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Quantum computing devices are inevitably subject to errors. To leverage quantum technologies for computational benefits in practical applications, quantum algorithms and protocols must be implemented reliably under noise and imperfections.…

Error-correcting codes were invented to correct errors on noisy communication channels. Quantum error correction (QEC), however, may have a wider range of uses, including information transmission, quantum simulation/computation, and…

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…

Studies of quantum error correction (QEC) typically focus on stochastic Pauli errors because the existence of a threshold error rate below which stochastic Pauli errors can be corrected implies that there exists a threshold below which…

Quantum simulation is a promising way toward practical quantum advantage, but noise in current quantum hardware poses a significant obstacle. We prove that not only the physical error but also the algorithmic error in a single Trotter step…

Most of the research done on quantum error correction studies an error model in which each qubit is affected by noise, independently of the other qubits. In this paper we study a different noise model -- one in which the noise may be…

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…

In the current quantum computing paradigm, significant focus is placed on the reduction or mitigation of quantum decoherence. When designing new quantum processing units, the general objective is to reduce the amount of noise qubits are…

Quantum error correction uses the measurement of syndromes and classical decoding algorithms to estimate the location and type of errors while protecting the encoded quantum bits. Here we consider how prior information and Bayesian updates…

Quantum error correction is capable of digitizing quantum noise and increasing the robustness of qubits. Typically, error correction is designed with the target of eliminating all errors - making an error so unlikely it can be assumed that…

The effects of noise are one of the most important factors to consider when it comes to quantum computing in the noisy intermediate-scale quantum computing (NISQ) era that we are currently in. Therefore, it is important not only to gain…

Decoherence of quantum states is a major hurdle towards scalable and reliable quantum computing. Lower decoherence (i.e., higher fidelity) can alleviate the error correction overhead and obviate the need for energy-intensive noise reduction…

As far as we know, a useful quantum computer will require fault-tolerant gates, and existing schemes demand a prohibitively large space and time overhead. We argue that a first generation quantum computer will be very valuable to design,…

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…

Errors in quantum computers are of two kinds: sudden perturbations to isolated qubits, and slow random drifts of all the qubits. The latter may be reduced, but not eliminated, by means of symmetrization, namely by using many replicas of the…

Running quantum programs is fraught with challenges on on today's noisy intermediate scale quantum (NISQ) devices. Many of these challenges originate from the error characteristics that stem from rapid decoherence and noise during…

The detrimental effect of noise accumulates as quantum computers grow in size. In the case where devices are too small or noisy to perform error correction, error mitigation may be used. Error mitigation does not increase the fidelity of…

Quantum error correcting codes have been shown to have the ability of making quantum information resilient against noise. Here we show that we can use quantum error correcting codes as diagnostics to characterise noise. The experiment is…

Quantum computation and communication are important branches of quantum information science. However, noise in realistic quantum devices fundamentally limits the utility of these quantum technologies. A conventional approach towards…

In this paper we study an error correcting protocol that specifically derives its error correcting properties from elementary units of coherence. The entire protocol from beginning to end is performed using non-coherence increasing…