Better Optimization of Variational Quantum Eigensolvers by combining the Unitary Block Optimization Scheme with Classical Post-Processing
arxiv(2024)
摘要
Variational Quantum Eigensolvers (VQE) are a promising approach for finding
the classically intractable ground state of a Hamiltonian. The Unitary Block
Optimization Scheme (UBOS) is a state-of-the-art VQE method which works by
sweeping over gates and finding optimal parameters for each gate in the
environment of other gates. UBOS improves the convergence time to the ground
state by an order of magnitude over Stochastic Gradient Descent (SGD). It
nonetheless suffers in both rate of convergence and final converged energies in
the face of highly noisy expectation values coming from shot noise. Here we
develop two classical post-processing techniques which improve UBOS especially
when measurements have large noise. Using Gaussian Process Regression (GPR) we
generate artificial augmented data using original data from the quantum
computer to reduce the overall error when solving for the improved parameters.
Using Double Robust Optimization plus Rejection (DROPR), we prevent outlying
data which are atypically noisy from resulting in a a particularly erroneous
single optimization step thereby increasing robustness against noisy
measurements. Combining these techniques further reduces the final relative
error that UBOS reaches by a factor of three without adding additional quantum
measurement or sampling overhead. This work further demonstrates that
developing techniques which use classical resources to post-process quantum
measurement results can significantly improve VQE algorithms.
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