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We present a fault-tolerant [[8, 1, 3]] non-CSS quantum error correcting code and study its logical error rates. We choose the unitary encoding procedure for stabilizer codes given by Gottesman and modify it to suit the setting of a class…

The stabiliser fragment of quantum theory is a foundational building block for quantum error correction and the fault-tolerant compilation of quantum programs. In this article, we develop a sound, universal and complete denotational…

Here we revisit one of the prototypical tasks for characterizing the structure of noise in quantum devices: estimating every eigenvalue of an $n$-qubit Pauli noise channel to error $\epsilon$. Prior work [14] proved no-go theorems for this…

As measurements are costly and prone to errors on certain quantum computing devices, we should reduce the number of measurements and the number of measured qudits as small as possible in quantum erasure correction. It is intuitively obvious…

Quantum effect enables enhanced estimation precision in metrology, with the Heisenberg limit (HL) representing the ultimate limit allowed by quantum mechanics. Although the HL is generally unattainable in the presence of noise, quantum…

We construct rotated logical states by applying rotation operators to stabilizer states, extending the logical basis and modifying stabilizer generators. Rotation operators affect the effective code distance $d_R$, which decays…

We describe a quantum error correction scheme aimed at protecting a flow of quantum information over long distance communication. It is largely inspired by the theory of classical convolutional codes which are used in similar circumstances…

The calculating of the coherent information is a fundamental step in obtaining the quantum capacity of a quantum channel. We introduce orthogonal and complete code basis to evaluate the coherent information per channel use when the input is…

Quantum error mitigation (QEM) is a promising technique of protecting hybrid quantum-classical computation from decoherence, but it suffers from sampling overhead which erodes the computational speed. In this treatise, we provide a…

We address the task of verifying whether a quantum computer, designed to be protected by a specific stabilizer code, correctly encodes the corresponding logical qubits. To achieve this, we develop a general framework for subspace…

Quantum error correction is an essential ingredient for universal quantum computing. Despite tremendous experimental efforts in the study of quantum error correction, to date, there has been no demonstration in the realisation of universal…

The intrinsic probabilistic nature of quantum systems makes error correction or mitigation indispensable for quantum computation. While current error-correcting strategies focus on correcting errors in quantum states or quantum gates, these…

The rapid advancement of quantum computing has led to an extensive demand for effective techniques to extract classical information from quantum systems, particularly in fields like quantum machine learning and quantum chemistry. However,…

Coherent noise can be much more damaging than incoherent (probabilistic) noise in the context of quantum error correction. One solution is to use twirling to turn coherent noise into incoherent Pauli channels. In this Article, we show that…

Quantum error correction is important to quantum information processing, which allows us to reliably process information encoded in quantum error correction codes. Efficient quantum error correction benefits from the knowledge of error…

Quantum error correction allows for faulty quantum systems to behave in an effectively error free manner. One important class of techniques for quantum error correction is the class of quantum subsystem codes, which are relevant both to…

We introduce the notion of fault-tolerant quantum metrology to overcome noise beyond our control -- associated with sensing the parameter, by reducing the noise in operations under our control -- associated with preparing and measuring…

With the rapid developments in quantum hardware comes a push towards the first practical applications on these devices. While fully fault-tolerant quantum computers may still be years away, one may ask if there exist intermediate forms of…

We present an algorithm for manipulating quantum information via a sequence of projective measurements. We frame this manipulation in the language of stabilizer codes: a quantum computation approach in which errors are prevented and…

Quantum error correction will likely be essential for building a large-scale quantum computer, but it comes with significant requirements at the level of classical control software. In particular, a quantum error-correcting code must be…