Numerical Analysis of Boosting Scheme for Scalable NMR Quantum Computation

Abstract

Among initialization schemes for ensemble quantum computation beginning at thermal equilibrium, the scheme proposed by Schulman and Vazirani [L. J. Schulman and U. V. Vazirani, in Proceedings of the 31st ACM Symposium on Theory of Computing (STOC'99) (ACM Press, New York, 1999), pp. 322-329] is known for the simple quantum circuit to redistribute the biases (polarizations) of qubits and small time complexity. However, our numerical simulation shows that the number of qubits initialized by the scheme is rather smaller than expected from the von Neumann entropy because of an increase in the sum of the binary entropies of individual qubits, which indicates a growth in the total classical correlation. This result--namely, that there is such a significant growth in the total binary entropy--disagrees with that of their analysis.

14 pages, 18 figures, RevTeX4, v2,v3: typos corrected, v4: minor changes in PROGRAM 1, conforming it to the actual programs used in the simulation, v5: correction of a typographical error in the inequality sign in PROGRAM 1, v6: this version contains a new section on classical correlations, v7: correction of a wrong use of terminology, v8: Appendix A has been added, v9: published in PRA

References in corpus (13)

• Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
• Classical, quantum and total correlations
• On the Power of One Bit of Quantum Information
• Experimental realization of a quantum algorithm
• Effective Pure States for Bulk Quantum Computation
• Efficient factorization with a single pure qubit and $logN$ mixed qubits
• Universal Quantum Information Compression
• Preparing high purity initial states for nuclear magnetic resonance quantum computing
• Limits for compression of quantum information carried by ensembles of mixed states
• Schumacher's quantum data compression as a quantum computation
• NMR implementation of a building block for scalable quantum computation
• Optimal compression for mixed signal states
• Generic Quantum Block Compression

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