Quantum parallel computing for the addition operation is the starting point for general-purpose computing. A 16 nonlocal operator–state relations are presented to show how parallel computing is achieved.
This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book introduces the motivation and presents and comment on recent related works in the literature about the quantum computing emulation by hardware and simulation by software. The conventional electronic computer is a machine that performs logical and arithmetic operations sequentially and/or in parallel on data coded according to binary logic. Quantum Computing has been the target of several researches due to its potential for increasing the speed of processing through the use of algorithms with intrinsic parallelism, pointing out to the possibility of polynomial time solutions for NP-Complete problems. The book describes the macro-architecture of the proposed quantum processor and its interaction with the conventional host wherein it is embedded. It defines quantum state measurement and propose an efficient micro-architecture for the unit that is responsible for the state observation of the quantum bits, thus allowing for quantum bit measurements.
We generalize Grover's unstructured quantum search algorithm to enable it to work with arbitrary starting superpositions and arbitrary unitary operators. We show that the generalized quantum search algorithm, when cast in a special orthonormal basis, can be understood as performing an exact rotation of a starting superposition into a target superposition. We derive a formula for the success probability of the generalized quantum search algorithm after n rounds of amplitude amplification. We then use this formula to determine the optimal strategy for a punctuated quantum search algorithm, i.e., one in which the amplitude amplified state is observed before the point of maximum success probability. On average, the optimal strategy is about 12% better than the naive use of Grover's algorithm. The speedup obtained is not dramatic but it illustrates that a hybrid use of quantum computing and classical computing techniques can yield a performance that is better than either alone. In addition, we show that a punctuated quantum algorithm that takes the same average computation time as Grover's standard algorithm only requires half the coherence time. We then extend the analysis to the case of a society of k quantum searches acting in parallel. We derive an analytic formula that connects the degree of parallelism with the expected computation time for k-parallel quantum search. The resulting parallel speedup scales as O(k), while the minimum number of agents needed to ensure success, k, decreases as the inverse of the square of the achievable coherence time. This result has practical significance for the design of rudimentary quantum computers that are likely to have a limited coherence time.
With current technologies, it seems to be very difficult to implement quantum computers with many qubits. It is therefore of importance to simulate quantum algorithms and circuits on the existing computers. However, for a large-size problem, the simulation often requires more computational power than is available from sequential processing. Therefore, simulation methods for parallel processors are required. We have developed a general-purpose simulator for quantum algorithms/circuits on the parallel computer (Sun Enterprise4500). It can simulate algorithms/circuits with up to 30 qubits. In order to test efficiency of our proposed methods, we have simulated Shor's factorization algorithm and Grover's database search, and we have analyzed robustness of the corresponding quantum circuits in the presence of both decoherence and operational errors. The corresponding results, statistics, and analyses are presented in this paper.