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While adiabatic quantum computing (AQC) has some robustness to noise and decoherence it is widely believed that encoding, error suppression and error correction will be required to scale AQC to large problem sizes. Previous works have…
Active quantum error correction using qubit stabilizer codes has emerged as a promising, but experimentally challenging, engineering program for building a universal quantum computer. In this review we consider the formalism of qubit…
We consider the problem of determining the weights of a quantum ensemble. That is to say, given a quantum system that is in a set of possible known states according to an unknown probability law, we give strategies to estimate the…
We show that a quantum architecture with an error correction procedure limited to geometrically local operations incurs an overhead that grows with the system size, even if arbitrary error-free classical computation is allowed. In…
Quantum error correction is an essential technique for constructing a scalable quantum computer. In order to implement quantum error correction with near-term quantum devices, a fast and near-optimal decoding method is demanded. A decoder…
Accurate methods of assessing the performance of quantum gates are extremely important. Quantum process tomography and randomized benchmarking are the current favored methods. Quantum process tomography gives detailed information, but…
Quantum error correction (QEC) is essential for quantum computers to perform useful algorithms, but large-scale fault-tolerant computation remains out of reach due to demanding requirements on operation fidelity and the number 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…
The new field of quantum error correction has developed spectacularly since its origin less than two years ago. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the environment.…
Quantum systems can be used to measure various quantities in their environment with high precision. Often, however, their sensitivity is limited by the decohering effects of this same environment. Dynamical decoupling schemes are widely…
Quantum error correction (QEC) is essential for enabling quantum advantages, with decoding as a central algorithmic primitive. Owing to its importance and intrinsic difficulty, substantial effort has been made to QEC decoder design, among…
Practical quantum computers will require resource-efficient error-correcting codes. The rotated surface code uses approximately half the number of qubits as the unrotated surface code to create a logical qubit with the same error-correcting…
We compare failure distributions of quantum error correction circuits for stochastic errors and coherent errors. We utilize a fully coherent simulation of a fault tolerant quantum error correcting circuit for a $d=3$ Steane and surface…
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 a convergent iterative algorithm for finding the optimal coding and decoding operations for an arbitrary noisy quantum channel. This algorithm does not require any error syndrome to be corrected completely, and hence also finds…
We present a semidefinite program optimization approach to quantum error correction that yields codes and recovery procedures that are robust against significant variations in the noise channel. Our approach allows us to optimize the…
We investigate a novel class of quantum error correcting codes to correct errors on both qubits and higher-state quantum systems represented as qudits. These codes arise from an original graph-theoretic representation of sets of quantum…
We investigate the performance of a quantum error-correcting code when pushed beyond its intended capacity to protect information against errors, presenting formulae for the probability of failure when the errors affect more qudits than…
We present a quantum error correcting code that is invariant under the conditional time evolution between spontaneous emissions and which can correct for one general error. The code presented here generalizes previous error correction codes…
There are well known necessary and sufficient conditions for a quantum code to correct a set of errors. We study weaker conditions under which a quantum code may correct errors with probabilities that may be less than one. We work with…