相关论文: A Classification of Transversal Clifford Gates for…
Clifford algebras are used for definition of spinors. Because of using spin-1/2 systems as an adequate model of quantum bit, a relation of the algebras with quantum information science has physical reasons. But there are simple mathematical…
Division algebras have demonstrated their utility in studying non-associative algebras and their connection to the Standard Model through complex Clifford algebras. This article focuses on exploring the connection between these complex…
In this paper we investigate the encoding of operator quantum error correcting codes i.e. subsystem codes. We show that encoding of subsystem codes can be reduced to encoding of a related stabilizer code making it possible to use all the…
We analyze the structure of the logical operators from a class of quantum codes that generalizes the surface codes. These are the hypergraph product codes, restricted to the vertical sector. By generalizing an argument of Bravyi and…
This is the second in a series of "graphical grokking" papers in which we study how stabiliser codes can be understood using the ZX-calculus. In this paper we show that certain complex rules involving ZX-diagrams, called spider nest…
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…
Magic state distillation and the Shor factoring algorithm make essential use of logical diagonal gates. We introduce a method of synthesizing CSS codes that realize a target logical diagonal gate at some level $l$ in the Clifford hierarchy.…
We propose a scheme that converts a stabilizer code into another stabilizer code in a fault tolerant manner. The scheme first puts both codes in specific forms, and proceeds the conversion from a source code to a target code by applying…
First, a canonical form for stabilizer parity check matrices of arbitrary size and rank is derived. Next, it is shown that the closely related canonical form of the Clifford group can be computed in time $O(n^3)$ for $n$ qubits, which…
Typical stabilizer codes aim to solve the general problem of fault-tolerance without regard for the structure of a specific system. By incorporating a broader representation-theoretic perspective, we provide a generalized framework that…
We provide a complete classification of Clifford quantum cellular automata (QCAs) on arbitrary metric spaces and any qudits (of prime or composite dimensions) in terms of algebraic L-theory. Building on the delooping formalism of Pedersen…
In quantum coding theory, stabilizer codes are probably the most important class of quantum codes. They are regarded as the quantum analogue of the classical linear codes and the properties of stabilizer codes have been carefully studied in…
For every integer $r\geq 2$ and every $\epsilon>0$, we construct an explicit infinite family of quantum LDPC codes supporting a transversal $C^{r-1}Z$ gate with length $N$, dimension $K\geq N^{1-\epsilon}$, distance $D\geq…
We describe stabilizer states and Clifford group operations using linear operations and quadratic forms over binary vector spaces. We show how the n-qubit Clifford group is isomorphic to a group with an operation that is defined in terms of…
We show that the Clifford gates and stabilizer circuits in the quantum computing literature, which admit efficient classical simulation, are equivalent to affine signatures under a unitary condition. The latter is a known class of tractable…
The stabilizer formalism for quantum error-correcting codes has been, without doubt, the most successful at producing examples of quantum codes with strong error-correcting properties. In this paper, we discuss strong automorphism groups of…
Motivated by their central role in fault-tolerant quantum computation, we study the sets of gates of the third-level of the Clifford hierarchy and their distinguished subsets of `nearly diagonal' semi-Clifford gates. The Clifford hierarchy…
The Clifford Hierarchy has been a central topic in quantum computation due to its strong connections with fault-tolerant quantum computation, magic state distillation, and more. Nevertheless, only sections of the hierarchy are fully…
We design flexible fault tolerant gate gadgets that allow the data and the ancilla to be encoded using different codes. By picking a stabilizer code for the ancilla we are able to perform both Clifford and non-Clifford gates fault…
Quantum error correction is believed to be essential for scalable quantum computation, but its implementation is challenging due to its considerable space-time overhead. Motivated by recent experiments demonstrating efficient manipulation…