Showing papers on "Quantum gate published in 1995"
TL;DR: U(2) gates are derived, which derive upper and lower bounds on the exact number of elementary gates required to build up a variety of two- and three-bit quantum gates, the asymptotic number required for n-bit Deutsch-Toffoli gates, and make some observations about the number of unitary operations on arbitrarily many bits.
Abstract: We show that a set of gates that consists of all one-bit quantum gates (U(2)) and the two-bit exclusive-or gate (that maps Boolean values (x,y) to (x,x ⊕y)) is universal in the sense that all unitary operations on arbitrarily many bits n (U(2 n )) can be expressed as compositions of these gates. We investigate the number of the above gates required to implement other gates, such as generalized Deutsch-Toffoli gates, that apply a specific U(2) transformation to one input bit if and only if the logical AND of all remaining input bits is satisfied. These gates play a central role in many proposed constructions of quantum computational networks. We derive upper and lower bounds on the exact number of elementary gates required to build up a variety of two- and three-bit quantum gates, the asymptotic number required for n-bit Deutsch-Toffoli gates, and make some observations about the number required for arbitrary n-bit unitary operations.
4,758 citations
TL;DR: A quantum computer can be implemented with cold ions confined in a linear trap and interacting with laser beams, where decoherence is negligible, and the measurement can be carried out with a high efficiency.
Abstract: A quantum computer can be implemented with cold ions confined in a linear trap and interacting with laser beams. Quantum gates involving any pair, triplet, or subset of ions can be realized by coupling the ions through the collective quantized motion. In this system decoherence is negligible, and the measurement (readout of the quantum register) can be carried out with a high efficiency.
4,269 citations
TL;DR: The operation of a two-bit "controlled-NOT" quantum logic gate is demonstrated, which, in conjunction with simple single-bit operations, forms a universal quantum logic Gate for quantum computation.
Abstract: We demonstrate the operation of a two-bit "controlled-NOT" quantum logic gate, which, in conjunction with simple single-bit operations, forms a universal quantum logic gate for quantum computation. The two quantum bits are stored in the internal and external degrees of freedom of a single trapped atom, which is first laser cooled to the zero-point energy. Decoherence effects are identified for the operation, and the possibility of extending the system to more qubits appears promising.
1,827 citations
IBM1
TL;DR: 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.
Abstract: 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 universality of three-bit gates, by analogy to the universality of the Toffoli three-bit gate of classical reversible computing. Two-bit quantum gates may be implemented by magnetic resonance operations applied to a pair of electronic or nuclear spins. A ``gearbox quantum computer'' proposed here, based on the principles of atomic-force microscopy, would permit the operation of such two-bit gates in a physical system with very long phase-breaking (i.e., quantum-phase-coherence) times. Simpler versions of the gearbox computer could be used to do experiments on Einstein-Podolsky-Rosen states and related entangled quantum states.
1,329 citations
TL;DR: A simple quantum logic gate, the quantum controlled-NOT, is described, and two possible physical realizations of the gate are discussed, one based on Ramsey atomic interferometry and the other on the selective driving of optical resonances of two subsystems undergoing a dipole-dipole interaction.
Abstract: Quantum logic gates provide fundamental examples of conditional quantum dynamics. They could form the building blocks of general quantum information processing systems which have recently been shown to have many interesting nonclassical properties. We describe a simple quantum logic gate, the quantum controlled-NOT, and analyze some of its applications. We discuss two possible physical realizations of the gate, one based on Ramsey atomic interferometry and the other on the selective driving of optical resonances of two subsystems undergoing a dipole-dipole interaction.
1,053 citations
TL;DR: Almost any quantum logic gate with two or more inputs is computationally universal in that copies of the gate can be "wired together" to effect any desired logic circuit, and to perform any desired unitary transformation on a set of quantum variables.
Abstract: It is shown that if one can apply some Hamiltonian repeatedly to a few variables at a time one can in general effect any desired unitary time evolution on an arbitrarily large number of variables. As a result, almost any quantum logic gate with two or more inputs is computationally universal in that copies of the gate can be ``wired together'' to effect any desired logic circuit, and to perform any desired unitary transformation on a set of quantum variables.
794 citations
TL;DR: This work identifies a 2-bit quantum gate that is sufficient to build any quantum logic network and proposes an explicit construction of this gate, which is based on cavity QED techniques and may be realizable with current technology.
Abstract: We identify a 2-bit quantum gate that is sufficient to build any quantum logic network. The existence of such a 2-bit universal gate considerably simplifies the search for physical realizations of quantum computational networks. We propose an explicit construction of this gate, which is based on cavity QED techniques and may be realizable with current technology.
566 citations
TL;DR: In this article, it was shown that in quantum computation, almost every gate that operates on two or more bits is a universal gate and discussed various physical considerations bearing on the proper definition of universality for computational components such as logic gates.
Abstract: We show that in quantum computation almost every gate that operates on two or more bits is a universal gate. We discuss various physical considerations bearing on the proper definition of universality for computational components such as logic gates.
449 citations
Journal Article•
34 citations
TL;DR: In this article, the sixteen distinct truth tables of classical logic are shown to be contained in the 8! reversible logic operations covered by the symmetric group S8, which permute the eight values of three logical variables.
Abstract: Embedding logical operations in non-dissipative physical processes requires the use of reversible logic. Following Feynman's (1986) approach, the sixteen distinct truth tables of classical logic are shown to be contained in the 8! reversible logic operations covered by the symmetric group S8, which permute the eight values of three logical variables. Small subgroups of S8 are shown to cover, respectively, reversible logic, reversible switching and reversible arithmetic. A new universal primitive is found which generates a covering group of reversible logic. It is shown that the octahedral group in four dimensions covers both reversible logic and switching and, hence, that the orthogonal group O(4) provides a covering group for quantum gates.
5 citations
TL;DR: The Fredkin gate is constructed using a combination of six two-body reversible (quantum) operators to do universal computation using reversible two-bit gates only.
Abstract: The Fredkin three-bit gate is universal for computational logic, and is reversible. Classically, it is impossible to do universal computation using reversible two-bit gates only. Here we construct the Fredkin gate using a combination of six two-body reversible (quantum) operators.
TL;DR: In this paper, the existence of a class of two-input, two-output (2oE) gates for quantum computation has been proved by explicitly constructing the three-bit gate introduced by Deutsch as a network consisting of replicas of a single 2oE gate.
Abstract: 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. Lond. A 425, 73 (1989)) as a network consisting of replicas of a single two-bit gate.
TL;DR: A simple scheme for a universal two-bit quantum logic gate using circular Rydberg atoms and a superconducting millimeter-wave cavity is presented.
Abstract: We present a simple scheme for a universal two-bit quantum logic gate using circular Rydberg atoms and a superconducting millimeter-wave cavity. We analyze in detail the performances of this gate, using the parameters of an experiment currently under way in our laboratory.