Disentangling magic states with classically simulable quantum circuits

TL;DR

This paper demonstrates that certain complex quantum states generated by shallow non-Clifford circuits can be efficiently disentangled and simulated classically, revealing new insights into their structure and potential for circuit compression.

Contribution

It introduces a method to completely disentangle states from deep random Clifford circuits with limited non-Clifford gates, enabling efficient classical simulation and new circuit representations.

Findings

States from shallow non-Clifford circuits are classically simulable.

Disentangling enables efficient simulation of complex quantum states.

New circuit compression scheme for Clifford circuits with non-Clifford gates.

Abstract

We show that states obtained from deep random Clifford circuits doped with non-Clifford phase gates (including T-gates and $\sqrt{\mathrm{T}}$-gates) can be disentangled completely, provided the number of non-Clifford gates is smaller or approximately equal to the number of qubits. This implies that Pauli expectation values of such states can be efficiently simulated classically, despite them exhibiting both extensive entanglement and extensive nonstabilizerness. We prove this result analytically using a quantum error correction formulation, demonstrate its applicability numerically, and discuss consequences for the disentanglability of states generated through Hamiltonian dynamics. We show that this result implies a novel representation of approximate state designs that can also facilitate their efficient generation, and we propose a novel quantum circuit compression scheme for Clifford circuits doped with non-Clifford phase gates.