L. Adelman, J. DeMarrais, and M. Huang. Quantum computability. sicom, 26:1524--1540, 1997.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... [5] A seminal paper is the in depth study of quantum complexity which was conducted by Bernstein and Vazirani [6] Research in this area continued with such papers as that of Bennett, Bernstein, Brassard and Vazirani [7] Simon [8] Berthiaume and Brassard [9] and Adleman, Demarrais and Huang [10], which broadened the study of quantum complexity classes in analogy with their classical counterparts. In this paper we continue in this examination and consider quantum circuit classes de ned in analogy with classical circuit classes. We show that these classes behave very di erently from the ....

....on the expectation NQACC, BQACC and EQACC, respectively. For example, the class NQACC corresponds to the case where x is in the language if the expectation of the observed state after applying the QACC operator is non zero. This is analogous to the de nition of the class NQP in Adleman et al. [10] and discussed in Fenner et al. 11] where it is shown that NQP is classically of high complexity, and in particular is hard for the polynomial time hierarchy. In this way we obtain natural classes of languages which correspond to those de ned classically by families of small depth circuits. In ....

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L. Adleman, J. DeMarrais, and M. Huang. Quantum computability. SIAM J. Computing 26 (1997) 1524-1540.

.... black boxes were given by Chuang and Nielsen[CN97] and Poyatos, Cirac and Zoller[PCZ97] however these procedures implicitly require apparatus that has already been tested and characterized. The idea of self testing in quantum devices is implicit in the work of Adleman, Demarrais and Huang[ADH97] They have developed a procedure by which a quantum Turing machine is able to estimate its internal angle by its own means under the hypothesis that the machine is unitary. In the context of quantum cryptography Mayers and Yao[MY98] have designed tests for deciding if a photon source is perfect. ....

L. Adleman, J. Demarrais, and M. Huang. Quantum computability. SIAM J. on Comput., 26:5, pp. 1524--1540, 1997.

....of quantum black boxes were given by Chuang and Nielsen[12] and Poyatos, Cirac and Zoller[26] however these procedures implicitly require apparatus that has already been tested and characterized. The idea of self testing in quantum devices is implicit in the work of Adleman, Demarrais and Huang[1]. They have developed a procedure by which a quantum Turing machine is able to estimate its internal angle by its own means under the hypothesis that the machine is unitary. In the context of quantum cryptography Mayers and Yao[25] have designed tests for deciding if a photon source is perfect. ....

....1, equivalently # is a pure state exactly when # 2 = #. A22 Hermitian matrix of unit trace is semi positive if and only if its determinant is between 0and1 4. Therefore in the case of one qubit, any density matrix # can be written as # = p 0##0 (1 p) 1##1 # 1##0 # # 0##1 ,wherep # [0, 1], and # is a complex number such that # 2 # p(1 p) This density matrix will be denoted by #(p, #) Remark that #(p, #) is a pure state exactly when # 2 = p(1 p) that is, its determinant is 0. 2.2 Superoperators The evolution of physical systems is described by specific ....

L. Adleman, J. Demarrais, and M. Huang. Quantum computability. SIAM J. on Comput., 26:5, pp. 1524--1540, 1997.

....that requires O( p N) steps to search an unsorted database of N records. Recently Grover s algorithm has also been used to explain genetic code [25] A signi cant amount of research is being done on the subject of computational complexity from a quantum computation point of view (see, e.g. [32, 1, 3, 5]) 4. FINITE AUTOMATA Classically, abstract machines models (such as Turing machines) have provided a basis to study computational power. Restricted models have been used to gain insight in particular aspects of computation, such as Two way Probabilistic Finite Automata and Interactive Proof ....

L. M. Adelman, J. Demarrais, M.-D. A. Huang, \Quantum computability", SIAM J. Comput., Vol. 26 (5), 1524-1540, 1997.

.... a bearing on the physical realizability of quantum Turing Machines in general, since it establishes that it is sufficient to physically realize a simple quantum operation on a single bit (in addition to maintaining coherence and carrying out deterministic operations, of course) Adleman, et al. [1] and Solovay and Yao [40] have further clarified this point by showing that quantum coin flips with amplitudes 3=5 and 4=5 are sufficient for universal quantum computation. Quantum computation is necessarily time reversible, since quantum physics requires unitary evolution. This makes it quite ....

....inputs therefore computes a function from ( Sigma Gamma #) to Sigma . We now give a slightly modified version of the definition of a QTM provided by Deutsch [20] As in the case of probabilistic TM, we must limit the transition amplitudes to efficiently computable numbers. Adleman, et al. [1] and Solovay and Yao [40] have separately shown that further restricting QTMs to rational amplitudes does not reduce their computational power. In fact, they have shown that the set of amplitudes f0; Sigma 3 5 ; Sigma 4 5 ; 1g are sufficient to construct a universal QTM. We give a ....

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Adleman, L., DeMarrais, J., and Huang, M., Quantum computability, manuscript, 1994.

....of quantum black boxes were given by Chuang and Nielsen[12] and Poyatos, Cirac and Zoller[26] however these procedures implicitly require apparatus that has already been tested and characterized. The idea of self testing in quantum devices is implicit in the work of Adleman, Demarrais and Huang[1]. They have developed a procedure by which a quantum Turing machine is able to estimate its internal angle by its own means under the hypothesis that the machine is unitary. In the context of quantum cryptography Mayers and Yao[25] have designed tests for deciding if a photon source is perfect. ....

L. Adleman, J. Demarrais, and M. Huang. Quantum computability. SIAM J. on Comput., 26:5, pp. 1524-- 1540, 1997.

....of quantum black boxes were given by Chuang and Nielsen[12] and Poyatos, Cirac and Zoller[26] however these procedures implicitly require apparatus that has already been tested and characterized. The idea of self testing in quantum devices is implicit in the work of Adleman, Demarrais and Huang[1]. They have developed a procedure by which a quantum Turing machine is able to estimate its internal angle by its own means under the hypothesis that the machine is unitary. In the context of quantum cryptography Mayers and Yao[25] have designed tests for deciding if a photon source is perfect. ....

L. Adleman, J. Demarrais, and M. Huang. Quantum computability. SIAM J. on Comput., 26:5, pp. 1524-1540, 1997.

....number of steps required to get this precision, and the like. In contrast, if we fix the rotation of all contemplated machines to a single primitive rotation with cos = 3=5 and sin = 4=5 then there are only countably many Turing machines and the universal machine simulates the others exactly [1]. Every quantum Turing machine computation using arbitrary real rotations can be approximated to any precision by machines with fixed rotation but in general cannot be simulated exactly just like in the case of the simulation of arbitrary quantum Turing machines by a universal quantum Turing ....

L.M. Adleman, J. Demarrais, M.-D. A. Huang, Quantum computability, SIAM J. Comput., 26:5(1997), 1524--1540.

....in classical and quantum machines. There are a number of problems left open. For the purposes of BQP computation it is sufficient to use a restricted set of rational amplitudes for quantum computation, namely amplitudes in the set f Gamma1; Gamma 4 5 ; Gamma 3 5 ; 0; 3 5 ; 4 5 ; 1g (see [ADH97, SY96]) However, it is not clear if our method would work using only such amplitudes. 2 This is a hierarchy built over the class PP instead of NP. See [Wag86b] for a definition. Also, we found here that if QAP 2 BQP, then the counting hierarchy collapses to PP. It would be interesting to see if it ....

L. Adelman, J. DeMarrais, and M. Huang. Quantum computability. sicom, 26:1524--1540, 1997.

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L. Adelman, J. DeMarrais, and M. Huang. Quantum computability. sicom, 26:1524--1540, 1997.

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L. Adleman, J. DeMarrais, and M.-D. Huang. Quantum computability, SIAM J. Comp. 26(5):1524-- 1540, 1997.

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L. M. Adleman, J. Demarrais, and M. -D. A. Huang, \Quantum computability," SIAM J. Computing, 26(1997), pp. 1524-1540.

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L. Adleman, J. DeMarrais, and M.-D. Huang. Quantum computability, SIAM J. Comp. 26(5):1524--1540, 1997.

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L. M. Adleman, J. Demarrais, and M.-D. A. Huang, "Quantum computability, " SIAM J. Comput., vol. 26, no. 5, pp. 1524--1540, 1997.

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L. M. Adelman, J. Demarrais and M.-D. A. Huang, "Quantum computability", SIAM J. Comput. 26 (1997) 1524--1540.

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