Realizing the Nishimori transition across the error threshold for constant-depth quantum circuits

TL;DR

This paper demonstrates a measurement-based protocol on a 127-qubit superconducting device to generate and analyze long-range order in quantum states, revealing a Nishimori transition influenced by measurement probabilities.

Contribution

It introduces an efficient, noise-resilient measurement-based protocol for preparing GHZ states on large quantum devices and uncovers a Nishimori transition driven by measurement-induced effects.

Findings

Higher fidelities for GHZ states compared to unitary protocols.

Stability of long-range order up to a critical error rate.

Observation of a Nishimori transition influenced by measurement probabilities.

Abstract

Preparing quantum states across many qubits is necessary to unlock the full potential of quantum computers. However, a key challenge is to realize efficient preparation protocols which are stable to noise and gate imperfections. Here, using a measurement-based protocol on a 127 superconducting qubit device, we study the generation of the simplest long-range order -- Ising order, familiar from Greenberger-Horne-Zeilinger (GHZ) states and the repetition code -- on 54 system qubits. Our efficient implementation of the constant-depth protocol and classical decoder shows higher fidelities for GHZ states compared to size-dependent, unitary protocols. By experimentally tuning coherent and incoherent error rates, we demonstrate stability of this decoded long-range order in two spatial dimensions, up to a critical point which corresponds to a transition belonging to the unusual Nishimori universality class. Although in classical systems Nishimori physics requires fine-tuning multiple parameters, here it arises as a direct result of the Born rule for measurement probabilities -- locking the effective temperature and disorder driving this transition. Our study exemplifies how measurement-based state preparation can be meaningfully explored on quantum processors beyond a hundred qubits.