D. Ventura, T. Martinez, Initializing the Amplitude Distribution of a Quantum State, (Online preprint quantph /9807054), (1998). Home/Search Document Details and Download
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Implementing Competitive Learning in a Quantum System - Ventura (1999) Self-citation (Dan) (Correct)
....require a wave function y such that y = 1 m p p P (4) where m is the number of patterns in the set P. This initialization of a quantum state is a process that is beyond the scope of this paper. However, an efficient quantum algorithm for doing something slightly more general is detailed in [11], and a slight modification presented in [12] accomplishes this specific initialization. Here we represent this entire initialization process as the single operator P, P 0 = y = 1 m p p P (5) Less formally, the P operator transforms the single basis state 0 state to the desired wave ....
Ventura, Dan and Tony Martinez, "Initializing the Amplitude Distribution of a Quantum State", submitted to Physical Review A, May 1999.
Quantum Associative Memory - Ventura, Martinez (1998) (3 citations) Self-citation (Martinez) (Correct)
....while after four passes through the loop it drops to 10 58 . This reveals the periodic nature of the algorithm and also demonstrates the fact that the first time that the probability for success is maximal is indeed after p 4 N steps of the algorithm. 3.2. Initializing the Quantum State [Ven98a] presents a polynomial time quantum algorithm for constructing a quantum state over a set of qubits to represent the information in a training set. The algorithm is implemented using a polynomial number (in the length and number of patterns) of elementary operations on one, two, or three qubits. ....
Ventura, Dan and Tony Martinez, "Initializing the Amplitude Distribution of a Quantum State", submitted to Physical Review Letters, June 16, 1998.
A Quantum Computational Learning Algorithm - Ventura, Martinez (1998) Self-citation (Dan Martinez) (Correct)
....f ; 2) The implementation of the operator B ; 3) The number of times this process must be repeated in order to identify a large coeffient; and 4) The classical approximation of that coefficient. Constructing the state f is nontrivial and a method for doing so in O(mn) time is detailed in [Ven98]. Implementing B turns out to be extremely easy on a quantum computer, and it is in fact the basis of most quantum algorithms discovered to date. Computing the Walsh transform of a quantum state is accomplished simply by applying the elementary quantum operator H = 1 2 1 1 1 1 ....
....the algorithm would require only 61 qubits. Although it appears that the algorithm presented here requires only n qubits, the algorithm depends on a method for representing 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 ....
Ventura, Dan and Tony Martinez, "Initializing the Amplitude Distribution of a Quantum State", submitted to Physical Review Letters, June 1998.
Artificial Associative Memory Using Quantum Processes - Ventura (1998) Self-citation (Ventura) (Correct)
....for their implementation were developed using unitary operators. The two algorithms are briefly described here with references provided for further detail. 3. 1 Storing Patterns A quantum algorithm for constructing a coherent state over n qubits to represent a set of m patterns is presented in [11]. The algorithm is implemented using a polynomial number (in the length and number of patterns) of elementary operations on one, two, or three qubits. The key operator in this process is S p = 1 0 0 0 0 1 0 0 0 0 p 1 p 1 p 0 0 1 p p 1 p , 4) ....
D. Ventura and T. Martinez, "Initializing the Amplitude Distribution of a Quantum State", submitted to Physical Review Letters, June 16, 1998.
Alternative Computational Models: A Comparison of Biomolecular and .. - Reif (1998) (1 citation) (Correct)
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D. Ventura, T. Martinez, Initializing the Amplitude Distribution of a Quantum State, (Online preprint quantph /9807054), (1998).
Quantum Information Processing: Compression, Coding, and Related.. - Reif (1985) (Correct)
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D. Ventura, T. Martinez, Initializing the Amplitude Distribution of a Quantum State, (Online preprint quant-ph/9807054), (1998).
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