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Quantum error-correcting codes (QECC's) are needed to combat the inherent noise affecting quantum processes. Using ZX calculus, we represent QECC's in a form called a ZX diagram, consisting of a tensor network. In this paper, we present…
In the era of noisy intermediate-scale quantum (NISQ) devices, the number of controllable hardware qubits is insufficient to implement quantum error correction (QEC). As an alternative, quantum error mitigation (QEM) can suppress errors in…
The implementation of practical error correction protocols is essential for deployment of quantum information technologies. Ways of exploiting high-spin nuclei, which have multi-level quantum resources, have attracted interest in this…
The behavior of real quantum hardware differs strongly from the simple error models typically used when simulating quantum error correction. Error processes are far more complex than simple depolarizing noise applied to single gates, and…
Compared to the more widely studied Pauli errors, coherent errors present several new challenges in quantum computing and quantum error correction (QEC). For example, coherent errors may interfere constructively over a long circuit and…
Quantum computers (QCs) must implement quantum error correcting codes (QECCs) to protect their logical qubits from errors, and modeling the effectiveness of QECCs on QCs is an important problem for evaluating the QC architecture. The…
Quantum error correction plays a critical role in enabling fault-tolerant quantum computing by protecting fragile quantum information from noise. While general-purpose quantum error correction codes are designed to address a wide range of…
The performance of a given quantum error correction (QEC) code depends upon the noise model that is assumed. Independent Pauli noise, applied after each quantum operation, is a simplistic noise model that is easy to simulate and understand…
The surface code represents a promising candidate for fault-tolerant quantum computation due to its high error threshold and experimental accessibility with nearest-neighbor interactions. However, current exact surface code threshold…
Quantum technologies have shown immeasurable potential to effectively solve several information processing tasks such as prime number factorization, unstructured database search or complex macromolecule simulation. As a result of such…
Noise and errors are inevitable parts of any practical implementation of a quantum computer. As a result, large-scale quantum computation will require ways to detect and correct errors on quantum information. Here, we present such a quantum…
Reducing errors is essential for reliable quantum computation. Quantum error mitigation (QEM) and quantum error correction (QEC) are two leading approaches for this task, each with challenges: QEM suffers from high sampling costs and cannot…
Fault-tolerant quantum computers compose elements of a discrete gate set in order to approximate a target unitary. The problem of minimising the number of gates is known as gate-synthesis. The approximation error is a form of coherent…
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…
Quantum error correction (QEC) is often implemented on hardware that experiences biased noise, where dephasing errors occur more frequently than other errors. This has motivated many recent efforts to develop bias-tailored QEC codes, such…
Quantum error correction (QEC) is considered a deciding component in enabling practical quantum computing. Stabilizer codes, and in particular topological surface codes, are promising candidates for implementing QEC by redundantly encoding…
Current approaches to fault-tolerant quantum computation will not enable useful quantum computation on near-term devices of 50 to 100 qubits. Leading proposals, such as the color code and surface code schemes, must devote a large fraction…
Current techniques in quantum process tomography typically return a single point estimate of an unknown process based on a finite albeit large amount of measurement data. Due to statistical fluctuations, however, other processes close to…
We develop a theory based on quasi-geometric (QG) approach to transform a small number of qubits into a larger number of error-correcting qubits by considering four different cases. More precisely, we use the 2-dimensional quasi-orthogonal…
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…