Quantum advantage from measurement-induced entanglement in random shallow circuits

TL;DR

This paper demonstrates that measurement-induced entanglement in random shallow quantum circuits can lead to a quantum advantage in sampling tasks, with evidence of a phase transition in computational complexity.

Contribution

It provides the first evidence of a quantum advantage phase transition in random Clifford circuits and introduces a new shallow circuit architecture exhibiting this advantage.

Findings

Long-range measurement-induced entanglement (MIE) enables quantum advantage.

Unconditional quantum advantage shown in certain shallow Clifford circuits.

A new depth-2, log(n)-qubit architecture exhibits long-range MIE and quantum advantage.

Abstract

We study random constant-depth quantum circuits in a two-dimensional architecture. While these circuits only produce entanglement between nearby qubits on the lattice, long-range entanglement can be generated by measuring a subset of the qubits of the output state. It is conjectured that this long-range measurement-induced entanglement (MIE) proliferates when the circuit depth is at least a constant critical value. For circuits composed of Haar-random two-qubit gates, it is also believed that this coincides with a quantum advantage phase transition in the classical hardness of sampling from the output distribution. Here we provide evidence for a quantum advantage phase transition in the setting of random Clifford circuits. Our work extends the scope of recent separations between the computational power of constant-depth quantum and classical circuits, demonstrating that this kind of advantage is present in canonical random circuit sampling tasks. In particular, we show that in any architecture of random shallow Clifford circuits, the presence of long-range MIE gives rise to an unconditional quantum advantage. In contrast, any depth-d 2D quantum circuit that satisfies a short-range MIE property can be classically simulated efficiently and with depth O(d). Finally, we introduce a two-dimensional, depth-2, "coarse-grained" circuit architecture, composed of random Clifford gates acting on O(log n) qubits, for which we prove the existence of long-range MIE and establish an unconditional quantum advantage.