Fast pseudothermalization

TL;DR

This paper introduces significantly improved quantum circuit implementations for generating pseudo-ensembles, reducing circuit depth and enabling near-term quantum devices to simulate complex quantum resources efficiently.

Contribution

It presents the fastest known quantum circuit constructions for pseudo-ensembles, nearly matching the theoretical lower bounds and facilitating practical near-term quantum experiments.

Findings

Achieved circuit depth of  ext{log} n imes O(t[ ext{log} t]^2)

Almost saturates the theoretical lower bound on circuit depth

Enables pseudo-ensemble generation with fewer entangling gates

Abstract

Quantum resources like entanglement and magic are essential for characterizing the complexity of quantum states. However, when the number of copies of quantum states and the computational time are limited by numbers polynomial in the system size $n$, accurate estimation of the amount of these resources becomes difficult. This makes it impossible to distinguish between ensembles of states with relatively small resources and one that has nearly maximal resources. Such ensembles with small resources are referred to as "pseudo-quantum" ensembles. Recent studies have introduced an ensemble known as the random subset phase state ensemble, which is pseudo-entangled, pseudo-magical, and pseudorandom. While the current state-of-the-art implementation of this ensemble is conjectured to be realized by a circuit with $O(nt)$ depth, it is still too deep for near-term quantum devices to execute for small $t$. In addition, the strict linear dependence on $t$ has only been established as a lower bound on the circuit depth. In this work, we present significantly improved implementations that only require $\omega(\log n)\cdot O(t[\log t]^2)$ depth circuits, which almost saturates the theoretical lower bound. This is also the fastest known for generating pseudorandom states to the best of our knowledge. We believe that our findings will facilitate the implementation of pseudo-ensembles on near-term devices, allowing executions of tasks that would otherwise require ensembles with maximal quantum resources, by generating pseudo-ensembles at a super-polynomially fewer number of entangling and non-Clifford gates.