Choosing a guiding state for the CVQE algorithm based on a probability distribution analysis
ORAL
Abstract
The cascaded variational quantum eigensolver (CVQE) saves iterative communication between the QPU and the CPU that occurs in the conventional VQE by utilizing one-time quantum measurement for classical optimization. While CVQE offers complete freedom to choose the guiding state as input, not all guiding states suffice for optimization efficiency. Therefore, our work aims to find a good guiding state that facilitates efficient energy convergence with minimal resource consumption.
In this work, we prepare the guiding state through discretized adiabatic evolution. By analyzing the state probabilities from different stages of CVQE, we intend to determine the limit and optimal setting of this state preparation approach. We use an example of the ion-neutral bi-hydrogen-molecular reaction: $H_2 + H_2^+ \rightarrow H_3^+ + H$ with the geometry at the minimum energy to demonstrate the analysis numerically. By tuning the adiabatic evolution step size $dt$ and number of steps $N_t$, we define three regimes: “Minimal Guiding State”, “Ideal Unitary Matrix Multiplied Guiding State”, and “Single-step Guiding State.” For this reaction, a “Single-step Guiding State” saves quantum resources while keeping the CVQE-optimized results as good as other types of guiding states. Most importantly, we show that a “Single-step Guiding State” can be applicable on noisy-intermediate-scale quantum (NISQ) computers when it is prepared with a large step $dt$ and proper pruning, along with post-processing the quantum sampling data. The protocol and demonstration from this system contribute to a better choice of the guiding state generically for large many-body systems simulated by the CVQE algorithm in the future.
In this work, we prepare the guiding state through discretized adiabatic evolution. By analyzing the state probabilities from different stages of CVQE, we intend to determine the limit and optimal setting of this state preparation approach. We use an example of the ion-neutral bi-hydrogen-molecular reaction: $H_2 + H_2^+ \rightarrow H_3^+ + H$ with the geometry at the minimum energy to demonstrate the analysis numerically. By tuning the adiabatic evolution step size $dt$ and number of steps $N_t$, we define three regimes: “Minimal Guiding State”, “Ideal Unitary Matrix Multiplied Guiding State”, and “Single-step Guiding State.” For this reaction, a “Single-step Guiding State” saves quantum resources while keeping the CVQE-optimized results as good as other types of guiding states. Most importantly, we show that a “Single-step Guiding State” can be applicable on noisy-intermediate-scale quantum (NISQ) computers when it is prepared with a large step $dt$ and proper pruning, along with post-processing the quantum sampling data. The protocol and demonstration from this system contribute to a better choice of the guiding state generically for large many-body systems simulated by the CVQE algorithm in the future.
*This work has been supported by the Office of Naval Research through the U.S. Naval Research Laboratory. We acknowledge QC resources from IBM through a collaboration with the Air Force Research Laboratory (AFRL). Yi-Hua Lai thanks the National Research Council Research Associateship Programs for support during her post-doctoral tenure at NRL.
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Presenters
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Yi-Hua Lai
- Naval Research Laboratory