Related papers: Generalised Clifford groups and simulation of asso…
In this article we investigate the possibility of encoding classical information onto multipartite quantum states in the distant laboratory framework. We show that for all states generated by Clifford operation there always exist such an…
By the Gottesman-Knill Theorem, the outcome probabilities of Clifford circuits can be computed efficiently. We present an alternative proof of this result for quopit Clifford circuits (i.e., Clifford circuits on collections of $p$-level…
Unitary t-designs are some of the most versatile tools in quantum information theory. Their applications range from randomized benchmarking and shadow tomography, to more fundamental ones such as emulating quantum chaos and establishing…
The Bernstein-Vazirani (BV) algorithm is frequently taught as a canonical example of quantum parallelism, yet the standard interference-based explanation often obscures its underlying simplicity. We present a geometric reframing in which…
The classical simulation of quantum dynamics plays an important role in our understanding of quantum complexity, and in the development of quantum technologies. Efficient techniques such as those based on the Gottesman-Knill theorem for…
Quantum magic is a necessary resource for quantum computers to be not efficiently simulable by classical computers. Previous results have linked the amount of quantum magic, characterized by the number of $T$ gates or stabilizer rank, to…
We propose an efficient scheme for verifying quantum computations in the `high complexity' regime i.e. beyond the remit of classical computers. Previously proposed schemes remarkably provide confidence against arbitrarily malicious…
Motivated by a connection, described here for the first time, between the hidden normal subgroup problem (HNSP) and abelian hypergroups (algebraic objects that model collisions of physical particles), we develop a stabilizer formalism using…
We provide a generalized definition for the quantized Clifford algebra introduced by Hayashi using another parameter $k$ that we call the twist. For a field of characteristic not equal to $2$, we provide a basis for our quantized Clifford…
We develop quantum information processing primitives for the planar rotor, the state space of a particle on a circle. By interpreting rotor wavefunctions as periodically identified wavefunctions of a harmonic oscillator, we determine the…
We study the algebra of complex polynomials which remain invariant under the action of the local Clifford group under conjugation. Within this algebra, we consider the linear spaces of homogeneous polynomials degree by degree and construct…
The quantum Schur transform is a fundamental building block that maps the computational basis to a coupled basis consisting of irreducible representations of the unitary and symmetric groups. Equivalently, it may be regarded as a change of…
Knill introduced a generalization of stabilizer codes, in this note called Clifford codes. It remained unclear whether or not Clifford codes can be superior to stabilizer codes. We show that Clifford codes are stabilizer codes provided that…
Due to the technical difficulty of building large quantum computers, it is important to be able to estimate how faithful a given implementation is to an ideal quantum computer. The common approach of completely characterizing the…
The non commuting matrix elements of matrices from quantum group $GL_q(2;C)$ with $q\equiv \omega $ being the $n$-th root of unity are given a representation as operators in Hilbert space with help of $C_4^{(n)}$ generalized Clifford…
We start by studying the subgroup structures underlying stabilizer circuits and we use our results to propose a new normal form for stabilizer circuits. This normal form is computed by induction using simple conjugation rules in the…
Symmetries of the finite Heisenberg group represent an important tool for the study of deeper structure of finite-dimensional quantum mechanics. As is well known, these symmetries are properly expressed in terms of certain normalizer. This…
In this work, we develop a graphical calculus for multi-qudit computations with generalized Clifford algebras, building off the algebraic framework developed in our prior work. We build our graphical calculus out of a fixed set of graphical…
Recently developed quantum algorithms suggest that quantum computers can solve certain problems and perform certain tasks more efficiently than conventional computers. Among other reasons, this is due to the possibility of creating…
Recent studies have highlighted the combination of tensor network methods and the stabilizer formalism as a very effective framework for simulating quantum many-body systems, encompassing areas from ground state to time evolution…