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Quantum error correction (QEC) and fault-tolerant quantum computation represent one of the most vital theoretical aspect of quantum information processing. It was well known from the early developments of this exciting field that the…
We propose a new method to autonomously correct for errors of a logical qubit induced by energy relaxation. This scheme encodes the logical qubit as a multi-component superposition of coherent states in a harmonic oscillator, more…
In this introduction we motivate and explain the ``decoding'' and ``subsystems'' view of quantum error correction. We explain how quantum noise in QIP can be described and classified, and summarize the requirements that need to be satisfied…
A quantum error-correcting code is defined to be a unitary mapping (encoding) of k qubits (2-state quantum systems) into a subspace of the quantum state space of n qubits such that if any t of the qubits undergo arbitrary decoherence, not…
We develop a theory for finding quantum error correction (QEC) procedures which are optimized for given noise channels. Our theory accounts for uncertainties in the noise channel, against which our QEC procedures are robust. We demonstrate…
Quantum error correction has recently emerged as a tool to enhance quantum sensing under Markovian noise. It works by correcting errors in a sensor while letting a signal imprint on the logical state. This approach typically requires a…
Quantum error correction codes are usually designed to correct errors regardless of their physical origins. In large-scale devices, this is an essential feature. In smaller-scale devices, however, the main error sources are often…
A major milestone of quantum error correction is to achieve the fault-tolerance threshold beyond which quantum computers can be made arbitrarily accurate. This requires extraordinary resources and engineering efforts. We show that even…
Practical quantum computing will require error rates that are well below what is achievable with physical qubits. Quantum error correction offers a path to algorithmically-relevant error rates by encoding logical qubits within many physical…
Continuous quantum error correction has been found to have certain advantages over discrete quantum error correction, such as a reduction in hardware resources and the elimination of error mechanisms introduced by having entangling gates…
Due to the fragility of quantum mechanical effects, real quantum computers are plagued by frequent noise effects that cause errors during computations. Quantum error-correcting codes address this problem by providing means to identify and…
Quantum computing promises to solve problems previously deemed infeasible. However, high error rates necessitate quantum error correction for practical applications. Seminal experiments with zoned neutral atom architectures have shown…
This paper investigates quantum error correction schemes for fully-correlated noise channels on an $n$-qubit system, where error operators take the form $W^{\otimes n}$, with $W$ being an arbitrary $2\times 2$ unitary operator. In previous…
Fault-tolerant quantum computing demands many qubits with long lifetimes to conduct accurate quantum gate operations. However, external noise limits the computing time of physical qubits. Quantum error correction codes may extend such…
Errors in the current generation of quantum processors pose a significant challenge towards practical-scale implementations of quantum machine learning (QML) as they lead to trainability issues arising from noise-induced barren plateaus, as…
Quantum error correction in general is experimentally challenging as it requires significant expansion of the size of quantum circuits and accurate performance of quantum gates to fulfill the error threshold requirement. Here we propose a…
To solve classically hard problems, quantum computers need to be resilient to the influence of noise and decoherence. In such a fault-tolerant quantum computer, noise-induced errors must be detected and corrected in real-time to prevent…
Performing experiments on small-scale quantum computers is certainly a challenging endeavor. Many parameters need to be optimized to achieve high-fidelity operations. This can be done efficiently for operations acting on single qubits as…
Quantum error correction is expected to be essential in large-scale quantum technologies. However, the substantial overhead of qubits it requires is thought to greatly limit its utility in smaller, near-term devices. Here we introduce a new…
Noise is typically treated as the adversary of quantum information processing. For open quantum dynamics, however, dissipation is part of the target physics, creating a tension with fault-tolerant architectures designed to suppress…