Related papers: Standard Form of Qudit Stabilizer Groups
This paper investigates the relation between linear codes and the stabilizer in ${\rm GL}_2(\mathbb{C})$ of their weight enumerators. We prove a result on the finiteness of stabilizers and give a complete classification of linear codes with…
CSS codes are a subfamily of stabilizer codes especially appropriate for fault-tolerant quantum computations. A very simple method is proposed to encode a general qudit when a Calderbank-Shor-Steane quantum code, defined over a q-ary…
Verifying prepared quantum states is crucial for hybrid systems whose subsystems may have different local dimensions. We present a generalized stabilizer framework and associated test that apply to general multi-qudit states, including…
The challenge of quantum computing is to combine error resilience with universal computation. Diagonal gates such as the transversal $T$ gate play an important role in implementing a universal set of quantum operations. This paper…
We investigate the emergence of quantum complexity and chaos in doped Clifford circuits acting on qudits of odd prime dimension $d$. Using doped Clifford Weingarten calculus and a replica tensor network formalism, we derive exact results…
Stabilizer codes are a powerful method for implementing fault-tolerant quantum memory and in the case of topological codes, they form useful models for topological phases of matter. In this paper, we discuss the theory of stabilizer codes…
For a quantum computer acting on d-dimensional systems, we analyze the computational power of circuits wherein stabilizer operations are perfect and we allow access to imperfect non-stabilizer states or operations. If the noise rate…
We present a general protocol for stabilizer measurements and pumping in a system of N superconducting qubits. We assume always-on, equal dispersive couplings to a single mode of a high-Q microwave resonator in the ultra-strong dispersive…
We show how to perform scalable fault-tolerant non-Clifford gates in two dimensions by introducing domain walls between the surface code and a non-Abelian topological code whose codespace is stabilized by Clifford operators. We formulate a…
Quantum error correction is an important ingredient for scalable quantum computing. Stabilizer codes are one of the most promising and straightforward ways to correct quantum errors, are convenient for logical operations, and improve…
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…
We present an entirely 2D transversal realization of phase gates at any level of the Clifford hierarchy, and beyond, using non-Abelian surface codes. Our construction encodes a logical qubit in the quantum double $D(G)$ of a non-Abelian…
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…
In this work we improve the runtime of recent classical algorithms for strong simulation of quantum circuits composed of Clifford and T gates. The improvement is obtained by establishing a new upper bound on the stabilizer rank of $m$…
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…
Symmetry is at the heart of coding theory. Codes with symmetry, especially cyclic codes, play an essential role in both theory and practical applications of classical error-correcting codes. Here we examine symmetry properties for codeword…
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…
New stabilizer codes with parameters better than the ones available in the literature are provided in this work, in particular quantum codes with parameters $[[127,63, \geq 12]]_2$ and $[[63,45, \geq 6]]_4$ that are records. These codes are…
Amongst quantum error-correcting codes the surface code has remained of particular promise as it has local and very low-weight checks, even despite only encoding a single logical qubit no matter the lattice size. In this work we discuss new…
We study subsystem codes whose gauge group has local generators in the 2D geometry. It is shown that there exists a family of such codes defined on lattices of size LxL with the number of logical qubits k and the minimum distance d both…