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Quantum error-correcting codes protect fragile quantum information by encoding it redundantly, but identifying codes that perform well in practice with minimal overhead remains difficult due to the combinatorial search space and the high…
Logical qubits can be protected from decoherence by performing QEC cycles repeatedly. Algorithms for fault-tolerant QEC must be compiled to the specific hardware platform under consideration in order to practically realize a quantum memory…
We develop a generalized theory of quantum error correction (QEC) that applies to any linear map, in particular maps that are not completely positive (CP). This theory describes entanglement-assisted QEC for invertible noise maps, which we…
High-rate quantum error correcting codes mitigate the imposing scale of fault-tolerant quantum computers but require efficient generation of non-local, many-body entanglement. We provide a linear-optical architecture with these properties,…
Quantum error correction protocols will play a central role in the realisation of quantum computing; the choice of error correction code will influence the full quantum computing stack, from the layout of qubits at the physical level to…
Large-scale quantum computers have the potential to hold computational capabilities beyond conventional computers for certain problems. However, the physical qubits within a quantum computer are prone to noise and decoherence, which must be…
Noise is one of the central obstacles to building useful quantum computers, and quantum error correction (QEC) provides the framework for protecting quantum information against it. Unlike classical error correction, QEC must preserve…
Quantum algorithms rely on quantum computers for implementation, but the physical connectivity constraints of modern quantum processors impede the efficient realization of quantum algorithms. Qubit mapping, a critical technology for…
Quantum error correction (QEC) enables reliable computation on noisy hardware by encoding logical information across many physical qubits and periodically measuring parities to detect errors. A decoder is the classical algorithm that uses…
Quantum error correction (QEC) is believed to be essential for the realization of large-scale quantum computers. However, due to the complexity of operating on the encoded `logical' qubits, understanding the physical principles for building…
Quantum error correction protects quantum information against environmental noise. When using qubits, a measure of quality of a code is the maximum number of errors that it is able to correct. We show that a suitable notion of ``number of…
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…
Recent work on approximate quantum error correction (QEC) has opened up the possibility of constructing subspace codes that protect information with high fidelity in scenarios where perfect error correction is impossible. Motivated by this,…
Quantum error correction (QEC) is crucial for ensuring the reliability of quantum computers. However, implementing QEC often requires a significant number of qubits, leading to substantial overhead. One of the major challenges in quantum…
To build a universal quantum computer from fragile physical qubits, effective implementation of quantum error correction (QEC) is an essential requirement and a central challenge. Existing demonstrations of QEC are based on a schedule of…
Quantum error correction is a critical technique for transitioning from noisy intermediate-scale quantum (NISQ) devices to fully fledged quantum computers. The surface code, which has a high threshold error rate, is the leading quantum…
We study how well topological quantum codes can tolerate coherent noise caused by systematic unitary errors such as unwanted $Z$-rotations. Our main result is an efficient algorithm for simulating quantum error correction protocols based on…
Correcting errors due to noise in quantum circuits run on current and near-term quantum hardware is essential for any convincing demonstration of quantum advantage. Indeed, in many cases it has been shown that noise renders quantum circuits…
Quantum error correcting (QEC) codes protect quantum information from decoherence, as long as error rates fall below critical error thresholds. In general, obtaining thresholds implies simulating the QEC procedure using, in general,…
Quantum computers hold the promise of solving computational problems which are intractable using conventional methods. For fault-tolerant operation quantum computers must correct errors occurring due to unavoidable decoherence and limited…