Quantum Advantage from Measurement-Induced Entanglement in Random Shallow Circuits

We study random constant-depth quantum circuits in a two-dimensional (2D) 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 l...

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Main Authors: Adam Bene Watts, David Gosset, Yinchen Liu, Mehdi Soleimanifar
Format: Article
Language:English
Published: American Physical Society 2025-03-01
Series:PRX Quantum
Online Access:http://doi.org/10.1103/PRXQuantum.6.010356
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author Adam Bene Watts
David Gosset
Yinchen Liu
Mehdi Soleimanifar
author_facet Adam Bene Watts
David Gosset
Yinchen Liu
Mehdi Soleimanifar
author_sort Adam Bene Watts
collection DOAJ
description We study random constant-depth quantum circuits in a two-dimensional (2D) 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 d^{∗}. 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 2D 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.
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spelling doaj-art-bb59a188bd1d4f7ab752b6c3eb8ffcd22025-08-20T02:51:00ZengAmerican Physical SocietyPRX Quantum2691-33992025-03-016101035610.1103/PRXQuantum.6.010356Quantum Advantage from Measurement-Induced Entanglement in Random Shallow CircuitsAdam Bene WattsDavid GossetYinchen LiuMehdi SoleimanifarWe study random constant-depth quantum circuits in a two-dimensional (2D) 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 d^{∗}. 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 2D 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.http://doi.org/10.1103/PRXQuantum.6.010356
spellingShingle Adam Bene Watts
David Gosset
Yinchen Liu
Mehdi Soleimanifar
Quantum Advantage from Measurement-Induced Entanglement in Random Shallow Circuits
PRX Quantum
title Quantum Advantage from Measurement-Induced Entanglement in Random Shallow Circuits
title_full Quantum Advantage from Measurement-Induced Entanglement in Random Shallow Circuits
title_fullStr Quantum Advantage from Measurement-Induced Entanglement in Random Shallow Circuits
title_full_unstemmed Quantum Advantage from Measurement-Induced Entanglement in Random Shallow Circuits
title_short Quantum Advantage from Measurement-Induced Entanglement in Random Shallow Circuits
title_sort quantum advantage from measurement induced entanglement in random shallow circuits
url http://doi.org/10.1103/PRXQuantum.6.010356
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