Adriano Barenco. A universal two-bit gate for quantum computation. Proc. R.Soc. Lond. A, 449:679-683, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of unitary transformations on quantum state. It is thought of, after initialisation, as achieving all superposed evolutions simultaneously, which provides much of the reason for quantum computation s eciency. Again, evolution is feasible: it may be implemented using universal quantum gates [3, 9]. For example on B , after initialisation, evolution by the Hadamard transformation H 1 results in = 0 (because H 1 is not only unitary but equal to its own conjugate transpose and so self inverse) Thus our de nition of initialisation does not exclude setting state to equal 0 (or any other ....

Adriano Barenco. A universal two-bit gate for quantum computation. Proc. R.Soc. Lond. A, 449:679-683, 1995.

....be built from them, which means that they can simulate (approximately) any unitary transformation on an arbitrary number of qubits. The first universal quantum gate which operates on three qubits was identified by Deutsch[Deu89] After a long sequence of works on universal quantum gates [DiV95, Bar95, DBE95, Llo95, BBC 95, Sho96, KLZ96, Kit97] Boykin et al. BMP 99] have recently shown that the set consisting of a Hadamard gate, a c NOT gate, and a phase rotation gate of angle =4 is universal. In order to form a practical basis for quantum computation, a universal set must also be ....

A. Barenco. A universal two-bit gate for quantum computation. In Proc. Roy. Soc. London, Ser. A, 449, pp. 679--683, 1995.

....of gates can be built from them, which means that they can simulate (approximately) any unitary transformation on an arbitrary number of qubits. The first universal quantum gate which operates on three qubits was identified by Deutsch[14] After a long sequence of work on universal quantum gates [17, 4, 15, 24, 6, 32, 21, 20], Boykin et al. 8] have recently shown that the set consisting of a Hadamard gate, a c NOT gate, and a phase rotation gate of angle # 4 is universal. In order to form a practical basis for quantum computation, a universal set must also be able to operate in a noisy environment, and therefore has ....

A. Barenco. A universal two-bit gate for quantum computation. In Proc. Roy. Soc. London, Ser. A, 449, pp. 679--683, 1995.

....the probability of occupancy of the binary quantum states of each qubit must be accurately measured. The algorithm presented in this paper is part quantum mechanical and part classical. The quantum part of the algorithm requires quantum state preparation, application of a two qubit quantum gate [6, 7, 8], and measurement of each of the probability of occupancies of the one and zero states of both qubits involved in each quantum gate operation. Consequently, the state preparation, quantum gate operation, and measurement process must be either repeated in time over and over again on a pairs of ....

Adriano Barenco. A universal two-bit gate for quantum computation. Proceedings Royal Society London, 449A:679--683, 1995. pages 3

....of gates can be built from them, which means that they can simulate (approximately) any unitary transformation on an arbitrary number of qubits. The rst universal quantum gate which operates on three qubits was identi ed by Deutsch[14] After a long sequence of work on universal quantum gates [17, 4, 15, 24, 6, 32, 21, 20], Boykin et al. 8] have recently shown that the set consisting of a Hadamard gate, a c NOT gate, and a phase rotation gate of angle =4 is universal. In order to form a practical basis for quantum computation, a universal set must also be able to operate in a noisy environment, and therefore has ....

A. Barenco. A universal two-bit gate for quantum computation. In Proc. Roy. Soc. London, Ser. A, 449, pp. 679-683, 1995.

....of unitary transformations on quantum state. It is thought of, after initialisation, as achieving all superposed evolutions simultaneously, which provides much of the reason for quantum computation s eciency. Again, evolution is feasible: it may be implemented using universal quantum gates [1, 7]. For example on B , after initialisation, evolution by the Hadamard transformation H 1 results in = 0 (because H 1 is not only unitary but equal to its own conjugate transpose and so self inverse) Thus our de nition of initialisation does not exclude setting state to equal 0 (or any other ....

Adriano Barenco. A universal two-bit gate for quantum computation. Proc. R. Soc. Lond. A, 449:679-683, 1995.

....dealing with oracle gates below, we de ne the size of a quantum circuit to be the number of gates in the circuit plus the number of qubits upon which the circuit acts. A note is in order in regard to our choice of the Shor basis. This collection of gates is universal (in the sense described in [13, 14, 19, 20], for instance) see [24] for a proof of this fact. While our results hold for any other reasonable choice for a universal set of gates, we have chosen this basis for de niteness and convenience; by allowing reversible computations and Hadamard transforms to be performed without error, we avoid ....

A. Barenco. A universal two-bit gate for quantum computation. Proceedings of the Royal Society of London, 449:679-683, 1995.

....are much easier to implement than three bit ones, since they only require arranging for two state carrying particles to be brought together and participate in a two way interaction, rather than requiring three particles to be brought together and interact just right; this is much easier. Barenco [1] extended this result further by showing the existence of a large class of two bit gates, 8 each one of which is universal by itself, and a newer paper by Deutsch and colleagues [18] shows that almost all quantum gates operating on two or more bits are universal That is, the non universal ....

Adriano Barenco. A universal two-bit gate for quantum computation. Proceedings of the Royal Society of London Ser. A, 449:679--683, 1995. Preprint at Los Alamos Physics Preprint Archive, http://xxx.lanl.gov/abs/quant-ph/9505016.

....common assumption is that the quantum mechanical device is composed of reversible quantum gates. It has been recently shown that there exist simple quantum gates which are also computation universal. The simplest such gate is a two input and two output gate and was found independently by Barenco [13] and DiVincenzo et al. 14, 15] The states of the two incoming qubits, are entangled by a unitary operation which is a member of the U(2) U(1)# SU(2) unitary group. For any reversible computation, one can describe the algorithm by specifying a unitary evolution operation, in our case formally ....

Adriano Barenco. A universal two-bit gate for quantum computation. Proceedings Royal Society London, 449A:679--683, 1995.

....for QC if any unitary operation on arbitrarily many qubits can be expressed as compositions of these gates. Deutsch defined the extended quantum XOR 3 qubit gate (known as the Deutsch Toffoli gate) and proved this gate, in combination with certain one qubit gates, is universal. Barenco [Bar95] Sleator et al. [DMS 95] Barenco et al. [BBC 95] and DiVincenzo [DiV95] proved the 2 qubit XOR gates with certain 1 qubit gates can implement the Deutsch Toffoli gate, so are universal for QC (also see Smolin and DiVincenzo [SD95] DiVincenzo et al. [DiV96, DS98] Poyatos et al. [PCZ96] Mozyrsky ....

A. Barenco, A Universal Two--Bit Gate for Quantum Computation, (Online preprint quant-ph/9505016), (1995).

....mapping V : Sigma Theta f1; kg Sigma (for k = bm=2 1c) where each V (x; j) is an encoding of a quantum circuit composed of quantum gates from some appropriately chosen universal set of gates. Universal sets of gates transformations have been investigated in a number of papers [1, 7, 8, 14, 15]; for the purposes of this paper, we will assume only that this set includes the Hadamard gate and any universal gate for reversible computation such as the Fredkin gate or Toffoli gate. Each encoding V (x; j) is identified with the quantum circuit it encodes. It is assumed that this encoding is ....

A. Barenco. A universal two-bit gate for quantum computation. Proceedings of the Royal Society of London, 449:679-- 683, 1995.

....of the greater power of quantum computing as a formal system there are many more choices for the universal gate than in classical reversible computing. In particular, DiVincenzo [27] has shown that a certain set of four gates each operating on two qubits is adequate in quantum computation. Barenco [1] extended this to show that almost any two bit gate is universal: any two bit gate whose action is given by the unitary matrix # # # # 1 0 0 0 0 1 0 0 0 0 e i# cos # ie i(# #) sin # 0 0 ie i(# #) sin # e i# cos # # # # # 1.5. Reversible Computation 11 is universal where #, # and # ....

....can be found with certainty after a single iteration (see [17] Actually, by Theorem 3.7.1 it is possible to nd a solution in a single query for all t # N 4. See Chi and Kim [19] for summaries. Theorem 3.9.2. Let t # [ N 4 , N ] Take # in [# 3, 5# 3] such that cos # = 1 N 2t # [ 1, 1 2 ]. Then we have G F,# #(k 0 , k 0 )# = # # #( e i# 1)k 0 , 0) # . When t is unknown we can use the following algorithm [16, 35] Algorithm 3.9.2 (General quantum database search) 1. Set m = 1 and # = 6 5. 2. Choose j # Zm uniformly at random. 3. Apply j iterations of G F,# to the ....

A. Barenco, A universal two-bit gate for quantum computation, Proc. Roy. Soc. London Ser. A 449 (1995), 679683.

....for QC if any unitary operation on arbitrarily many qubits can be expressed as compositions of these gates. Deutsch defined the extended quantum XOR 3 qubit gate (known as the DeutschToffoli gate) and proved this gate, in combination with certain one qubit gates, is universal. Barenco [Bar95] Sleator et al. [DMS 95] Barenco et al. [BBC 95] and DiVincenzo [DiV95] proved the 2 qubit XOR gates with certain 1 qubit gates can implement the Deutsch Toffoli gate, so are universal for QC (also see Smolin and DiVincenzo [SD95] DiVincenzo et al. [DiV96, DS98] Poyatos et al. [PCZ96] Mozyrsky ....

A. Barenco, A Universal Two--Bit Gate for Quantum Computation, (Online preprint quantph /9505016), (1995).

....quantum logic gate. As a consequence of the greater power of quantum computing as a formal system, there are many more choices for the universal gate than in classical reversible computing. In particular, DiVincenzo[28] showed that two bit universal quantum gates are also possible; Barenco[29] extended this to show than almost any two bit gate (within a certain restricted class) is universal, and Lloyd[33] and Deutsch et al. 34] have shown that in fact almost any two bit or n bit (n 2) gate is also universal. A closely related construction for the Fredkin gate has been given[35] In ....

....with m 1 input bits, which maps jx 1 ; xm ; yi to jx 1 ; xm ; V m k=1 x k ) Phi yi. For a general U , m (U) can be regarded as a generalization of the Toffoli gate, which, on input jx 1 ; xm ; yi, applies U to y if and only if V m k=1 x k = 1. As shown by one of us [29], almost any single 1 (U) gate is universal in the sense that: by successive application of this gate to pairs of bits in an n bit network, any unitary transformation may be approximated with arbitrary accuracy. It suffices for U to be specified by Euler angles which are not a rational ....

A. Barenco, "A universal two-bit gate for quantum computation", preprint (1994).

....quantum logic gate. As a consequence of the greater power of quantum computing as a formal system, there are many more choices for the universal gate than in classical reversible computing. In particular, DiVincenzo[27] showed that two bit universal quantum gates are also possible; Barenco[28] extended this to show than almost any two bit gate (within a certain restricted class) is universal, and Lloyd[29] and Deutsch et al. 30] have shown that in fact almost any two bit or n bit (n 2) gate is also universal. A closely related construction for the Fredkin gate has been given[31] In ....

....with m 1 input bits, which maps jx 1 ; xm ; yi to jx 1 ; xm ; V m k=1 x k ) Phi yi. For a general U , m (U) can be regarded as a generalization of the Toffoli gate, which, on input jx 1 ; xm ; yi, applies U to y if and only if V m k=1 x k = 1. As shown by one of us [30, 28], almost any single 1 (U) gate is universal in the sense that: by successive application of this gate to pairs of bits in an n bit network, any unitary transformation may be approximated with arbitrary accuracy. It suffices for U to be specified by Euler angles which are not a rational ....

A. Barenco, "A universal two-bit gate for quantum computation", preprint (1994).

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Barenco, A., "A universal two-bit gate for quantum computation." quant-ph/9505016.

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A. Barenco. A universal two-bit gate for quantum computation. In Proc. Roy. Soc. London, Ser. A, 449, pp. 679--683, 1995.

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A. Barenco. A universal two-bit gate for quantum computation. Proceedings of the Royal Society of London, 449:679-683, 1995.

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