Related papers: Quantum gates and quantum algorithms with Clifford…
Quantum computing carries significant potential for addressing practical problems. However, currently available quantum devices suffer from noisy quantum gates, which degrade the fidelity of executed quantum circuits. Therefore, quantum…
A real representation theory of real Clifford algebra has been studied in further detail, especially in connection with Fierz identities. As its application, we have constructed real octonion algebras as well as related octonionic triple…
We construct a class of topological quantum codes to perform quantum entanglement distillation. These codes implement the whole Clifford group of unitary operations in a fully topological manner and without selective addressing of qubits.…
Finite projective geometries, especially the Fano plane, have been observed to arise in the context of certain quantum gate operators. We use Clifford algebras to explain why these geometries, both planar and higher dimensional, appear in…
Using a technique \cite{holgernorma2002} to construct a basis for spinors and ``families'' of spinors in terms of Clifford algebra objects, we define other Clifford algebra objects, which transform the state of one ''family'' of spinors…
Using electrostatic gates to control the electron positions, we present a new controlled-NOT gate based on quantum dots. The qubit states are chosen to be the spin states of an excess conductor electron in the quantum dot; and the main…
Quantum information science strives to leverage the quantum-mechanical nature of our universe in order to achieve large improvements in certain information processing tasks. In deep-space optical communications, current receivers for the…
We give a pair of algorithms that efficiently learn a quantum state prepared by Clifford gates and $O(\log n)$ non-Clifford gates. Specifically, for an $n$-qubit state $|\psi\rangle$ prepared with at most $t$ non-Clifford gates, our…
We describe an efficient quantum algorithm for the quantum Schur transform. The Schur transform is an operation on a quantum computer that maps the standard computational basis to a basis composed of irreducible representations of the…
Achieving near-term quantum advantage will require accurate estimation of quantum observables despite significant hardware noise. For this purpose, we propose a novel, scalable error-mitigation method that applies to gate-based quantum…
Modern advances in general-purpose computer algebra systems offer solutions to a variety of problems, which in the past required substantial time investments by trained mathematicians. An excellent example of such development are the…
The paper is devoted to projective Clifford groups of quantum $N$-dimensional systems. Clearly, Clifford gates allow only the simplest quantum computations which can be simulated on a classical computer (Gottesmann-Knill theorem). However,…
The Wigner function formalism has played a pivotal role in examining the non-classical aspects of quantum states and their classical simulatability. Nevertheless, its application in qubit systems faces limitations due to negativity induced…
We investigate the construction and properties of Clifford algebras by a similar manner as our previous construction of the octonions, namely as a twisting of group algebras of Z_2^n by a cocycle. Our approach is more general than the usual…
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…
This paper is meant to be an informative introduction to spinor representations of Clifford algebras. In this paper we will have a look at Clifford algebras and the octonion algebra. We begin the paper looking at the quaternion algebra…
One particular approach to quantum groups (matrix pseudo groups) provides the Manin quantum plane. Assuming an appropriate set of non-commuting variables spanning linearly a representation space one is able to show that the endomorphisms on…
Clifford algebras have broad applications in science and engineering. The use of Clifford algebras can be further promoted in these fields by availability of computational tools that automate tedious routine calculations. We offer an…
This paper describes a novel approach to emulate a universal quantum computer with a wholly classical system, one that uses a signal of bounded duration and amplitude to represent an arbitrary quantum state. The signal may be of any…
We describe a new method for approximating an arbitrary $n$ qubit unitary with precision $\varepsilon$ using a Clifford and T circuit with $O(4^{n}n(\log(1/\varepsilon)+n))$ gates. The method is based on rounding off a unitary to a unitary…