## Abstracts

### 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.

(Session 5 : Sunday from 5:00pm - 7:00pm)

SQuInT Chief Organizer
Akimasa Miyake, Associate Professor
amiyake@unm.edu

SQuInT Local Organizers
Rafael Alexander, Postdoctoral Fellow
Chris Jackson, Postdoctoral Fellow