Related papers: Stacked codes: universal fault-tolerant quantum co…
Encoding logical quantum information in harmonic oscillator modes is a promising and hardware-efficient approach to the realization of a quantum computer. In this work, we propose to encode logical qubits in grid states of an ensemble of…
Solid-state spin qubits are a promising platform for quantum computation and quantum networks. Recent experiments have demonstrated high-quality control over multi-qubit systems, elementary quantum algorithms and non-fault-tolerant error…
As there is no quantum error correction code with universal set of transversal gates, several approaches have been proposed which, in combination of transversal gates, make universal fault-tolerant quantum computation possible. Magic state…
We formulate a bounded distance decoding strategy applicable to all stabilizer codes including both CSS and non-CSS code-families. The framework emerges out of the local Clifford equivalence between arbitrary stabilizer states and graph…
The recently introduced tile codes are a promising alternative to surface codes, combining two-dimensional locality with higher encoding efficiency. While surface codes are well understood in terms of their logical operators and boundary…
We study the use of triorthogonal codes for universal fault-tolerant quantum computation and propose two methods to circumvent the Eastin-Knill theorem, which prohibits any single quantum error-correcting code from supporting both…
With respect to the transversal gate group (an invariant of quantum codes), we demonstrate that non-additive codes can outperform stabilizer codes. We do this by constructing spin codes that correspond to permutation-invariant multiqubit…
Quantum computing can be realized with numerous different hardware platforms and computational protocols. A highly promising approach to foster scalability is to apply a photonic platform combined with a measurement-induced quantum…
Divisible codes are defined by the property that codeword weights share a common divisor greater than one. They are used to design signals for communications and sensing, and this paper explores how they can be used to protect quantum…
Non-Clifford gates are frequently exclusively implemented on fault-tolerant architectures by first distilling magic states in specialised magic-state factories. In the rest of the architecture, the computational space, magic states can then…
This paper introduces a framework for constructing Calderbank-Shor-Steane (CSS) codes that support fault-tolerant logical transversal $Z$-rotations. Using this framework, we obtain asymptotically good CSS codes that fault-tolerantly realize…
We study the error threshold of topological color codes on Union Jack lattices that allow for the full implementation of the whole Clifford group of quantum gates. After mapping the error-correction process onto a statistical mechanical…
The topological surface code is a leading candidate for harnessing long-range entanglement to protect logical quantum information against errors, and teleportation of logical states is desirable for robust quantum information processing.…
Quantum error-correcting codes are used to protect qubits involved in quantum computation. This process requires logical operators, acting on protected qubits, to be translated into physical operators (circuits) acting on physical quantum…
By defining projective error models we study the mathematical structure of Clifford codes and stabilizer codes using tools from projective representation theory. Furthermore, we introduce a new class of codes which we have called weak…
The construction of a quantum computer remains a fundamental scientific and technological challenge, in particular due to unavoidable noise. Quantum states and operations can be protected from errors using protocols for fault-tolerant…
We derive the spectral domain properties of two-dimensional (2-D) $(\lambda_1, \lambda_2)$-constacyclic codes over $\mathbb{F}_q$ using the 2-D finite field Fourier transform (FFFT). Based on the spectral nulls of 2-D $(\lambda_1,…
Lattice surgery with two-dimensional quantum error correcting codes is among the leading schemes for fault-tolerant quantum computation, motivated by superconducting hardware architectures. In conventional lattice surgery compilation…
We provide a detailed study of the general structure of two-dimensional topological stabilizer quantum error correcting codes, including subsystem codes. Under the sole assumption of translational invariance, we show that all such codes can…
We study two-qubit circuits over the Clifford+CS gate set, which consists of the Clifford gates together with the controlled-phase gate CS=diag(1,1,1,i). The Clifford+CS gate set is universal for quantum computation and its elements can be…