Related papers: Ancilla-free quantum error correction codes for qu…
The purpose of this little survey is to give a simple description of the main approaches to quantum error correction and quantum fault-tolerance. Our goal is to convey the necessary intuitions both for the problems and their solutions in…
Quantum error-correcting codes are constructed that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. These codes exploit the noncommutative geometry of…
Methods to control errors will be essential for quantum information processing. It is widely believed that fault-tolerant quantum error correction is the leading contender to achieve this goal. Although the theory of fault-tolerant quantum…
Quantum metrology with entangled resources aims to achieve sensitivity beyond the standard quantum limit by harnessing quantum effects even in the presence of environmental noise. So far, sensitivity has been mainly discussed from the…
The effect of noise on a quantum system can be described by a set of operators obtained from the interaction Hamiltonian. Recently it has been shown that generalized quantum error correcting codes can be derived by studying the algebra of…
Quantum computers are inherently noisy, and a crucial challenge for achieving large-scale, fault-tolerant quantum computing is to implement quantum error correction. A promising direction that has made rapid recent progress is to design…
In this thesis we examine a variety of techniques for reducing the resources required for fault-tolerant quantum computation. First, we show how to simplify universal encoded computation by using only transversal gates and standard error…
In adversarial settings, where attackers can deliberately and strategically corrupt quantum data, standard quantum error correction reaches its limits. It can only correct up to half the code distance and must output a unique answer.…
We introduce a technique for recovering noise-free observables in noisy quantum systems by combining the results of many slightly different experiments. Our approach is applicable to a variety of quantum systems but we illustrate it with…
Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than…
We investigate the precision limits and optimal protocols for sensing single qubit signals in the presence of erasure noise. We study a hierarchy of precision limits achievable with metrological strategies of differing complexity, and…
A major challenge in performing quantum error correction (QEC) is implementing reliable measurements and conditional feed-forward operations. In quantum computing platforms supporting unconditional qubit resets, or a constant supply of…
Quantum computers have the potential to provide exponential speedups over their classical counterparts. Quantum principles are being applied to fields such as communications, information processing, and artificial intelligence to achieve…
A promising approach to overcome decoherence in quantum computing schemes is to perform active quantum error correction using topology. Topological subsystem codes incorporate both the benefits of topological and subsystem codes, allowing…
We present a quantum error correction code which protects a qubit of information against general one qubit errors which maybe caused by the interaction with the environment. To accomplish this, we encode the original state by distributing…
Fault-tolerant quantum computation with bosonic qubits often necessitates the use of noisy discrete-variable ancillae. In this work, we establish a comprehensive and practical fault-tolerance framework for such a hybrid system and…
We introduce a quantum error mitigation technique based on probabilistic error cancellation to eliminate errors which have accumulated during the application of a quantum circuit. Our approach is based on applying an optimal "denoiser"…
We calculate the fidelity with which an arbitrary state can be encoded into a [7,1,3] CSS quantum error correction code in a non-equiprobable Pauli operator error environment with the goal of determining whether this encoding can be used…
In this paper we introduce a general fault-tolerant quantum error correction protocol using flag circuits for measuring stabilizers of arbitrary distance codes. In addition to extending flag error correction beyond distance-three codes for…
We give an introduction to the theory of quantum error correction using stabilizer codes that is geared towards the working computer scientists and mathematicians with an interest in exploring this area. To this end, we begin with an…