Time-optimal generation of cluster states

Fisher, Robert A.; Yuan, Haidong; Spörl, Andreas; Glaser, Steffen J.

doi:10.1103/physreva.79.042304

Cited by 22 publications

(20 citation statements)

References 28 publications

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“…with the coupling J as a given constant parameter in the action (1)-(3) from the beginning (cf. [42]) and without the need of imposing the constraints (12)- (13). However, a simple calculation shows that both variational methods lead to the same result (17) for the time-optimal magnetic field BOP T (t) (with B0, Bz and Ω given, respectively, by (50), (51) and (52)) and to the same time-optimal duration (49).…”

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confidence: 90%

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Time-optimal CNOT between indirectly coupled qubits in a linear Ising chain

Carlini¹,

Hosoya²,

Koike³

et al. 2011

J. Phys. A: Math. Theor.

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We give analytical solutions for the time-optimal synthesis of entangling gates between indirectly coupled qubits 1 and 3 in a linear spin chain of three qubits subject to an Ising Hamiltonian interaction with a symmetric coupling J plus a local magnetic field acting on the intermediate qubit. The energy available is fixed, but we relax the standard assumption of instantaneous unitary operations acting on single qubits. The time required for performing an entangling gate which is equivalent, modulo local unitary operations, to the CNOT(1, 3) between the indirectly coupled qubits 1 and 3 is T = 3/2 J −1 , i.e. faster than a previous estimate based on a similar Hamiltonian and the assumption of local unitaries with zero time cost. Furthermore, performing a simple WalshHadamard rotation in the Hlibert space of qubit 3 shows that the time-optimal synthesis of the CNOT ± (1, 3) (which acts as the identity when the control qubit 1 is in the state |0 , while if the control qubit is in the state |1 the target qubit 3 is flipped as |± → |∓ ) also requires the same time T .

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confidence: 90%

“…(54) ing the couplings J12(t) and J23(t) as dynamical variables in the action (1)- (3), and we make them become constant on shell via the imposition of the constraints (12)- (13). On the other hand, one might have chosen to start with J12 = J23 := J = const, i.e.…”

mentioning

confidence: 99%

Time-optimal CNOT between indirectly coupled qubits in a linear Ising chain

Carlini¹,

Hosoya²,

Koike³

et al. 2011

J. Phys. A: Math. Theor.

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“…State preparation protocols include transport of atoms [436] and ions [437,438] as well as transport in a spin chain [86,356,359,363,369,439,440], photon storage [441], preparation of squeezed states [442], cluster-states [443], non-classical states in a cavity [444] or in spin chains [364,365], as well as preparation of a quantum register [122] and many-body entangled states [123,445,446] -to name just a few.…”

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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“…In addition to analytical bounds for the strong pulse limit, optimal-control based algorithms make it possible to numerically explore the physical limits of polarization transfer efficiency in realistic settings, where experimental limitations have to be taken into account. The GRAPE algorithm [29,30] has been successfully applied to problems in liquid-state NMR [31][32][33][34][35][36][37][38], solidstate NMR [39], and quantum information processing [40,41]. In the context of broadband heteronuclear decoupling, robust inversion pulses with minimal rf power [38] are potential candidates for inversion elements suitable for cyclic decoupling sequences.…”

Section: Introductionmentioning

confidence: 99%