Solving the quantum search problem in polynomial time on an NMR quantum computer

Abstract

The quantum search problem is an important problem due to the fact that a general NP problem can be solved efficiently by an unsorted quantum search algorithm. Here it has been shown that the quantum search problem could be solved in polynomial time on an NMR quantum computer. The NMR ensemble quantum computation is based on the quantum mechanical unitary dynamics that both a closed quantum system and its ensemble obey the same quantum mechanical unitary dynamics instead of on the pseudopure state or the effective pure state of the classical NMR quantum computation. Based on the new principle the conventional NMR multiple-quantum spectroscopy has been developed to solve experimentally the search problem. The solution information of the search problem is first loaded on the unitary evolution propagator which is constructed with the oracle unitary operation and oracle-independent unitary operations and is used to excite the multiple-quantum coherence in a spin ensemble. Then the multiple- quantum spectroscopy is used to extract experimentally the solution information. It has been discussed how to enhance the output NMR signal of the quantum search NMR multiple-quantum pulse sequence and some approaches to enhancing the NMR signal are also proposed. The present work could be helpful for conventional high field NMR machines to solve efficiently the quantum search problem.

34 pages without figures

References in corpus (9)

• Quantum Mechanics helps in searching for a needle in a haystack
• Strengths and Weaknesses of Quantum Computing
• Efficient Networks for Quantum Factoring
• A Limit on the Speed of Quantum Computation in Determining Parity
• Simulations of Many-Body Quantum Systems by a Quantum Computer
• A polynomial-time solution to the parity problem on an NMR quantum computer
• Universal construction of unitary transformation of quantum computation with one- and two-body interactions
• Universal construction for the unsorted quantum search algorithms
• A convenient method to prepare the effective pure state in a quantum ensemble

Cited by in corpus (4)

• Quantum search processes in the cyclic group state spaces
• A prime factorization based on quantum dynamics on a spin ensemble (I)
• The basic principles to construct a generalized state-locking pulse field and simulate efficiently the reversible and unitary halting protocol of a universal quantum computer
• Nuclear Spins as Quantum Testbeds: Singlet States, Quantum Correlations, and Delayed-choice Experiments