Thermal equilibrium as an initial state for quantum computation by NMR

Fahmy, Amr; Marx, Raimund; Bermel, Wolfgang; Glaser, Steffen J.

doi:10.1103/physreva.78.022317

Cited by 22 publications

(25 citation statements)

References 36 publications

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“…Second, it is known that using ancilla qubits entangled with "system" qubits enhances the possibility of successful discrimination between unitaries [11] and it is conceivable that this could also yield a larger set of quantum algorithms and improved lower bounds in the thermal equilibrium case. Finally, in the thermal equilibrium scenario, relaxation to the thermal equilibrium state could be followed by a non-unitary quantum operation [30] and we have not assessed bounds in any such cases.…”

Section: Discussionmentioning

confidence: 99%

Discrimination of unitary transformations in the Deutsch-Jozsa algorithm: Implications for thermal-equilibrium-ensemble implementations

Collins

2010

Phys. Rev. A

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We describe a general framework for regarding oracle-assisted quantum algorithms as tools for discriminating between unitary transformations. We apply this to the Deutsch-Jozsa problem and derive all possible quantum algorithms which solve the problem with certainty using oracle unitaries in a particular form. We also use this to show that any quantum algorithm that solves the DeutschJozsa problem starting with a quantum system in a particular class of initial, thermal equilibriumbased states of the type encountered in solution state NMR can only succeed with greater probability than a classical algorithm when the problem size exceeds n ∼ 10 5 .

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Section: Discussionmentioning

confidence: 99%

Discrimination of unitary transformations in the Deutsch-Jozsa algorithm: Implications for thermal-equilibrium-ensemble implementations

Collins

2010

Phys. Rev. A

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“…Together with proper temporal or spatial averaging procedures and evolution under spin interactions [23], the RF pulse can be specially designed to prepare any two-qubit computational base states, as well as their superpositions, starting from the thermal equilibrium state [2,[24][25][26].…”

Section: Measuring Quantum and Classical Correlations In Nuclear Magnmentioning

confidence: 99%

On the quantumness of correlations in nuclear magnetic resonance

Soares-Pinto

Auccaise

Maziero

et al. 2012

Phil. Trans. R. Soc. A.

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Nuclear magnetic resonance (NMR) was successfully employed to test several protocols and ideas in quantum information science. In most of these implementations, the existence of entanglement was ruled out. This fact introduced concerns and questions about the quantum nature of such bench tests. In this paper, we address some issues related to the non-classical aspects of NMR systems. We discuss some experiments where the quantum aspects of this system are supported by quantum correlations of separable states. Such quantumness, beyond the entanglement-separability paradigm, is revealed via a departure between the quantum and the classical versions of information theory. In this scenario, the concept of quantum discord seems to play an important role. We also present an experimental implementation of an analogue of the single-photon MachZehnder interferometer employing two nuclear spins to encode the interferometric paths. This experiment illustrates how non-classical correlations of separable states may be used to simulate quantum dynamics. The results obtained are completely equivalent to the optical scenario, where entanglement (between two field modes) may be present.

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“…It has been shown that even with very low (or no) entanglement, quantum information processing can still be performed using nonclassical correlations as characterized by the presence of quantum discord [11,12]. However, computing and measuring quantum discord typically involves complicated numerical optimization and furthermore it has been shown that computing quantum discord is NP-hard [13].…”

Section: Introductionmentioning

confidence: 99%

Witnessing nonclassical correlations via a single-shot experiment on an ensemble of spins using nuclear magnetic resonance

2017

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A bipartite quantum system in a mixed state can exhibit nonclassical correlations, which can go beyond quantum entanglement. While quantum discord is the standard measure of quantifying such general quantum correlations, the nonclassicality can be determined by simpler means via the measurement of witness operators. We experimentally construct a positive map to witness nonclassicality of two qubits in an NMR system. The map can be decomposed so that a single run of an experiment on an ensemble of spins suffices to detect the nonclassicality in the state, if present. We let the state evolve in time and use the map to detect nonclassicality as a function of time. To evaluate the efficacy of the witness operator as a means to detect nonclassicality, we measure quantum discord by performing full quantum state tomography at each time point and obtained a fairly good match between the two methods.

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Thermal equilibrium as an initial state for quantum computation by NMR

Cited by 22 publications

References 36 publications

Discrimination of unitary transformations in the Deutsch-Jozsa algorithm: Implications for thermal-equilibrium-ensemble implementations

Discrimination of unitary transformations in the Deutsch-Jozsa algorithm: Implications for thermal-equilibrium-ensemble implementations

On the quantumness of correlations in nuclear magnetic resonance

Witnessing nonclassical correlations via a single-shot experiment on an ensemble of spins using nuclear magnetic resonance

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