Postselection-free entanglement dynamics via spacetime duality

TL;DR

This paper introduces a spacetime duality-based method to study entanglement dynamics in non-unitary quantum circuits without requiring postselection, enabling practical experimental and simulation approaches.

Contribution

It presents a novel approach using spacetime duality to analyze entanglement in hybrid circuits, avoiding exponential postselection overhead and facilitating experimental implementation.

Findings

The method maps mixed state purification to correlation functions in unitary circuits.

Numerical simulations demonstrate the effectiveness of the approach.

The protocol enables measurement of subsystem purity and insights into quantum error correction.

Abstract

The dynamics of entanglement in `hybrid' non-unitary circuits (for example, involving both unitary gates and quantum measurements) has recently become an object of intense study. A major hurdle toward experimentally realizing this physics is the need to apply \emph{postselection} on random measurement outcomes in order to repeatedly prepare a given output state, resulting in an exponential overhead. We propose a method to sidestep this issue in a wide class of non-unitary circuits by taking advantage of \emph{spacetime duality}. This method maps the purification dynamics of a mixed state under non-unitary evolution onto a particular correlation function in an associated unitary circuit. This translates to an operational protocol which could be straightforwardly implemented on a digital quantum simulator. We discuss the signatures of different entanglement phases, and demonstrate examples via numerical simulations. With minor modifications, the proposed protocol allows measurement of the purity of arbitrary subsystems, which could shed light on the properties of the quantum error correcting code formed by the mixed phase in this class of hybrid dynamics.