1 research outputs found
Realizing the Nishimori transition across the error threshold for constant-depth quantum circuits
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.Comment: 16 pages, 18 figure