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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 computing has attracted much attention in recent decades, since it is believed to solve certain problems substantially faster than traditional computing methods. Theoretically, such an advance can be obtained by networks of the…

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…

Quantum simulators, machines that can replicate the dynamics of quantum systems, are being built as useful devices and are seen as a stepping stone to universal quantum computers. A key difference between the two is that computers have the…

Quantum gates are the building blocks of quantum circuits, which in turn are the cornerstones of quantum information processing. In this work, we theoretically investigate a single-step implementation of both a universal two- (CNOT) and…

We present protocols for implementation of universal quantum gates on an arbitrary superposition of quantum states in a scalable solid-state Ising spin quantum computer. The spin chain is composed of identical spins 1/2 with the Ising…

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…

Most quantum computer realizations require the ability to apply local fields and tune the couplings between qubits, in order to realize single bit and two bit gates which are necessary for universal quantum computation. We present a scheme…

We present a nonlocal construction of universal gates by means of holonomic (geometric) quantum teleportation. The effect of the errors from imperfect control of the classical parameters, the looping variation of which builds up holonomic…

We offer an alternative to the conventional network formulation of quantum computing. We advance the analog approach to quantum logic gate/circuit construction. As an illustration, we consider the spatially extended NOT gate as the first…

In this paper we study the ways to use a global entangling operator to efficiently implement circuitry common to a selection of important quantum algorithms. In particular, we focus on the circuits composed with global Ising entangling…

Quantum gates, that play a fundamental role in quantum computation and other quantum information processes, are unitary evolution operators $\hat U$ that act on a composite system changing its entanglement. In the present contribution we…

A quantum computer based on an asymmetric coupled dot system has been proposed and shown to operate as the controlled-NOT-gate. The basic idea is (1) the electron is localized in one of the asymmetric coupled dots. (2)The electron transfer…

An essential element of classical computation is the "if-then" construct, that accepts a control bit and an arbitrary gate, and provides conditional execution of the gate depending on the value of the controlling bit. On the other hand,…

We have shown that quantum systems on finite-dimensional Hilbert spaces are equivalent under local transformations. Using these transformations give rise to a gauge group that connects the hamiltonian operators associated with each quantum…

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…

In conventional circuit-based quantum computing architectures, the standard gate set includes arbitrary single-qubit rotations and two-qubit entangling gates. This choice is not always aligned with the native operations available in certain…

Quantum computing employs controllable interactions to perform sequences of logical gates and entire algorithms on quantum registers. This paradigm has been widely explored, e.g., for simulating dynamics of manybody systems by decomposing…

Quantum computation is based on implementing selected unitary transformations which represent algorithms. A generalized optimal control theory is used to find the driving field that generates a prespecified unitary transformation. The…

Hamiltonian quantum gates controlled by classical electromagnetic fields form the basis of any realistic model of quantum computers. In this letter, we derive a lower bound on the field energy required to implement such gates and relate…