By removing a C atom from the tetrahedral configuration of the diamond, replacing it by a C atom, and repeating this in a linear direction, it is possible to have a linear chain of nuclear spins one half and to build a solid state quantum computer. One qubit rotation, controlled-not (CNOT) and controlled-controlled-not (CCNOT) quantum gates are obtained immediately from this configuration. CNOT...

We derive an explicit Hamiltonian for copying the basis up and down states of a quantum two-state system—a qubit—onto n " copy " qubits (n ≥ 1) initially all prepared in the down state. In terms of spin components , for spin-1 2 particle spin states, the resulting Hamiltonian involves n-and (n + 1)-spin interactions. The case n = 1 also corresponds to a quantum-computing controlled-NOT gate.

We describe the construction of a conditional quantum control-not (CNOT) gate from linear optical elements following the program of Knill, Laflamme and Milburn [Nature 409, 46 (2001)]. We show that the basic operation of this gate can be tested using current technology. We then simplify the scheme significantly.

We provide several schemes to construct the continuous-variable SWAP gate and present a Hermitian generalized many-body continuous controlled-NOT gate. We introduce and study the hybrid controlled-NOT gate and controlledSWAP gate, and their physical realizations are discussed in trapped-ion systems. These continuous-variable and hybrid quantum gates may be used in the corresponding continuous-v...

Implementing a unitary operation using a universal gate set is a fundamental problem in quantum computing. The problem naturally arises when we want to implement some quantum algorithm on a fault tolerant quantum computer. Most fault tolerant protocols allow one to implement only Clifford circuits (those generated by CNOT, Hadamard and Phase gates). To achieve universal quantum computation one ...

A new modified version of the Oxford purification protocol is proposed. This version is based on the controlled-controlled NOT gate instead of controlled NOT in the original one. Comparisons between the results of the new version and the original and an earlier modification are given. It is found that the new version converges faster and consumes fewer initial qubit pairs of low fidelity per fi...

In the comment [1], Zanardi and Rasetti argue that several claims in our recent letter [2] are questionable. Here we show these claims remain true. Our points are that (i) the Hamiltonian (1) in Ref. [2] describes amplitude damping as well as phase damping; (ii) the free-Hamiltonian-elimination (FHE) has feasible implementation in practice and there exists a simple FHE procedure which is design...

We derive an exact and explicit Kraus decomposition for the reduced density of a quantum system simultaneously interacting with time-dependent external fields and a chaotic environment of thermodynamic dimension. We test the accuracy of the Kraus decomposition against exact numerical results for a CNOT gate performed on two qubits of an (N+2)-qubit statically flawed isolated quantum computer. H...

We report on an all-optical AND-gate using simultaneous Four-Wave Mixing (FWM) and Cross-Gain Modulation (XGM) in a semiconductor optical amplifier (SOA). The operation of the proposed AND gate is simulated and the results demonstrate its effectiveness. This AND gate could provide a new possibility for all-optical computing and all-optical routing in future all-optical networks. In an AND ( AB ...

We give a finite presentation by generators and relations of unitary operators expressible over the {CNOT, T, X} gate set, also known as CNOT-dihedral operators. To this end, we introduce a notion of normal form for CNOT-dihedral circuits and prove that every CNOT-dihedral operator admits a unique normal form. Moreover, we show that in the presence of certain structural rules only finitely many...