Related papers: Fault-tolerant Preparation of Stabilizer States fo…
With gate error rates in multiple technologies now below the threshold required for fault-tolerant quantum computation, the major remaining obstacle to useful quantum computation is scaling, a challenge greatly amplified by the huge…
Fault-tolerant operations based on stabilizer codes are the state of the art in suppressing error rates in quantum computations. Most such codes do not permit a straightforward implementation of non-Clifford logical operations, which are…
We discuss stabilizer quantum-error correction codes implemented in a single multi-level qudit to avoid resource escalation typical of multi-qubit codes. These codes can be customized to the specific physical errors on the qudit,…
Storing quantum information in a quantum error correction code can protect it from errors, but the ability to transform the stored quantum information in a fault tolerant way is equally important. Logical Pauli group operators can be…
For a number of quantum channels of interest, phase-flip errors occur far more frequently than bit-flip errors. When transmitting across these asymmetric channels, the decoding error rate can be reduced by tailoring the code used to the…
Ancilla post-selection is a common means of achieving fault-tolerance in quantum error-correction. However, it can lead to additional data errors due to movement or wait operations. Alternatives to post-selection may achieve lower overall…
Topological measurement-based quantum computation (MBQC) enables one to carry out universal fault-tolerant quantum computation via single-qubit Pauli measurements with a family of large entangled states called cluster states as resources.…
A fault-tolerant way to prepare logical code-states of Q1 codes, i.e., quantum polar codes encoding one qubit, has been recently proposed. The fault tolerance therein is guaranteed by an error detection gadget, where if an error is detected…
We introduce a class of cyclic quantum codes, basing the construction not on the simplicity of the stabilizers, but rather on the simplicity of preparation of a code state (at least in the absence of noise). We show how certain known codes,…
The blind quantum computation (BQC) protocol allows for privacy-preserving remote quantum computations. In this paper, we introduce a remote quantum error correction code preparation protocol for BQC using a cluster state and analyze its…
Large-scale quantum computation is likely to require massive quantum error correction (QEC). QEC codes and circuits are described via the stabilizer formalism, which represents stabilizer states by keeping track of the operators that…
We introduce a high-level graphical framework for designing and analysing quantum error correcting codes, centred on what we term the coherent parity check (CPC). The graphical formulation is based on the diagrammatic tools of the…
Scalable quantum computing and communication requires the protection of quantum information from the detrimental effects of decoherence and noise. Previous work tackling this problem has relied on the original circuit model for quantum…
Construction of a fault-tolerant quantum computer remains a challenging problem due to unavoidable noise in quantum states and the fragility of quantum entanglement. However, most of the error-correcting codes increases the complexity of…
Mapping an error syndrome to the error operator is the core of quantum decoding network and is also the key step of recovery. The definitions of the bit-flip error syndrome matrix and the phase-flip error syndrome matrix were presented, and…
Realizing universal fault-tolerant quantum computation is a key goal in quantum information science. By encoding quantum information into logical qubits utilizing quantum error correcting codes, physical errors can be detected and…
We develop the theory of entanglement-assisted quantum error correcting (EAQEC) codes, a generalization of the stabilizer formalism to the setting in which the sender and receiver have access to pre-shared entanglement. Conventional…
A classical coding across a block of logical qubits is presented. We characterize subgroups of the product stabilizer group on a block of logical qubits corresponding to dual codes of classical error correcting codes. We prove conditions on…
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…
Fault-tolerant cluster states form the basis for scalable measurement-based quantum computation. Recently, new stabilizer codes for scalable circuit-based quantum computation have been introduced that have very high thresholds under biased…