A circuit-generated quantum subspace algorithm for the variational quantum eigensolver

Area of Science:

• Quantum Computing
• Computational Chemistry
• Quantum Algorithms

Background:

• Wavefunction evolution in real and imaginary time generates quantum subspaces for accurate ground state energy determination.
• The variational quantum eigensolver (VQE) is a prominent algorithm for finding ground state energies on quantum computers.
• Conventional VQE can struggle with convergence and local minima, limiting accuracy.

Purpose of the Study:

• To propose a novel algorithm, the circuit subspace variational quantum eigensolver (CSVQE), by integrating quantum subspace techniques with VQE.
• To enhance the accuracy and convergence rates of ground state energy calculations in quantum chemistry.
• To develop a method capable of mitigating issues associated with local minima in VQE optimization landscapes.

Main Methods:

• Dividing a parameterized quantum circuit into smaller, sequential subcircuits.
• Generating a quantum subspace through the sequential application of these subcircuits to an initial state.
• Utilizing the generated quantum subspace within the VQE framework to compute ground state energies.

Main Results:

• CSVQE achieves significant error reduction compared to conventional VQE, especially for poorly optimized circuits.
• The algorithm demonstrates greatly improved convergence rates across various quantum chemistry problems.
• CSVQE successfully identifies energies close to the global minimum when applied to circuits trapped in local minima.

Conclusions:

• The circuit subspace variational quantum eigensolver (CSVQE) algorithm offers a powerful enhancement to VQE for accurate ground state energy calculations.
• CSVQE shows particular promise in improving convergence and overcoming local minima challenges in quantum computational chemistry.
• This technique presents a valuable tool for diagnosing and potentially escaping local minima in quantum optimization problems.