Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0607155 · Physical Review Letters

Resilient Quantum Computation in Correlated Environments: A Quantum Phase Transition Perspective

E. Novais, Eduardo R. Mucciolo, Harold U. Baranger

Published Jan 23, 2007• 30 citations
arXivHTMLPDF

Abstract

We analyze the problem of a quantum computer in a correlated environment protected from decoherence by quantum error correction using a perturbative renormalization group approach. The scaling equation obtained reflects the competition between the dimension of the computer and the scaling dimension of the correlations. For an irrelevant flow, the error probability is reduced to a stochastic form for a long time and/or a large number of qubits; thus, the traditional derivation of the threshold theorem holds for these error models. In this way, the "threshold theorem" of quantum computing is rephrased as a dimensional criterion.

DOI
10.1103/physrevlett.98.040501

Related papers

Hamiltonian formulation of quantum error correction and correlated noise: Effects of syndrome extraction in the long-time limit

E. Novais, Eduardo R. Mucciolo, Harold U. Baranger

We analyze the long-time behavior of a quantum computer running a quantum error correction (QEC) code in the presence of a correlated environment. Starting from a Hamiltonian formulation of realistic noise models, and assuming that QEC is indeed possible, we find formal expressions for the probability of a given syndrome history and the associated residual decoherence encoded in the reduced density matrix. Systems with nonzero gate times (``long gates'') are included in our analysis by using an upper bound on the noise. In order to introduce the local error probability for a qubit, we assume that propagation of signals through the environment is slower than the QEC period (hypercube assumption). This allows an explicit calculation in the case of a generalized spin-boson model and a quantum frustration model. The key result is a dimensional criterion: If the correlations decay sufficiently fast, the system evolves toward a stochastic error model for which the threshold theorem of fault-tolerant quantum computation has been proven. On the other hand, if the correlations decay slowly, the traditional proof of this threshold theorem does not hold. This dimensional criterion bears many similarities to criteria that occur in the theory of quantum phase transitions.

arXiv:0710.1624•Physical Review A•Jul 9, 2008•24 citations

Decoherence by Correlated Noise and Quantum Error Correction

E. Novais, Harold U. Baranger

We study the decoherence of a quantum computer in an environment which is inherently correlated in time and space. We first derive the nonunitary time evolution of the computer and environment in the presence of a stabilizer error correction code, providing a general way to quantify decoherence for a quantum computer. The general theory is then applied to the spin-boson model. Our results demonstrate that effects of long-range correlations can be systematically reduced by small changes in the error correction codes.

arXiv:quant-ph/0508228•Physical Review Letters•Jul 24, 2006•41 citations

Quantum Error Correction Phase Transition

Jincheng Zhang

Quantum error correction (QEC) is the cornerstone of fault‑tolerant quantum computation, enabling logical qubits to be protected against physical noise by encoding them into highly entangled states. In this paper we propose that the very ability of a QEC code to protect against errors is itself subject to a phase transition. We formulate a theory of the Quantum Error Correction Phase Transition (QECP), in which the system undergoes a sharp change from a regime of successful error suppression to a regime where logical errors proliferate, as a control parameter – such as the physical error rate, the code distance, or the connectivity of the underlying hardware – is varied. Drawing analogies to conventional symmetry‑breaking and topological phase transitions, we construct a statistical mechanical model that captures the competition between error‑correction resources and noise. We analyze the critical behavior, derive scaling relations, and discuss implications for the design of scalable quantum architectures. The existence of a QECP provides a new physical lens through which to view quantum information processing and suggests that fault‑tolerance thresholds may be understood as critical points in an extended parameter space.

•Aug 19, 2026•0 citations

Effect of correlated decay on fault-tolerant quantum computation

B. Lemberger, Deniz D. Yavuz

We analyze noise in the circuit model of quantum computers when the qubits are coupled to a common bosonic bath and discuss the possible failure of scalability of quantum computation. Specifically, we investigate correlated (super-radiant) decay between the qubit energy levels from a two- or three-dimensional array of qubits without imposing any restrictions on the size of the sample. We first show that regardless of how the spacing between the qubits compares with the emission wavelength, correlated decay produces errors outside the applicability of the threshold theorem. This is because the sum of the norms of the two-body interaction Hamiltonians (which can be viewed as the upper bound on the single-qubit error) that decoheres each qubit scales with the total number of qubits and is unbounded. We then discuss two related results: (1) We show that the actual error (instead of the upper bound) on each qubit scales with the number of qubits. As a result, in the limit of large number of qubits in the computer, $N\ensuremath{\rightarrow}\ensuremath{\infty}$, correlated decay causes each qubit in the computer to decohere in ever shorter time scales. (2) We find the complete eigenvalue spectrum of the exchange Hamiltonian that causes correlated decay in the same limit. We show that the spread of the eigenvalue distribution grows faster with $N$ compared to the spectrum of the unperturbed system Hamiltonian. As a result, as $N\ensuremath{\rightarrow}\ensuremath{\infty}$, quantum evolution becomes completely dominated by the noise due to correlated decay. These results argue that scalable quantum computing may not be possible in the circuit model in a two- or three- dimensional geometry when the qubits are coupled to a common bosonic bath.

Physical Review A•Dec 29, 2017•12 citations

Quantum Error Correction Phase Transition (QECP)

Jincheng Zhang

The ability of quantum error correction (QEC) to protect logical qubits against physical noise is traditionally quantified by a noise threshold: a critical noise level below which the logical error rate decreases exponentially with code distance. This paper proposes that QEC itself can undergo a phase transition analogous to a physical phase change. We develop a theoretical framework that treats the logical error rate as an order parameter and maps the behavior of large stabilizer codes onto a statistical mechanics model. By analyzing the scaling of logical error probabilities with code distance and noise strength, we identify a continuous phase transition at the threshold, characterized by critical exponents that depend on the code family and noise model. The transition separates a "fault‑tolerant" phase where logical errors are exponentially suppressed from a "fault‑unreliable" phase where logical errors proliferate. We discuss implications for the design of large‑scale quantum computers, potential experimental signatures in current quantum hardware, and the prospect of discovering new quantum information physics through this phase‑transition perspective.

•Aug 17, 2026•0 citations

Fault-Tolerant Quantum Computation with Long-Range Correlated Noise

Dorit Aharonov, Alexei Kitaev, John P. Preskill

We prove a new version of the quantum accuracy threshold theorem that applies to non-Markovian noise with algebraically decaying spatial correlations. We consider noise in a quantum computer arising from a perturbation that acts collectively on pairs of qubits and on the environment, and we show that an arbitrarily long quantum computation can be executed with high reliability in D spatial dimensions, if the perturbation is sufficiently weak and decays with the distance r between the qubits faster than 1/r(D).

arXiv:quant-ph/0510231•Physical Review Letters•Feb 7, 2006•243 citations
We analyze the problem of a quantum computer in a correlated environment protected from decoherence by quantum error correction using a perturbative renormalization group approach. The scaling equation obtained reflects the competition between the dimension of the computer and the scaling dimension of the correlations. For an irrelevant flow, the error probability is reduced to a stochastic form for a long time and/or a large number of qubits; thus, the traditional derivation of the threshold theorem holds for these error models. In this way, the "threshold theorem" of quantum computing is rephrased as a dimensional criterion.
We analyze the long-time behavior of a quantum computer running a quantum error correction (QEC) code in the presence of a correlated environment. Starting from a Hamiltonian formulation of realistic noise models, and assuming that QEC is indeed possible, we find formal expressions for the probability of a given syndrome history and the associated residual decoherence encoded in the reduced density matrix. Systems with nonzero gate times (``long gates'') are included in our analysis by using an upper bound on the noise. In order to introduce the local error probability for a qubit, we assume that propagation of signals through the environment is slower than the QEC period (hypercube assumption). This allows an explicit calculation in the case of a generalized spin-boson model and a quantum frustration model. The key result is a dimensional criterion: If the correlations decay sufficiently fast, the system evolves toward a stochastic error model for which the threshold theorem of fault-tolerant quantum computation has been proven. On the other hand, if the correlations decay slowly, the traditional proof of this threshold theorem does not hold. This dimensional criterion bears many similarities to criteria that occur in the theory of quantum phase transitions.
We study the decoherence of a quantum computer in an environment which is inherently correlated in time and space. We first derive the nonunitary time evolution of the computer and environment in the presence of a stabilizer error correction code, providing a general way to quantify decoherence for a quantum computer. The general theory is then applied to the spin-boson model. Our results demonstrate that effects of long-range correlations can be systematically reduced by small changes in the error correction codes.
Quantum error correction (QEC) is the cornerstone of fault‑tolerant quantum computation, enabling logical qubits to be protected against physical noise by encoding them into highly entangled states. In this paper we propose that the very ability of a QEC code to protect against errors is itself subject to a phase transition. We formulate a theory of the Quantum Error Correction Phase Transition (QECP), in which the system undergoes a sharp change from a regime of successful error suppression to a regime where logical errors proliferate, as a control parameter – such as the physical error rate, the code distance, or the connectivity of the underlying hardware – is varied. Drawing analogies to conventional symmetry‑breaking and topological phase transitions, we construct a statistical mechanical model that captures the competition between error‑correction resources and noise. We analyze the critical behavior, derive scaling relations, and discuss implications for the design of scalable quantum architectures. The existence of a QECP provides a new physical lens through which to view quantum information processing and suggests that fault‑tolerance thresholds may be understood as critical points in an extended parameter space.
We analyze noise in the circuit model of quantum computers when the qubits are coupled to a common bosonic bath and discuss the possible failure of scalability of quantum computation. Specifically, we investigate correlated (super-radiant) decay between the qubit energy levels from a two- or three-dimensional array of qubits without imposing any restrictions on the size of the sample. We first show that regardless of how the spacing between the qubits compares with the emission wavelength, correlated decay produces errors outside the applicability of the threshold theorem. This is because the sum of the norms of the two-body interaction Hamiltonians (which can be viewed as the upper bound on the single-qubit error) that decoheres each qubit scales with the total number of qubits and is unbounded. We then discuss two related results: (1) We show that the actual error (instead of the upper bound) on each qubit scales with the number of qubits. As a result, in the limit of large number of qubits in the computer, $N\ensuremath{\rightarrow}\ensuremath{\infty}$, correlated decay causes each qubit in the computer to decohere in ever shorter time scales. (2) We find the complete eigenvalue spectrum of the exchange Hamiltonian that causes correlated decay in the same limit. We show that the spread of the eigenvalue distribution grows faster with NNN compared to the spectrum of the unperturbed system Hamiltonian. As a result, as $N\ensuremath{\rightarrow}\ensuremath{\infty}$, quantum evolution becomes completely dominated by the noise due to correlated decay. These results argue that scalable quantum computing may not be possible in the circuit model in a two- or three- dimensional geometry when the qubits are coupled to a common bosonic bath.
The ability of quantum error correction (QEC) to protect logical qubits against physical noise is traditionally quantified by a noise threshold: a critical noise level below which the logical error rate decreases exponentially with code distance. This paper proposes that QEC itself can undergo a phase transition analogous to a physical phase change. We develop a theoretical framework that treats the logical error rate as an order parameter and maps the behavior of large stabilizer codes onto a statistical mechanics model. By analyzing the scaling of logical error probabilities with code distance and noise strength, we identify a continuous phase transition at the threshold, characterized by critical exponents that depend on the code family and noise model. The transition separates a "fault‑tolerant" phase where logical errors are exponentially suppressed from a "fault‑unreliable" phase where logical errors proliferate. We discuss implications for the design of large‑scale quantum computers, potential experimental signatures in current quantum hardware, and the prospect of discovering new quantum information physics through this phase‑transition perspective.
We prove a new version of the quantum accuracy threshold theorem that applies to non-Markovian noise with algebraically decaying spatial correlations. We consider noise in a quantum computer arising from a perturbation that acts collectively on pairs of qubits and on the environment, and we show that an arbitrarily long quantum computation can be executed with high reliability in D spatial dimensions, if the perturbation is sufficiently weak and decays with the distance r between the qubits faster than 1/r(D).