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数理解析研究所講究録

Preparation of effective pure states $\mid 00 \cdots 0 \rangle$ on an NMR quantum computer with any number of spins (Analytical Study of Quantum Information and Related Fields)

Ushio Sakaguchi, Hiroshi Ozawa, Toshio Fukumi

Published Apr 1, 2001• 0 citations
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Abstract

A method is proposed to prepare an effective pure state corresponding to the pure state $|0\rangle$ $|0\rangle$ $\cdots|0\rangle$ for any number of spins on a nuclear magnetic resonance quantum computer, where $|0\rangle$ stands for the spin-up state of a nuclear spin.The method is based on the spatial labeling proposed by Cory et al.

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Effective pure states for bulk quantum computation

Emanuel H. Knill, Isaac L. Chuang, Raymond Laflamme

In bulk quantum computation one can manipulate a large number of indistinguishable quantum computers by parallel unitary operations and measure expectation values of certain observables with limited sensitivity. The initial state of each computer in the ensemble is known but not pure. Methods for obtaining effective pure input states by a series of manipulations have been described by Gershenfeld and Chuang (logical labeling) [Science 275, 350 (1997)] and Cory et al. (spatial averaging) [Proc. Natl. Acad. Sci. USA 94, 1634 (1997)] for the case of quantum computation with nuclear magnetic resonance. We give a different technique called temporal averaging. This method is based on classical randomization, requires no ancilla quantum bits, and can be implemented in nuclear magnetic resonance without using gradient fields. We introduce several temporal averaging algorithms suitable for both high-temperature and low-temperature bulk quantum computing and analyze the signal-to-noise behavior of each. Most of these algorithms require only a constant multiple of the number of experiments needed by the other methods for creating effective pure states.

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Preparation of effective pure states ∣00⋯0⟩\mid 00 \cdots 0 \rangle∣00⋯0⟩ on an NMR quantum computer with any number of spins (Analytical Study of Quantum Information and Related Fields)
A method is proposed to prepare an effective pure state corresponding to the pure state ∣0⟩|0\rangle∣0⟩ ∣0⟩|0\rangle∣0⟩ ⋯∣0⟩\cdots|0\rangle⋯∣0⟩ for any number of spins on a nuclear magnetic resonance quantum computer, where ∣0⟩|0\rangle∣0⟩ stands for the spin-up state of a nuclear spin.The method is based on the spatial labeling proposed by Cory et al.
A method is proposed to prepare an effective pure state corresponding to the pure state $|0〉|0〉\ensuremath{\cdot}\ensuremath{\cdot}\ensuremath{\cdot}|0〉$ for any number of spins on a nuclear magnetic resonance quantum computer, where ∣0〉|0〉∣0〉 stands for the spin-up state of a nuclear spin. The method is based on the spatial labeling proposed by Cory et al. [Proc. Natl. Acad. Sci. USA 94, 1634 (1997)].
Preparation of effective pure states ∣00⋯0⟩\mid 00 \cdots 0 \rangle∣00⋯0⟩ on an NMR quantum computer with any number of spins (Analytical Study of Quantum Information and Related Fields)
Abstract In nuclear magnetic resonance (NMR) quantum computing systems, it is very important to prepare an effective pure state rather than a true pure state. Our main objective is to present a general algorithm that provides quantum circuits for preparing an effective pure state from any mixed state, consisting only of controlled‐not (CNOT) quantum gates for homonuclear spin systems. Our algorithm is based on the product operator approach and could be applicable to NMR quantum computing systems with more than eight qubits. Optimization of the number of controlled‐not quantum gates is discussed. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005
Abstract A fast method to prepare effective pure states for NMR‐quantum computer in homo‐nuclear spin system is proposed. The temporal averaging method has been introduced to prepare an effective pure state in NMR‐quantum computer, but the method requires many experiments, whose number increases exponentially with the number of quantum bits (qubits), and it seems that a huge number of logical gates are required. The proposed method avoids this problem by eliminating a part of elements in the density matrices. This method requires only one ancillary qubit and two different experiments; the steps have been confirmed to be proportional to the number of qubits up to four‐qubit. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004
In bulk quantum computation one can manipulate a large number of indistinguishable quantum computers by parallel unitary operations and measure expectation values of certain observables with limited sensitivity. The initial state of each computer in the ensemble is known but not pure. Methods for obtaining effective pure input states by a series of manipulations have been described by Gershenfeld and Chuang (logical labeling) [Science 275, 350 (1997)] and Cory et al. (spatial averaging) [Proc. Natl. Acad. Sci. USA 94, 1634 (1997)] for the case of quantum computation with nuclear magnetic resonance. We give a different technique called temporal averaging. This method is based on classical randomization, requires no ancilla quantum bits, and can be implemented in nuclear magnetic resonance without using gradient fields. We introduce several temporal averaging algorithms suitable for both high-temperature and low-temperature bulk quantum computing and analyze the signal-to-noise behavior of each. Most of these algorithms require only a constant multiple of the number of experiments needed by the other methods for creating effective pure states.