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Simple Diagonal Designs with Reconfigurable Real-Time Circuits

Yizhi Shen
(
- LBL, Berkeley
)
,
Katherine Klymko
(
- LBL, Berkeley
)
,
Eran Rabani
(
- LBNL, Berkeley and
- UC, Berkeley, Chem. Dept. and
- Tel Aviv U.
)
,
Norm M. Tubman
(
- NASA, Ames
)
,
Daan Camps
(
- LBL, Berkeley
)

Jan 8, 2024

e-Print:

2401.04176 [quant-ph]

Report number:

FERMILAB-PUB-24-0903-SQMS-V

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Abstract: (arXiv)

Unitary designs are widely used in quantum computation, but in many practical settings it suffices to construct a diagonal state design generated with unitary gates diagonal in the computational basis. In this work, we introduce a simple and efficient diagonal state design based on real-time evolutions. Our construction is inspired by the classical Girard-Hutchinson trace estimator in that it involves the stochastic preparation of random-phase states. Although the exact Girard-Hutchinson states are not tractably implementable on a quantum computer, we can construct states that match the statistical moments of the Girard-Hutchinson states with real-time evolution. Importantly, our random states are all generated using the same Hamiltonians for real-time evolution, with the randomness arising solely from stochastic variations in the durations of the evolutions. In this sense, the circuit is fully reconfigurable and thus suited for near-term realizations on both digital and analog platforms.

energy: ground state
Hamiltonian
estimator
quantum algorithm
free energy
many-body problem
stochastic

References(32)

Figures(3)

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