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Correlated noise across multiple qubits poses a significant challenge for achieving scalable and fault-tolerant quantum processors. Despite recent experimental efforts to quantify this noise in various qubit architectures, a comprehensive…
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…
We study variants of Shor's code that are adept at handling single-axis correlated idling errors, which are commonly observed in many quantum systems. By using the repetition code structure of the Shor's code basis states, we calculate the…
We present a general framework for applying linear quantum error mitigation (QEM) techniques directly to physical qubits within a logical qubit to suppress logical errors. By exploiting the linearity of quantum error correction (QEC), we…
Whether it is at the fabrication stage or during the course of the quantum computation, e.g. because of high-energy events like cosmic rays, the qubits constituting an error correcting code may be rendered inoperable. Such defects may…
The first generation of multi-qubit quantum technologies will consist of noisy, intermediate-scale devices for which active error correction remains out of reach. To exploit such devices, it is thus imperative to use passive error…
This is an expository article aiming to introduce the reader to the underlying mathematics and geometry of quantum error correction. Information stored on quantum particles is subject to noise and interference from the environment. Quantum…
Learning problems involving quantum data are natural candidates for demonstrating an advantage in quantum machine learning. Recent results indicate that, for certain tasks and under noiseless conditions, coherent processing of quantum data…
The accumulation of quantum phase in response to a signal is the central mechanism of quantum sensing, as such, loss of phase information presents a fundamental limitation. For this reason approaches to extend quantum coherence in the…
With fault-tolerant quantum computing (FTQC) on the horizon, it is critical to understand sources of logical error in plausible hardware implementations of quantum error-correcting codes (QECC). In this work, we consider logical error rates…
We consider the problem of correcting the errors incurred from sending quantum information through a noisy quantum environment by using classical information obtained from a measurement on the environment. For discrete time Markovian…
The surface code is a quantum error-correcting code for one logical qubit, protected by spatially localized parity checks in two dimensions. Due to fundamental constraints from spatial locality, storing more logical qubits requires either…
We study the exact dynamics of optical qubits encoded via coherent states with opposite phases which are interacting with an environment modeled as a collection of simple harmonic oscillators. Making use of a coherent-state path integral…
Quantum error correction (QEC) protects quantum systems against inevitable noises and control inaccuracies, providing a pathway towards fault-tolerant (FT) quantum computation. Stabilizer codes, including surface code and color code, have…
We present a method for quantum error mitigation on partially error-corrected quantum computers - i.e., computers with some logical qubits and some noisy qubits. Our method is inspired by the error cancellation method and is implemented via…
The performance of a given quantum error correction (QEC) code depends upon the noise model that is assumed. Independent Pauli noise, applied after each quantum operation, is a simplistic noise model that is easy to simulate and understand…
Recent progress in fault-tolerant quantum computing suggests that leveraging error-syndrome information at the logical layer can substantially improve performance, including the estimation of logical observables from noisy states. In this…
The ambition of harnessing the quantum for computation is at odds with the fundamental phenomenon of decoherence. The purpose of quantum error correction (QEC) is to counteract the natural tendency of a complex system to decohere. This…
The execution of quantum circuits on real systems has largely been limited to those which are simply time-ordered sequences of unitary operations followed by a projective measurement. As hardware platforms for quantum computing continue to…
In the scale-up of quantum computers, the framework underpinning fault-tolerance generally relies on the strong assumption that environmental noise affecting qubit logic is uncorrelated (Markovian). However, as physical devices progress…