Related papers: Designing the Quantum Channels Induced by Diagonal…
A decision diagram (DD) is a graph-like data structure for homomorphic compression of Boolean and pseudo-Boolean functions. Over the past decades, decision diagrams have been successfully applied to verification, linear algebra, stochastic…
The stabiliser formalism plays a central role in quantum computing, error correction, and fault tolerance. Conversions between and verifications of different specifications of stabiliser states and Clifford gates are important components of…
Recent years have seen rapid development in the subject of quantum coding theory, with breakthroughs on many exciting classes of codes, including quantum LDPC codes, quantum locally testable codes, and quantum codes with interesting…
Given a quantum error correcting code, an important task is to find encoded operations that can be implemented efficiently and fault-tolerantly. In this Letter we focus on topological stabilizer codes and encoded unitary gates that can be…
Quantum error correction codes (QECCs) play a central role in both quantum communications and quantum computation. Practical quantum error correction codes, such as stabilizer codes, are generally structured to suit a specific use, and…
Qubits are a great way to build a quantum computer, but a limited way to program one. We replace the usual "states and gates" formalism with a "props and ops" (propositions and operators) model in which (a) the C*-algebra of observables…
Braiding defects in topological stabiliser codes has been widely studied as a promising approach to fault-tolerant quantum computing. Here, we explore the potential and limitations of such schemes in codes of all spatial dimensions. We…
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…
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…
Physical platforms such as trapped ions suffer from coherent noise where errors manifest as rotations about a particular axis and can accumulate over time. We investigate passive mitigation through decoherence free subspaces, requiring the…
In the context of measurement-based quantum computation a way of maintaining the coherence of a graph state is to measure its stabilizer operators. Aside from performing quantum error correction, it is possible to exploit the information…
We show how to perform measurement-based quantum computing on qudits (high-dimensional quantum systems) using alternative resource states beyond the cluster state. Estimating overheads for gate decomposition, we find that generalizing…
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…
A triorthogonal code is a binary quantum Calderbank-Shor-Steane (CSS) code defined by a triorthogonal matrix. Triorthogonal codes are a key ingredient in magic-state distillation, since they allow for transversal $\mathsf{T}$ gates, a…
Silicon-based quantum computing has the potential advantages of low cost, high integration density, and compatibility with CMOS technologies. The detuning mechanism has been used to experimentally achieve silicon two-qubit quantum gates and…
Codeword stabilized quantum codes provide a unified approach to constructing quantum error-correcting codes, including both additive and non-additive quantum codes. Standard codeword stabilized quantum codes encode quantum information into…
The disjointness of a stabilizer code is a quantity used to constrain the level of the logical Clifford hierarchy attainable by transversal gates and constant-depth quantum circuits. We show that for any positive integer constant $c$, the…
Certain types of quantum computing platforms, such as those realized using Rydberg atoms or Kerr-cat qubits, are natively more susceptible to Pauli-Z noise than Pauli-X noise, or vice versa. On such hardware, it is useful to ensure that…
The development of quantum computing systems for large scale algorithms requires targeted error rates unachievable through hardware advancements alone. Quantum Error Correction (QEC) allows us to use systems with a large number of physical…
An interesting concept in quantum computation is that of global control (GC), where there is no need to manipulate qubits individually. One can implement a universal set of quantum gates on a one-dimensional array purely via signals that…