Resource-Efficient Quantum Algorithms for Selected Hamiltonian Subspace Diagonalization

Area of Science:

• Quantum computing
• Computational chemistry
• Quantum algorithms

Background:

• Variational algorithms are common in the NISQ era for quantum chemistry.
• Existing quantum selected configuration interaction (QSCI) and sample-based quantum diagonalization (SQD) algorithms use inefficient second quantization in Fock space.
• This leads to high qubit resource requirements.

Purpose of the Study:

• Introduce the first QSCI algorithm in the CI-Matrix (CIM) framework for optimal qubit scaling.
• Develop a novel single-bit flip error mitigation technique.
• Enhance QSCI to achieve performance comparable to classical methods.

Main Methods:

• Developed QSCI in the CI-Matrix (CIM) framework with optimal qubit scaling.
• Implemented a novel single-bit flip error mitigation using one additional qubit.
• Combined QSCI with stochastic approximate Trotterization (qDRIFT).
• Introduced Quantum Selected Heat-Bath CI (QSHCI) using quantum sampling.

Main Results:

• Simulations of N2 and naphthalene molecules showed similar accuracy to SQD but with fewer quantum resources.
• The CIM-QSCI algorithm and SQD methods did not match classical heat-bath CI (HCI) performance.
• QSHCI achieved performance comparable to classical HCI.

Conclusions:

• The CIM-QSCI algorithm offers improved qubit efficiency for quantum chemistry.
• QSHCI provides a quantum alternative to classical heat-bath methods.
• Preprocessing cost for CIM construction and Pauli decomposition is a current drawback.