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arXiv:quant-ph/0612158 · Journal of Physics A Mathematical and Theoretical

Attainable entanglement of unitary transformed thermal states in liquid-state nuclear magnetic resonance with the chemical shift

Yukihiro Ota, Shuji Mikami, Motoyuki Yoshida, Ichiro Ohba

Published Nov 6, 2007• 0 citations
arXivHTMLPDF

Abstract

Recently, Yu, Brown, and Chuang [Phys. Rev. A {\bf 71}, 032341 (2005)] investigated the entanglement attainable from unitary transformed thermal states in liquid-state nuclear magnetic resonance (NMR). Their research gave an insight into the role of the entanglement in a liquid-state NMR quantum computer. Moreover, they attempted to reveal the role of mixed-state entanglement in quantum computing. However, they assumed that the Zeeman energy of each nuclear spin which corresponds to a qubit takes a common value for all; there is no chemical shift. In this paper, we research a model with the chemical shifts and analytically derive the physical parameter region where unitary transformed thermal states are entangled, by the positive partial transposition (PPT) criterion with respect to any bipartition. We examine the effect of the chemical shifts on the boundary between the separability and the nonseparability, and find it is negligible.

DOI
10.1088/1751-8113/40/47/016

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Recently, Yu, Brown, and Chuang [Phys. Rev. A {\bf 71}, 032341 (2005)] investigated the entanglement attainable from unitary transformed thermal states in liquid-state nuclear magnetic resonance (NMR). Their research gave an insight into the role of the entanglement in a liquid-state NMR quantum computer. Moreover, they attempted to reveal the role of mixed-state entanglement in quantum computing. However, they assumed that the Zeeman energy of each nuclear spin which corresponds to a qubit takes a common value for all; there is no chemical shift. In this paper, we research a model with the chemical shifts and analytically derive the physical parameter region where unitary transformed thermal states are entangled, by the positive partial transposition (PPT) criterion with respect to any bipartition. We examine the effect of the chemical shifts on the boundary between the separability and the nonseparability, and find it is negligible.
The role of mixed-state entanglement in liquid-state nuclear magnetic resonance (NMR) quantum computation is not yet well understood. In particular, despite the success of quantum-information processing with NMR, recent work has shown that quantum states used in most of those experiments were not entangled. This is because these states, derived by unitary transforms from the thermal equilibrium state, were too close to the maximally mixed state. We are thus motivated to determine whether a given NMR state is entanglable---that is, does there exist a unitary transform that entangles the state? The boundary between entanglable and nonentanglable thermal states is a function of the spin system size NNN and its temperature TTT. We provide bounds on the location of this boundary using analytical and numerical methods; our tightest bound scales as $N\ensuremath{\sim}T$, giving a lower bound requiring at least $N\ensuremath{\sim}22\phantom{\rule{0.2em}{0ex}}000$ proton spins to realize an entanglable thermal state at typical laboratory NMR magnetic fields. These bounds are tighter than known bounds on the entanglability of effective pure states.
Abstract Decoherence of the bipartite entangled mixed state in a five‐qubit system has been studied experimentally with liquid‐state nuclear magnetic resonance (NMR). The experimental results indicate that when only two qubits of the five qubits are partially initialized, the decoherence process of the bipartite entangled mixed state is not quantized, as the entanglability is weak. In contrast, when all five qubits are initialized, the decoherence process is quantized, which is understood to indicate that the entanglability is actually strong. From these results, it is conceivable that the entropy of the deviation density matrix is a crucial factor in measuring the entanglement in the liquid‐state NMR quantum computer. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005
This research explores the integration of quantum mechanics, machine learning, and quantum computing to advance predictive modeling of nuclear magnetic resonance (NMR) parameters. The aim is to develop a hybrid quantum-enhanced machine learning model that combines the accuracy of quantum calculations with the efficiency of machine learning techniques for predicting NMR chemical shifts. The conceptual framework involves quantum mechanical calculations for accurate reference NMR parameters, supervised machine learning models trained on diverse molecular datasets, and hybrid quantum-classical algorithms to leverage quantum computing resources. A simplified numerical example demonstrates the potential of the proposed model for predicting NMR chemical shifts for small molecular systems. The results showcase the model's ability to capture underlying relationships between molecular features and NMR observables, indicating promise for larger and more complex systems. This interdisciplinary approach opens new avenues for advancing NMR spectroscopy and understanding molecular structures, dynamics, and interactions in various scientific domains. The research also discusses challenges and opportunities in integrating quantum mechanics, machine learning, and quantum computing, emphasizing the importance of diverse datasets and quantum algorithm selection. The proposed model holds significant implications for transforming NMR parameter predictions and contributing to chemistry, biochemistry, and materials science research
A proposal for applying nonadiabatic geometric phases to quantum computing, called double-loop method [S.-L. Zhu and Z. D. Wang, Phys. Rev. A 67, 022319 (2003)], is demonstrated in a liquid-state nuclear magnetic-resonance quantum computer. Using a spin-echo technique, the original method is modified so that quantum gates are implemented in a standard high-precision nuclear magnetic-resonance system for chemical analysis. We show that a dynamical phase is successfully eliminated and a one-qubit quantum gate is realized although the gate fidelity is not high.
We report the implementation of an entanglement transfer on a four-qubit liquid-state nuclear-magnetic resonance quantum information processor. This consists of creating an (pseudopure) entangled state among two directly coupled spins, and then transferring this two-spin state to another pair of spins whose direct interactions are negligible. Such transfers are expected to be an essential operation in scalable quantum computer architectures, and provide a useful benchmark for the coherent control available in specific implementations.