Lloyd S 1995 Almost any quantum logic gate is universal, Phys. Rev. Lett. 75, 346-349  Home/Search   Document Not in Database   Summary   Related Articles   Check

....[23] that there exists a universal three bit quantum logic gate. This gate, if applied enough times to three member subsets of n qubits can simulate any unitary U(n) with arbitrary precision. Subsequently, DiVincenzo [24] showed that two bit universal quantum gates are also possible, and Lloyd [25] and Deutsch [26] extended this result to show that almost any two bit gate is universal. The proofs for universality of two qubit gates rely on two properties of a general Hamiltonian H which produces entanglement between two qubits. First, the phases of the eigenvalues of U are generally ....

S. Lloyd, "Almost Any Quantum Logic Gate is Universal", Phys. Rev. Lett. 75, 346 (1995).

....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 able to operate ....

S. Lloyd. Almost any quantum logic gate is universal. Phys. Rev. Let., 75, pp. 346--349, 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 ....

S. Lloyd. Almost any quantum logic gate is universal. Phys. Rev. Let., 75, pp. 346--349, 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 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 ....

S. Lloyd. Almost any quantum logic gate is universal. Phys. Rev. Let., 75, pp. 346-349, 1995.

.... [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 et al. [MPH96a,MPH97, MPH98] Poyatos et al. [PCZ96] Lloyd [Llo97c] then proved that almost any 2 qubit quantum logic gate (with certain 1 qubit gates) is universal for QC. Monroe et al. [MMK95] DiVincenz et al. [DVL98] gave experimental demonstrations of quantum gates. Deu89] defined a quantum computing model known as a quantum gate array which allows execution ....

S. Lloyd, Almost any quantum logic gate is universal, Los Alamos National Laboratory preprint (1997c).

....computation, which is a special case of quantum computation, there is no set of two bit gates which is universal. Note that one qubit gate is certainly not enough to construct all operations. Barenco[13] and Deutsch et.al[81] showed that almost any two bit gate is universal (See also Lloyd [141, 143]) An improvement of DiVincenzo s result was achieved later by Barenco et.al[16] where it was shown that the classical controlled not gate, together with all one qubit gates construct a universal set as well In fact, one 1 qubit gate and the controlled not gate will do. This is perhaps the ....

Lloyd S 1995 Almost any quantum logic gate is universal, Phys. Rev. Lett. 75, 346-349

....operations at once, rather than serially, we can solve larger problems before our computer decoheres. Consider a quantum circuit operating on a set of qubits, containing onequbit gates (2 Theta 2 unitary matrices) and the two qubit controlled not gate; these are universal for quantum computation [1, 4]. We can define the depth of this circuit as the number of layers, where each layer consists of gates operating on mutually disjoint sets of qubits; that is, each qubit interacts with at most one other qubit at a time. In a model of quantum computation where one qubit can simultaneously interact ....

S. Lloyd, "Almost any quantum logic gate is universal." Phys. Rev. Lett. 75 (1995) 346-349.

....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 the present paper we take a somewhat different tack, showing that a non universal, classical two bit gate, in ....

S. Lloyd, "Almost any quantum logic gate is universal", preprint (1994).

.... ie i(# #) sin # e i# cos # # # # # 1.5. Reversible Computation 11 is universal where #, # and # are xed irrational multiples of # and of each other. This gate is depicted in Figure 1.4.3 (b) with U(#, #, #) # e i# cos # ie i(# #) sin # ie i(# #) sin # e i# cos # # . Lloyd [44] and Deutsch et al. 25] have shown that in fact almost any two bit or n bit for n # 2 gate is universal. Barenco et al. 2] have shown that a nonuniversal classical two bit gate in conjunction with quantum one bit gates is also universal. 1.5 Reversible Computation Until recently, it was thought ....

S. Lloyd, Almost any quantum logic gate is universal, preprint, 1994.

....to execute this algorithm increases with L proportionally to 10 L=2 . Even if the computer can perform as much as 10 10 divisions per second it would take about a second to factor a 20 digit number, about a year to factor a 34 digit number and more than the estimated age of the Universe (10 17 s) to factor a 60 digit long number Since the invention of public key cryptosystems in the seventies there has been a significant progress in designing good factoring algorithms. The best algorithms such as the Multiple Polynomial Quadratic Sieve [7] and the Number Field Sieve [8] have the ....

....of six different types of two bit gates; then Barenco [14] and, independently, Sleator and Weinfurter [15] showed that a single two bit gate suffices to implement the Deutsch gate. More recently it has been shown that almost any non trivial two bit gate is universal (Deutsch et al. 16] Lloyd [17] It implies that almost any unitary transformation can approximate any other unitary transformation with an arbitrary precision However, in practice we usually tend to restrict our choice of elementary gates to those which perform operations of some clear logical meaning. From the experimental ....

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S. Lloyd, "Almost any quantum logic gate is universal", to appear in Phys. Rev. Lett. (1995).

....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 the present paper we take a somewhat different tack, showing that a non universal, classical two bit gate, in ....

S. Lloyd, "Almost any quantum logic gate is universal", preprint (1994).

.... [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 et al. [MPH96a,MPH97, MPH98] Poyatos et al. [PCZ96] Lloyd [Llo97c] then proved that almost any 2 qubit quantum logic gate (with certain 1 qubit gates) is universal for QC. Monroe et al. [MMK95] DiVincenz et al. [DVL98] gave experimental demonstrations of quantum gates. Deu89] defined a quantum computing model known as a quantum gate array which allows execution ....

S. Lloyd, Almost any quantum logic gate is universal, Los Alamos National Laboratory preprint (1997c).

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Lloyd S 1995 Almost any quantum logic gate is universal, Phys. Rev. Lett. 75, 346-349

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Lloyd, S., "Almost any quantum logic gate is universal." PRL. 75.2:346. 10 July 1995.

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S. Lloyd. Almost any quantum logic gate is universal. Phys. Rev. Let., 75, pp. 346--349, 1995.

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S. Lloyd (1994b) "Almost any quantum logic gate is universal," Los Alamos National Laboratory preprint.

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