Control aspects of quantum computing using pure and mixed states

A closed quantum system is defined as completely controllable if an arbitrary unitary transformation can be executed using the available controls. In practice, control fields are a source of unavoidable noise, which has to be suppressed to retain controllability. Can one design control fields such that the effect of noise is negligible on the time-scale of the transformation? This question is intimately related to the fundamental problem of a connection between the computational complexity of the control problem and the sensitivity of the controlled system to noise. The present study considers a paradigm of control, where the Lie-algebraic structure of the control Hamiltonian is fixed, while the size of the system increases with the dimension of the Hilbert space representation of the algebra. We find two types of control tasks, easy and hard. Easy tasks are characterized by a small variance of the evolving state with respect to the operators of the control operators. They are relatively immune to noise and the control field is easy to find. Hard tasks have a large variance, are sensitive to noise and the control field is hard to find. The influence of noise increases with the size of the system, which

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“…In fact, purity loss can be associated with the average fidelity of the state to state transformation. The fidelity is defined by [8,34]…”

Section: Purity and Fidelitymentioning

confidence: 99%

“…controlling a unitary transformation. Such an application sets the foundation for a quantum gate operation [5][6][7][8]. Controllability of a closed quantum system has been addressed by Tarn and Clark [9].…”

Section: Introductionmentioning

confidence: 99%

Quantum control with noisy fields: computational complexity versus sensitivity to noise

2014

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“…The Jones polynomial, i.e., a central invariant in knot theory, can be evaluated, using an NMR spin ensemble at ambient temperature, in an algorithm equivalent to deterministic quantum computing with a single pure qubit [467][468][469].…”

Section: State Of the Artmentioning

confidence: 99%

Training Schrödinger’s cat: quantum optimal control

et al. 2015

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Abstract. It is control that turns scientific knowledge into useful technology: in physics and engineering it provides a systematic way for driving a dynamical system from a given initial state into a desired target state with minimized expenditure of energy and resources. As one of the cornerstones for enabling quantum technologies, optimal quantum control keeps evolving and expanding into areas as diverse as quantumenhanced sensing, manipulation of single spins, photons, or atoms, optical spectroscopy, photochemistry, magnetic resonance (spectroscopy as well as medical imaging), quantum information processing and quantum simulation. In this communication, state-of-the-art quantum control techniques are reviewed and put into perspective by a consortium of experts in optimal control theory and applications to spectroscopy, imaging, as well as quantum dynamics of closed and open systems. We address key challenges and sketch a roadmap for future developments. ForewordThe authors of this paper represent the QUAINT consortium, a European Coordination Action on Optimal Control of Quantum Systems, funded by the European Commission Framework Programme 7, Future Emerging Technologies FET-OPEN programme and the Virtual Facility for Quantum Control (VF-QC). This consortium has considerable expertise in optimal control theory and its applications to quantum systems, both in existing areas, such as spectroscopy and imaging, and in emerging quantum technologies, such as quantum information processing, quantum communication, quantum simulation a e-mail: fwm@lusi.uni-sb.de and quantum sensing. The list of challenges for quantum control has been gathered by a broad poll of leading researchers across the communities of general and mathematical control theory, atomic, molecular-, and chemical physics, electron and nuclear magnetic resonance spectroscopy, as well as medical imaging, quantum information, communication and simulation. 144 experts in these fields have provided feedback and specific input on the state of the art, mid-term and long-term goals. Those have been summarized in this document, which can be viewed as a perspectives paper, providing a roadmap for the future development of quantum control. Because such an endeavour can hardly ever be complete (there are many additional areas of quantum control applications, such as spintronics, nano-optomechanical technologies etc.), this roadmap

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“…Such a topic is reviewed by Schulte-Herbrüggen et al [4], which illustrates the techniques of quantum control in mixed-state scenarios considering some algorithm classes, such as characterizing the Jones polynomial in order to distinguish between different knots. The quantum control of phases is also the main topic exploited in Simmons et al [5].…”

Section: Introductionmentioning

confidence: 99%

Nuclear magnetic resonance quantum information processing

Serra

2012

Phil. Trans. R. Soc. A.

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For the past decade, nuclear magnetic resonance (NMR) has been established as a main experimental technique for testing quantum protocols in small systems. This Theme Issue presents recent advances and major challenges of NMR quantum information possessing (QIP), including contributions by researchers from 10 different countries. In this introduction, after a short comment on NMR-QIP basics, we briefly anticipate the contents of this issue.

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Control aspects of quantum computing using pure and mixed states

Cited by 20 publications

References 80 publications

Quantum control with noisy fields: computational complexity versus sensitivity to noise

Quantum control with noisy fields: computational complexity versus sensitivity to noise

Training Schrödinger’s cat: quantum optimal control

Nuclear magnetic resonance quantum information processing

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