V. Vedral, A. Barenco, and A. Ekert, "Quantum networks for elementary arithmetic operations", report no. quant-ph/9511018 (1995).  Home/Search   Document Not in Database   Summary   Related Articles   Check

....out of the output (a, a b) and there is no loss of information in the computation, the calculation can be implemented reversibly. The sum operation can be implemented with two CNOT gates (Fig. 5, time goes from left to right) while the carry has to be obtained in a more complicated way [9] (Fig. 6) A sequence of RF pulses with different frequencies and duration time are injected into the quantum network during operation. During a pulse the involved qubits switch their states. IV. SHOR S ALGORITHM Although there is still a long way to go before quantum computers come into ....

....superpositions a and the other is in 0 state. We compute ( n x mod in the second register and keep the first register in the a state, i.e. performing the modular exponentiation ( n x a a U n x mod , 0 , which can be basically built on a reversible network of quantum sum and carry [9]. Next, we perform quantum Fourier transformation on the first register to get period r . The discrete Fourier transform is a unitary transformation and can be implemented by a network of quantum CNOT and qubit rotation gates [5] Finally, we calculate the factors of n with Euclid s algorithm by ....

V. Vedral, A. Barenco, A. Ekert, "Quantum Networks for Elementary Arithmetic Operations", Physical Review A, Vol. 54, No.1, July 1996.

....MA 02139 February 2, 1996 Abstract This paper surveys the state of the field of quantum computation, with an emphasis on the recent effort to devise simple quantum computational primitives upon which more complex quantum calculations can be built. This effort is exemplified by the recent papers [2, 49], which we review. We also discuss Shor s [38] paper, which describes the quantum polynomial time factoring algorithm that has provided a major motivation for much of the recent activity. 1 Introduction Quantitative Church s Thesis. The Quantitative Church s Thesis [50, 48] claims that Turing ....

....to produce an implementation soon. Arithmetic Operations. Having universal primitive quantum operations is well and good, but to carry out interesting computations we need to know how to build up more complex operations out of these simple ones. Vedral, Barenco and Ekert address this issue in [49], in which they show how to use primitive quantum logic operations to build up efficient addition, multiplication, and modular exponentiation operations in a way that preserves the coherence of quantum states, an issue we will discuss later. Performing these operations is made more difficult than ....

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Vlatko Vedral, Adriano Barenco, and Artur K. Ekert. Quantum networks for elementary arithmetic operations. Submitted to Physical Review A, November 1995. Los Alamos Physics Preprint Archive, http://xxx.lanl.gov/abs/quant-ph/9511018.

.... of the quantum Fourier transform: to the approximate quantum Fourier transform (Coppersmith [Cop94] over various domains (Griffiths, Niu [GN96] Hoyer [Hoy97] over symmetric groups (Beals [Bea98] over certain non abelian groups (Pueschel, Roetteler, Bet [PRB98] Vedral, Barenco, Ekert [VBE96] give efficient quantum networks for elementary arithmetic operations, using the quantum Fourier transform. Grigoriev [Gri97] used the quantum Fourier transform to test shift equivalence of polynomials. ffl Quantum Factoring. The most notable algorithmic result in QC to date is the quantum ....

V. Vedral, A. Barenco, A. Ekert, Quantum Networks for Elementary Arithmetic Operations, (Online preprint quant-ph/9511018), (1996).

....language seems like a very tedious task Just like higher languages in ordinary computer programming, it is desirable that quantum operations which are commonly used can be treated as black boxes, without rewriting them from the beginning with elementary gates. Steps in this direction were made by [16, 15, 24, 155, 193]. 27 5 Quantum Algorithms The first and simplest quantum algorithm which achieves advantage over classical algorithms was presented by Deutsch and Jozsa[79] Deutsch and Jozsa s algorithm addresses a problem which we have encountered before, in the context of probabilistic algorithms. f is a ....

Vedral V, Barenco A and Ekert A 1996 Quantum networks for elementary arithmetic operations, Phys. Rev. A 54 147-153

....1 2 k 0 =k 3 1 1 k 1 =k 2 : The scaling matrix D 4 m can then be factorized using two Kronecker products D 4 m = i I m=2 Omega R C 1 j Theta Pm Theta i I m=2 Omega R C 0 j : 7) Set n = dlog me. The permutation transform Pm can be implemented in Theta(n) basic operations [34]. Each of the other two factors on the right hand side of Equation (7) can be implemented in one basic operation. Thus, D 4 m can be implemented in Theta(n) basic operations. We remark that we have not been able to find this factorization of D 4 m elsewhere in the literature despite the ....

Vlatko Vedral, Adriano Barenco, and Artur Ekert. Quantum networks for elementary arithmetic operations. Physical Review A, 54:147 -- 153, 1996.

....classically. For example, Shor s algorithm requires hundreds or thousands of qubits to perform a factorization that can not be done classically. Vedral, et al. give estimates for number of qubits needed for modular exponentiation, which dominates Shor s algorithm, anywhere from 7n 1 down to 4n 3 [Ved96]. For a 512 bit number (which RSA actually claims may not be large enough to be safe anymore, even classically) this translates into anywhere from 3585 down to 2051 qubits. As for elementary operations, they claim O(n 3 ) which in this case would be O(10 8 ) Therefore, the algorithm ....

Vedral, Vlatko, Adriano Barenco, and Artur Ekert, "Quantum Networks for Elementary Arithmetic Operations", Physical Review A, vol. 54 no. 1, pp. 147-53, 1996.

.... QED [4] and on ions in linear traps [5] One can estimate the time T needed for a single run of Shor s algorithm to be equal to the time el required to execute an elementary logical operation multiplied by the required number of elementary operations, which is of the form fflL 3 O(L 2 ) [6]. It should be noted that in general a single run of Shor s algorithm will not be sufficient because it is a stochastic algorithm. In the following we will discuss the time required to perform one run of Shor s algorithm and if not stated explicitly the calculation time is just the time required ....

....able to factorize on the quantum computer. For a given value of el that means that the total computation time scales like L 3 . To factorize a number representable by L qubits, one requires 5L 2 qubits (in what follows we neglect the 2 here) as work space for the necessary calculations [6]. If we assume that each qubit couples to a different bath the decoherence time of 5L qubits is given by [7, 8] dec = qb 5L (2) where qb the decoherence time of a single qubit. The case of qubits coupling to the same bath leads to smaller decoherence times dec [8] Combining eq. 1) and ....

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V. Vedral, A. Barenco, and A. Ekert, Quantum Networks for Elementary Arithmetic Operations submitted to Phys. Rev. A

....the training set as a quantum state. As mentioned before, an explicit algorithm for constructing such a quantum state exists [Ven98] however it requires 2n 1 qubits. In contrast, Shor s algorithm requires hundreds or thousands of qubits to perform an interesting factorization. For example, [Ved96] gives estimates for the number of qubits needed for modular exponentiation, which dominates Shor s algorithm anywhere from 7n 1 down to 4n 3. For a 512 bit number (which RSA actually claims may not be large enough to be safe anymore, even classically) this translates into anywhere from 3585 ....

Vedral, Vlatko, Adriano Barenco, and Artur Ekert, "Quantum Networks for Elementary Arithmetic Operations", Physical Review A, vol. 54 no. 1, pp. 147-53, 1996.

....is inverted conditional on the value of X 0 . In FIRST TRY, S is a multibit register, in fact it must have about log 2 n bits. Implementation of these multi bit functions in terms of primitive operations involving no more than three bits is straightforward, and is presented in Sec. IV and in Ref. [12,13]. Using quantum gates, all the three bit primitives may be reduced to sequences of two bit operations [10] A few more points about FIRST TRY are in order. Given the constraints of reversibility, it is a relatively straightforward transcription of Eq. 12) The first for loop (indexed by j) ....

.... from y, leaving in Y the value of the index I[x; n; m] Actually, the m loop continues to subtract binomial coefficients from Y after it is supposed to; this is why Y is indicated to be a signed register, which can be handled by doing ordinary arithmetic in a register with one extra bit (see [12]) This approach has the benefit that testing that Y is non negative only requires the examination of one bit see the first part of Sec. IV. We might be tempted to avoid negative numbers by terminating the loop at the right moment, viz: for m = 0 to n do if Y i n m j then exit ....

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V. Vedral, A. Barenco, and A. Ekert, "Quantum networks for elementary arithmetic operations", report no. quant-ph/9511018 (1995).

.... of the quantum Fourier transform: to the approximate quantum Fourier transform (Coppersmith [Cop94] over various domains (Griffiths, Niu [GN96] Hoyer [Hoy97] over symmetric groups (Beals [Bea98] over certain non abelian groups (Pueschel, Roetteler, Bet [PRB98] Vedral, Barenco, Ekert [VBE96] give efficient quantum networks for elementary arithmetic operations, using the quantum Fourier transform. Grigoriev [Gri97] used the quantum Fourier transform to test shift equivalence of polynomials. ffl Quantum Factoring. The most notable algorithmic result in QC to date is the quantum ....

V. Vedral, A. Barenco, A. Ekert, Quantum Networks for Elementary Arithmetic Operations, (Online preprint quant-ph/9511018), (1996).

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V. Vedral, A. Barenco, and A. Ekert, "Quantum networks for elementary arithmetic operations", report no. quant-ph/9511018 (1995).

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V. Vedral, A. Barenco, and A. Ekert, "Quantum networks for elementary arithmetic operations", report no. quant-ph/9511018 (1995).

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Vlatko Vedral, Adriano Barenco, and Artur Ekert. Quantum networks for elementary arithmetic operations. In Physical Review A, volume 54 no. 1, pages 147--153, 1996.

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Vedral V, Barenco A and Ekert A 1996 Quantum networks for elementary arithmetic operations, Phys. Rev. A 54 147-153

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V. Vedral, A. Barenco and A. Ekert, Quantum Networks for Elementary Arithmetic Operations, quant-ph/9511018

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V. Vedral, A. Barenco, and A. Ekert, Quantum networks for elementary arithmetic operations, report no. quant-ph/9511018 (1995).

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