Entanglement spectroscopy with a depth-two quantum circuit

Presenting Author: Yigit Subasi, Los Alamos National Laboratory
Contributing Author(s): Lukasz Cincio Patrick Coles

Noisy intermediate-scale quantum (NISQ) computers have gate errors and decoherence, limiting the depth of circuits that can be implemented on them. A strategy for NISQ algorithms is to reduce the circuit depth at the expense of increasing the qubit count. In this work we describe how this trade-off can be exploited for an application called entanglement spectroscopy. Here the goal is to compute the entanglement of a pure state on systems \(A\) and \(B\) by evaluating the Rényi entropy of the reduced state on subsystem \(A\). This can be done by computing the trace of integer powers of the reduced density matrix of \(A\). Johri, Steiger, and Troyer [PRB 96, 195136 (2017)] introduced a quantum algorithm that requires \(n\) copies of the state and whose depth scales linearly in \(k\) times \(n\), where \(n\) is the integer power to which the density matrix is raised and \(k\) is the number of qubits in the subsystem \(A\). Here, we present a quantum algorithm requiring twice the qubit resources (2n copies) but with a depth that is independent of both \(k\) and \(n\). Surprisingly this depth is only two gates. Numerical simulations show that this short depth leads to an increased robustness to noise.

Read this article online: https://arxiv.org/abs/1806.08863

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