Bravyi-Kitaev Superfast simulation of electronic structure on a quantum computer

Area of Science:

• Quantum Computing
• Computational Chemistry
• Quantum Simulation

Background:

• Quantum computers utilize distinguishable qubits.
• Simulating indistinguishable fermionic particles requires mapping fermionic states to qubit states.
• The Bravyi-Kitaev Superfast (BKSF) algorithm is a method for this mapping.

Purpose of the Study:

• To provide a detailed exposition of the BKSF algorithm for molecular simulation.
• To implement and test the BKSF fermion-to-qubits transform in OpenFermion.
• To compare the BKSF algorithm with Jordan-Wigner and Bravyi-Kitaev transforms.

Main Methods:

• Implementation of the BKSF fermion-to-qubits transform in OpenFermion.
• Comparison of BKSF, Jordan-Wigner, and Bravyi-Kitaev transforms for a hydrogen molecule simulation.
• Analysis of gate counts and Trotter errors under the Trotter approximation.

Main Results:

• The BKSF algorithm has a lower gate count than Jordan-Wigner but higher than Bravyi-Kitaev.
• The study found lower Trotter errors for BKSF compared to previously reported results for Jordan-Wigner and Bravyi-Kitaev.
• BKSF mapping shows connections to quantum error correction and topological quantum simulation.

Conclusions:

• The BKSF algorithm is a promising method for fermionic quantum simulation.
• Further research into the BKSF algorithm for quantum simulation is warranted.
• The BKSF algorithm offers new perspectives on fermionic simulation in a topological context.