Unified multivariate trace estimation and quantum error mitigation
- URL: http://arxiv.org/abs/2301.12358v1
- Date: Sun, 29 Jan 2023 04:42:12 GMT
- Title: Unified multivariate trace estimation and quantum error mitigation
- Authors: Jin-Min Liang, Qiao-Qiao Lv, Zhi-Xi Wang, Shao-Ming Fei
- Abstract summary: Calculating the trace of the product of $m$ $n$-qubit density matrices is a crucial subroutine in quantum error mitigation and information measures estimation.
We propose an unified multivariate trace estimation (UMT) which conceptually unifies the previous qubit-optimal and depth-optimal approaches.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Calculating the trace of the product of $m$ $n$-qubit density matrices
(multivariate trace) is a crucial subroutine in quantum error mitigation and
information measures estimation. We propose an unified multivariate trace
estimation (UMT) which conceptually unifies the previous qubit-optimal and
depth-optimal approaches with tunable quantum circuit depth and the number of
qubits. The constructed circuits have $\lceil(m-1)/s\rceil$ or
$n\lceil(m-1)/s\rceil$ depth corresponding to $(s+m)n$ or $s+mn$ qubits for
$s\in\{1,\cdots,\lfloor m/2\rfloor\}$, respectively. Such flexible circuit
structures enable people to choose suitable circuits according different
hardware devices. We apply UMT to virtual distillation for achieving
exponential error suppression and design a family of concrete circuits to
calculate the trace of the product of $8$ and $9$ $n$-qubit density matrices.
Numerical example shows that the additional circuits still mitigate the noise
expectation value under the global depolarizing channel.
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