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Computations with a future quantum computer will be implemented through the operations by elementary quantum gates. It is now well known that the collection of 1-bit and 2-bit quantum gates are universal for quantum computation, i.e., any…

A problem of universality in simulation of evolution of quantum system and in theory of quantum computations is related with the possibility of expression or approximation of arbitrary unitary transformation by composition of specific…

We study the quantum computational power of a generic class of anisotropic solid state Hamiltonians. A universal set of encoded logic operations are found which do away with difficult-to-implement single-qubit gates in a number of quantum…

Any unitary transformation of quantum computational networks is explicitly decomposed, in an exact and unified form, into a sequence of a limited number of one-qubit quantum gates and the two-qubit diagonal gates that have diagonal unitary…

We show that an n-th root of the Walsh-Hadamard transform (obtained from the Hadamard gate and a cyclic permutation of the qubits), together with two diagonal matrices, namely a local qubit-flip (for a fixed but arbitrary qubit) and a…

In this paper we study universality for quantum gates acting on qudits.Qudits are states in a Hilbert space of dimension d where d is at least two. We determine which 2-qudit gates V have the properties (i) the collection of all 1-qudit…

Superposed orders of quantum channels have already been proved - both theoretically and experimentally - to enable unparalleled opportunities in the quantum communication domain. As a matter of fact, superposition of orders can be exploited…

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…

A universal quantum gate is introduced for tensors of vector spaces. By using integer powers of such a gate and by using classical reversible gates one can approximate any element of the unitary group to any accuracy needed. The proof uses…

Fibonacci anyons are non-Abelian particles for which braiding is universal for quantum computation. Reichardt has shown how to systematically generate nontrivial braids for three Fibonacci anyons which yield unitary operations with…

Exchanging particles on graphs, or more concretely on networks of quantum wires, has been proposed as a means to perform fault tolerant quantum computation. This was inspired by braiding of anyons in planar systems. However, exchanges on a…

Universal quantum computation requires the implementation of arbitrary control operations on the quantum register. In most cases, this is achieved by external control fields acting selectively on each qubit to drive single-qubit operations.…

We show, within the circuit model, how any quantum computation can be efficiently performed using states with only real amplitudes (a result known within the Quantum Turing Machine model). This allows us to identify a 2-qubit (in fact…

We show that a class of quantum computations that was recently shown to be efficiently simulatable on a classical computer by Valiant corresponds to a physical model of noninteracting fermions in one dimension. We give an alternative proof…

Topological quantum computation is an implementation of a quantum computer in a way that radically reduces decoherence. Topological qubits are encoded in the topological evolution of two-dimensional quasi-particles called anyons and…

What resources are universal for quantum computation? In the standard model, a quantum computer consists of a sequence of unitary gates acting coherently on the qubits making up the computer. This paper shows that a very different model…

In quantum computation every unitary operation can be decomposed into quantum circuits-a series of single-qubit rotations and a single type entangling two-qubit gates, such as controlled-NOT (CNOT) gates. Two measures are important when…

We propose an experimentally feasible scheme to achieve quantum computation based on a pair of orthogonal cyclic states. In this scheme, quantum gates can be implemented based on the total phase accumulated in cyclic evolutions. In…

The universal quantum computation is obtained when there exists asymmetric anisotropic exchange between electron spins in coupled semiconductor quantum dots. The asymmetric Heisenberg model can be transformed into the isotropic model…

The non-adiabatic holonomic quantum computation with the advantages of fast and robustness attracts widespread attention in recent years. Here, we propose the first scheme for realizing universal single-qubit gates based on an…