Quantum phase estimation of multiple eigenvalues for small-scale (noisy) experiments
Quantum phase estimation is the workhorse behind any quantum algorithm and a promising method for determining ground state energies of strongly correlated quantum systems. Low-cost quantum phase estimation techniques make use of circuits which only use a single ancilla qubit, requiring classical pos...
Saved in:
Main Authors | , , |
---|---|
Format | Journal Article |
Language | English |
Published |
25.09.2018
|
Subjects | |
Online Access | Get full text |
Cover
Loading…
Summary: | Quantum phase estimation is the workhorse behind any quantum algorithm and a
promising method for determining ground state energies of strongly correlated
quantum systems. Low-cost quantum phase estimation techniques make use of
circuits which only use a single ancilla qubit, requiring classical
post-processing to extract eigenvalue details of the system. We investigate
choices for phase estimation for a unitary matrix with low-depth noise-free or
noisy circuits, varying both the phase estimation circuits themselves as well
as the classical post-processing to determine the eigenvalue phases. We work in
the scenario when the input state is not an eigenstate of the unitary matrix.
We develop a new post-processing technique to extract eigenvalues from phase
estimation data based on a classical time-series (or frequency) analysis and
contrast this to an analysis via Bayesian methods. We calculate the variance in
estimating single eigenvalues via the time-series analysis analytically,
finding that it scales to first order in the number of experiments performed,
and to first or second order (depending on the experiment design) in the
circuit depth. Numerical simulations confirm this scaling for both estimators.
We attempt to compensate for the noise with both classical post-processing
techniques, finding good results in the presence of depolarizing noise, but
smaller improvements in $9$-qubit circuit-level simulations of superconducting
qubits aimed at resolving the electronic ground-state of a $H_4$-molecule. |
---|---|
DOI: | 10.48550/arxiv.1809.09697 |