Toward Chemical Accuracy with Shallow Quantum Circuits: A Clifford-Based Hamiltonian Engineering Approach

Abstract

Achieving chemical accuracy with shallow quantum circuits is a significant challenge in quantum computational chemistry, particularly for near-term quantum devices. In this work, we present a Clifford-based Hamiltonian engineering algorithm, namely CHEM, that addresses the trade-off between circuit depth and accuracy. Based on a variational quantum eigensolver and hardware-efficient ansatz, our method designs the Clifford-based Hamiltonian transformation that (1) ensures a set of initial circuit parameters corresponding to the Hartree−Fock energy can be generated, (2) effectively maximizes the initial energy gradient with respect to circuit parameters, (3) imposes negligible overhead for classical processing and does not require additional quantum resources, and ( 4) is compatible with any circuit topology. We demonstrate the efficacy of our approach using a quantum hardware emulator, achieving chemical accuracy for systems as large as 12 qubits with fewer than 30 two-qubit gates. Our Clifford-based Hamiltonian engineering approach offers a promising avenue for practical quantum computational chemistry on near-term quantum devices.

Efficient and Robust Parameter Optimization of the Unitary Coupled-Cluster Ansatz

“…Next, we show that SOAP is a general method that is not limited to the UCCSD ansatz. We employ HEA with Clifford-based Hamiltonian Engineering for Molecules (CHEM) that ensures the initial state is the HF state and the initial gradients are maximized . The CHEM algorithm finds a Clifford transformation U CHEM that transforms the Hamiltonian based on the HEA circuit topology.…”

“…However, its scalability is hindered by optimization challenges, which need to be addressed for broader practical application . Furthermore, there is a growing interest in integrating the hardware-efficient ansatz with chemical and physical insights. , …”