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The large-scale execution of quantum algorithms requires basic quantum operations to be implemented fault-tolerantly. The most popular technique for accomplishing this, using the devices that can be realised in the near term, uses…
Pre-fault tolerant quantum computers have already demonstrated the ability to estimate observable values accurately, at a scale beyond brute-force classical computation. This has been enabled by error mitigation techniques that often rely…
Quantum error correction becomes a practical possibility only if the physical error rate is below a threshold value that depends on a particular quantum code, syndrome measurement circuit, and decoding algorithm. Here we present an…
We discuss stabilizer quantum-error correction codes implemented in a single multi-level qudit to avoid resource escalation typical of multi-qubit codes. These codes can be customized to the specific physical errors on the qudit,…
The goal of this paper is to review the theoretical basis for achieving a faithful quantum information transmission and processing in the presence of noise. Initially encoding and decoding, implementing gates and quantum error correction…
Post-selection strategies that discard low-confidence computational results can significantly improve the effective fidelity of quantum error correction at the cost of reduced acceptance rates, which can be particularly useful for offline…
The conventional circuit paradigm, utilizing a limited number of gates to construct arbitrary quantum circuits, is hindered by significant noise overhead. For instance, the standard gate paradigm employs two CNOT gates for the partial…
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…
Noise-biased qubits are a promising route toward significantly reducing the hardware overhead associated with quantum error correction. The squeezed cat code, a non-local encoding in phase space based on squeezed coherent states, is an…
Concatenated bosonic-stabilizer codes have recently gained prominence as promising candidates for achieving low-overhead fault-tolerant quantum computing in the long term. In such systems, analog information obtained from the syndrome…
Obtaining high-fidelity and robust quantum gates is the key for scalable quantum computation, and one of the promising ways is to implement quantum gates using geometric phases, where the influence of local noises can be greatly reduced. To…
The main ideas of quantum error correction are introduced. These are encoding, extraction of syndromes, error operators, and code construction. It is shown that general noise and relaxation of a set of 2-state quantum systems can always be…
Quantum noise is a central challenge in quantum computing across many applications. Extensive work has examined how qubits couple to their environment, leading to decoherence and relaxation, which is irreversible. Current studies focus on…
In the context of measurement-based quantum computation a way of maintaining the coherence of a graph state is to measure its stabilizer operators. Aside from performing quantum error correction, it is possible to exploit the information…
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…
To produce an operable quantum computer that is made with imperfect hardware, we must design and test scalable quantum error correcting codes that are suited for the devices we can build and, in unison, develop decoding strategies that…
Quantum low-density parity-check (QLDPC) codes with asymptotically non-zero rates are prominent candidates for achieving fault-tolerant quantum computation, primarily due to their syndrome-measurement circuit's low operational depth.…
Given that quantum error correction processes are unreliable, an efficient error syndrome extraction circuit should use fewer ancillary qubits, quantum gates, and measurements, while maintaining low circuit depth, to minimizing the circuit…
Low check weight is practically crucial code property for fault-tolerant quantum computing, which underlies the strong interest in quantum low-density parity-check (qLDPC) codes. Here, we explore the theory of weight-constrained stabilizer…
Proposals for quantum computing devices are many and varied. They each have unique noise processes that make none of them fully reliable at this time. There are several error correction/avoidance techniques which are valuable for reducing…