相关论文: Un-Weyl-ing the Clifford Hierarchy

In fault-tolerant quantum computation and quantum error-correction one is interested on Pauli matrices that commute with a circuit/unitary. We provide a fast algorithm that decomposes any Clifford gate as a $\textit{minimal}$ product of…

We have generalized the well-known statement that the Clifford group is a unitary 3-design into symmetric cases by extending the notion of unitary design. Concretely, we have proven that a symmetric Clifford group is a symmetric unitary…

We study a scheme to implement an asymptotic unitary 3-design. The scheme implements a random Pauli once followed by the implementation of a random transvection Clifford by using state twirling. Thus the scheme is implemented in the form of…

The representation theory of the Clifford group is playing an increasingly prominent role in quantum information theory, including in such diverse use cases as the construction of protocols for quantum system certification, quantum…

We study locality preserving automorphisms of operator algebras on $D$-dimensional uniform lattices of prime $p$-dimensional qudits (QCA), specializing in those that are translation invariant (TI) and map every prime $p$-dimensional Pauli…

Unitary $k$-designs are finite ensembles of unitary matrices that approximate the Haar distribution over unitary matrices. Several ensembles are known to be 2-designs, including the uniform distribution over the Clifford group, but no…

We constrain a broad class of teleportation protocols using insights from locality. In the "standard" teleportation protocols we consider, all outcome-dependent unitaries are Pauli operators conditioned on linear functions of the…

The Clifford group is a fundamental structure in quantum information with a wide variety of applications. We discuss the tensor representations of the $q$-qubit Clifford group, which is defined as the normalizer of the $q$-qubit Pauli group…

How much does local and time-periodic dynamics resemble a random unitary? In the present work we address this question by using the Clifford formalism from quantum computation. We analyse a Floquet model with disorder, characterised by a…

The n-qubit Pauli group and its normalizer the n-qubit Clifford group have applications in quantum error correction and device characterization. Recent applications have made use of the representation theory of the Clifford group. We apply…

We propose a mathematical framework that we call quantum, higher-order Fourier analysis. This generalizes the classical theory of higher-order Fourier analysis, which led to many advances in number theory and combinatorics. We define a…

A fundamental problem in fault-tolerant quantum computation is the tradeoff between universality and dimensionality, exemplified by the the Bravyi-K\"onig bound for $n$-dimensional topological stabilizer codes. In this work, we extend…

We introduce the magic hierarchy, a quantum circuit model that alternates between arbitrary-sized Clifford circuits and constant-depth circuits with two-qubit gates ($\textsf{QNC}^0$). This model unifies existing circuit models, such as…

Let ${\mathcal O}$ be an involutive discrete valuation ring with residue field of characteristic not 2. Let $A$ be a quotient of ${\mathcal O}$ by a nonzero power of its maximal ideal and let $*$ be the involution that $A$ inherits from…

Clifford quantum circuits are elementary invertible transformations of quantum systems that map Pauli operators to Pauli operators. We study periodic one-parameter families of Clifford circuits, called loops of Clifford circuits, acting on…

The non-linear binary Kerdock codes are known to be Gray images of certain extended cyclic codes of length $N = 2^m$ over $\mathbb{Z}_4$. We show that exponentiating these $\mathbb{Z}_4$-valued codewords by $\imath \triangleq \sqrt{-1}$…

We consider a model of quantum computation in which the set of elementary operations is limited to Clifford unitaries, the creation of the state $|0\rangle$ computational basis. In addition, we allow the creation of a one-qubit ancilla in a…

NOTE: PAPER WITHDRAWN (See Comments) The Clifford and Local Clifford groups for $d > 2$ dimensional systems have been topics of recent interest due to their applications in graph states, quantum codes, and possible applications in fast…

Here is discussed generalization of Clifford algebras, l^n-dimensional Weyl-Clifford algebras T(n,l) with n generators t_k satisfying equation $(\sum_{k=1}^n a_k t_k)^l = \sum_{k=1}^n a_k^l$. It is originated from two basic and well known…

When visualised as an operation on the Bloch sphere, the qubit "pi-over-eight" gate corresponds to one-eighth of a complete rotation about the vertical axis. This simple gate often plays an important role in quantum information theory,…