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

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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$12.2\times$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$8.67\times$</tex> speedup in UCCSD simulation time and total VQE execution time, respectively, compared to the baseline qiskit-aer simulator. Additionally, it is <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$4.88\times$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$3.11\times$</tex> faster than qiskit-aer simulator with fusion optimization enabled.