Related papers: Quantum $\mathcal{R}$-matrices as universal qubit …
A universal set of gates for (classical or quantum) computation is a set of gates that can be used to approximate any other operation. It is well known that a universal set for classical computation augmented with the Hadamard gate results…
We describe a method for achieving arbitrary 1-qubit gates and controlled-NOT gates within the context of the Single Cooper Pair Box (SCB) approach to quantum computing. Such gates are sufficient to support universal quantum computation.…
The central object of the quantum algebraic approach to the study of quantum integrable models is the universal $R$-matrix, which is an element of a completed tensor product of two copies of quantum algebra. Various integrability objects…
A proof is given, which relies on the commutator algebra of the unitary Lie groups, that quantum gates operating on just two bits at a time are sufficient to construct a general quantum circuit. The best previous result had shown the…
We discuss possible applications of the 1-D direct and inverse scattering problem to design of universal quantum gates for quantum computation. The potentials generating some universal gates are described.
Fundamental matrix operations and solving linear systems of equations are ubiquitous in scientific investigations. Using the "Sender-Receiver" model, we propose quantum algorithms for matrix operations such as matrix-vector product,…
Arbitrarily accurate fault-tolerant (FT) universal quantum computation can be carried out using the Clifford gates Z, S, CNOT plus the non-Clifford T gate. Moreover, a recent improvement of the Solovay-Kitaev theorem by Kuperberg implies…
Quantum walk has been regarded as a primitive to universal quantum computation. By using the operations required to describe the single particle discrete-time quantum walk on a position space we demonstrate the realization of the universal…
Quantum computers hold great promise, but it remains a challenge to find efficient quantum circuits that solve interesting computational problems. We show that finding optimal quantum circuits is essentially equivalent to finding the…
We propose to represent both $n$--qubits and quantum gates acting on them as elements in the complex Clifford algebra defined on a complex vector space of dimension $2n.$ In this framework, the Dirac formalism can be realized in…
I give analytical estimates and numerical simulation results for the performance of Kitaev's 2d topological error-correcting codes. By providing methods for the execution of an encoded three-qubit Toffoli gate, I complete a universal gate…
The gate version of quantum computation exploits several quantum key resources as superposition and entanglement to reach an outstanding performance. In the way, this theory was constructed adopting certain supposed processes imitating…
Topological states of matter are promising resources for composing fault-tolerant quantum computers, advancing beyond the limitations of current noisy intermediate-scale quantum devices. To enable this progress, a deep understanding of…
Optimal quantum machines can be implemented by linear projective operations. In the present work a general qubit symmetrization theory is presented by investigating the close links to the qubit purification process and to the programmable…
There are various gate sets that can be used to describe a quantum computation. A particularly popular gate set in the literature on quantum computing consists of arbitrary single-qubit gates and 2-qubit CNOT gates. A CNOT gate is however…
Within the general context of the architecture in quantum computer design, this paper aims is to provide a general strategy to obtain a block-matrix representation of quantum gates applied to qubits placed in arbitrary positions over an…
Measurement-based quantum computation describes a scheme where entanglement of resource states is utilized to simulate arbitrary quantum gates via local measurements. Recent works suggest that symmetry-protected topologically non-trivial,…
Variational quantum algorithms dominate contemporary gate-based quantum enhanced optimisation, eigenvalue estimation and machine learning. Here we establish the quantum computational universality of variational quantum computation by…
We present an idealized model involving interacting quantum dots that can support both the dynamical and geometrical forms of quantum computation. We show that by employing a structure similar to the one used in the Aharonov-Bohm effect we…
Constructing appropriate unitary matrix operators for new quantum algorithms and finding the minimum cost gate sequences for the implementation of these unitary operators is of fundamental importance in the field of quantum information and…