Related papers: Extending matchgates into universal quantum comput…

The notion of quantum matrix pairs is defined. These are pairs of matrices with non-commuting entries, which have the same pattern of internal relations, q-commute with each other under matrix multiplication, and are such that products of…

We propose an encoding for topological quantum computation utilizing quantum representations of mapping class groups. Leakage into a non-computational subspace seems to be unavoidable for universality in general. We are interested in the…

Simulating quantum physics with a device which itself is quantum mechanical, a notion Richard Feynman originated, would be an unparallelled computational resource. However, the universal quantum simulation of fermionic systems is daunting…

Say a collection of $n$-qu$d$it gates $\Gamma$ is eventually universal if and only if there exists $N_0 \geq n$ such that for all $N \geq N_0$, one can approximate any $N$-qu$d$it unitary to arbitrary precision by a circuit over $\Gamma$.…

The most general structure (in matrix form) of a single-qubit gate is presented. Subsequently, used that to obtain a set of conditions for testing (a) whether a given 2-qubit gate is genuinely a 2-qubit gate, i.e., not decomposable into two…

Quantum Fourier gates (QFG) constitute a family of quantum gates that result from an exact combination of the quantum Fourier transform (QFT) and the SWAP gate. As a direct consequence of this, the Feynman gate is a particular case of that…

Matrix powering is a fundamental computational primitive in linear algebra. It has widespread applications in scientific computing and engineering, and underlies the solution of time-homogeneous linear ordinary differential equations,…

In this paper, we firstly briefly review the duality quantum computer. Distinctly, the generalized quantum gates, the basic evolution operators in a duality quantum computer are no longer unitary, and they can be expressed in terms of…

The SWAP gate plays a central role in network designs for qubit quantum computation. However, there is a view to generalize qubit quantum computing to higher dimensional quantum systems. In this paper we construct a generalized SWAP gate…

We introduce group surface codes, which are a natural generalization of the $\mathbb{Z}_2$ surface code, and equivalent to quantum double models of finite groups with specific boundary conditions. We show that group surface codes can be…

Qubits are neither fermions nor bosons. A Fock space description of qubits leads to a mapping from qubits to parafermions: particles with a hybrid boson-fermion quantum statistics. We study this mapping in detail, and use it to provide a…

We present a quantum SWAP gate valid for quantum systems of an arbitrary dimension. The gate generalizes the CNOT implementation of the SWAP gate for qubits and keeps its most important properties, like symmetry and simplicity. We only use…

We relax one of the requirements for topological quantum computation with Majorana fermions. Topological quantum computation was discussed so far as manipulation of the wave function within degenerate many body ground state. The simplest…

Non-invertible symmetries of a quantum field theory (QFT) are a natural generalization of unitary symmetries, but in which the product of operators does not satisfy a group multiplication law. We show that such symmetry operations on states…

An algorithm is proposed to convert arbitrary unitary matrix to a sequence of $X$ gates and fully controlled $R_y, R_z$ and $R_1$ gates. This algorithm is used to generate Q# implementation for arbitrary unitary matrix. Some optimizations…

Universal quantum computation can be realised using both continuous-time and discrete-time quantum walks. We present a version based on single particle discrete-time quantum walk to realize multi-qubit computation tasks. The scalability of…

We prove the existence of a class of two--input, two--output gates any one of which is universal for quantum computation. This is done by explicitly constructing the three--bit gate introduced by Deutsch [Proc.~R.~Soc.~London.~A {\bf 425},…

Quantum computation has revolutionary potential for speeding algorithms and for simulating quantum systems such as molecules. We report here a quantum computer design that performs universal quantum computation within a single…

Realizing the theoretical promise of quantum computers will require overcoming decoherence. Here we demonstrate numerically that high fidelity quantum gates are possible within a framework of quantum dynamical decoupling. Orders of…

Full connectivity of qubits is necessary for most quantum algorithms, which is difficult to directly implement on Noisy Intermediate-Scale Quantum processors. However, inserting swap gate to enable the two-qubit gates between uncoupled…