of Pauli string generators, rather than the typical n + 2 m parameters, where m is the number of qubits. We evaluate the ground state energies and molecular dissociation curves of strongly correlated molecules, namely O 3 and Li 4, using active spaces of varying sizes in conjunction with our enhanced QCC ansatz, Unitary Coupled Cluster Single–Double (UCCSD) ansatz, and the classical Coupled Cluster Singles and Doubles (CCSD) method. Compared to UCCSD, our approach significantly reduces the number of parameters while maintaining high accuracy. Numerical simulations demonstrate the effectiveness of our approach, and experiments on superconducting and trapped-ion quantum computers showcase its practicality on real hardware. By eliminating the need for symmetry-restoring gates and reducing the number of parameters, our enhanced QCC ansatz enables accurate quantum chemistry calculations on near-term quantum devices for strongly correlated systems.
Abstract Variational quantum eigensolver (VQE) for electronic structure calculations is believed to be one major potential application of near term quantum computing. Among all proposed VQE algorithms, the unitary coupled cluster singles and doubles excitations (UCCSD) VQE ansatz has achieved high accuracy and received a lot of research interest. However, the UCCSD VQE based on fermionic excitations needs extra terms for the parity when using Jordan–Wigner transformation. Here we introduce a new VQE ansatz based on the particle preserving exchange gate to achieve qubit excitations. The proposed VQE ansatz has gate complexity up-bounded to O ( n 4 ) for all-to-all connectivity where n is the number of qubits of the Hamiltonian. Numerical results of simple molecular systems such as BeH 2 , H 2 O, N 2 , H 4 and H 6 using the proposed VQE ansatz gives very accurate results within errors about 10 −3 Hartree.
Abstract Variational quantum eigensolvers (VQE) are among the most promising approaches for solving electronic structure problems on near-term quantum computers. A critical challenge for VQE in practice is that one needs to strike a balance between the expressivity of the VQE ansatz versus the number of quantum gates required to implement the ansatz, given the reality of noisy quantum operations on near-term quantum computers. In this work, we consider an orbital-optimized pair-correlated approximation to the unitary coupled cluster with singles and doubles (uCCSD) ansatz and report a highly efficient quantum circuit implementation for trapped-ion architectures. We show that orbital optimization can recover significant additional electron correlation energy without sacrificing efficiency through measurements of low-order reduced density matrices (RDMs). In the dissociation of small molecules, the method gives qualitatively accurate predictions in the strongly-correlated regime when running on noise-free quantum simulators. On IonQ’s Harmony and Aria trapped-ion quantum computers, we run end-to-end VQE algorithms with up to 12 qubits and 72 variational parameters—the largest full VQE simulation with a correlated wave function on quantum hardware. We find that even without error mitigation techniques, the predicted relative energies across different molecular geometries are in excellent agreement with noise-free simulators.
Abstract Variational quantum eigensolver (VQE) with a unitary coupled cluster (UCC) ansatz has been suggested as a promising method for electronic structure calculations on future quantum computers. However, the complexity of the excitation terms for UCC with the single and double excitations (UCCSD) ansatz is up‐bounded to , where N is the number of electrons and M is the number of spin orbitals. The gate complexity of quantum circuit for the UCCSD ansatz is up‐bounded to using the Jordan–Wigner transformation. These complexities significantly limit the implementation of UCCSD on current Noisy Intermediate‐Scale Quantum (NISQ) devices. Herein, we developed a k‐QUpCCGSD ansatz which is based on the generalized paired double excitation operators and the particle preserving exchange gate. The former reduces the number of the excitation operators, the latter reduces the number of qubit gates for transforming excitation operators to quantum circuit. The gate complexity of the proposed k‐QUpCCGSD ansatz is up‐bounded to , which significantly reduce the complexity of the VQE algorithm on NISQ devices. The performance of the proposed ansatz on VQE is demonstrated by calculating ground‐state dissociation energy curves of the H6, LiH, H2O, and BeH2 molecules with the STO‐3G minimal basis set, and the accuracy is evaluated by comparing to the full configuration interaction (FCI) benchmarks. Moreover, we compare the number of quantum gates, especially the CNOT gates, and accuracies of various ansatzes. The assessments have shown that the accuracy of qubit unitary coupled cluster (QUCC) ansatzes is slightly worse than that of the UCC ones, but the circuit complexity of QUCC is much less than that of UCC. Among the tested QUCC ansatzes, k‐QUpCCGSD achieves higher accuracy with fewer quantum gates than QUCCSD, and k‐QUpCCGSD is a promising ansatz for VQE calculation on NISQ devices.