NMR Based Quantum Information Processing: Achievements and Prospects

Cory, D. G.; Boulant, N.; Boutis, G.; Fortunato, E.; Pravia, M.; Sharf, Y.; Laflamme, R.; Knill, E.; Martínez, Ramon Arcas; Negrevergne, C.; Zurek, W. H.; Havel, T. F.; Viola, L.; Lloyd, S.; Weinstein, Yaakov S.; Teklemariam, G.

doi:10.1002/3527603182.ch8

Cited by 8 publications

(16 citation statements)

References 59 publications

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“….3766 sec (9) .3294 sec (5) .2237 sec (5) .2308 sec (5) .3120 sec (3) .4137 sec (1) Placement with the 12-qubit histidine molecule [20] Circuit Threshold 50 100 200 500 1000 10000 phaseest 1.2022 sec (7) .6860 sec (4) .6860 sec (4) .1827 sec (3) .1517 sec (2) .1870 sec (1) qft6 1.9824 drv (9) .9519 sec (6) 1.1607 sec (5) .3123 sec (4) .5623 sec (3) .4412 sec (1) N × log(N) gates are created, we again randomly permute our N elements and then randomly generate N × log(N) gates in the chain nearest neighbor architecture that corresponds to this permutation. This is repeated log(N) times.…”

Section: Resultsmentioning

confidence: 99%

“…are done by changing the rotating reference frame [13] and require no pulse or a delay associated with respect to their application [5]) and a 90-degree zz-rotation (2 qubit gate). The delays are measured in terms of …”

Section: Example 1 Illustrated In Figure 1(a) Is the Acetyl Chloridementioning

confidence: 99%

“…While there are certain problems with using liquid state NMR to work with over 10 qubits [5,11,20], so far, it is the best developed methodology for quantum computing experiments. Liquid state NMR experiments provide a nice data set for both the interaction frequencies and the circuits of interest, and a test bed for development of suitable scalable spin-based quantum computing devices.…”

Section: Introductionmentioning

confidence: 99%

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Quantum Circuit Placement

Maslov

Falconer

Mosca

2008

IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.

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We study the problem of the practical realization of an abstract quantum circuit when executed on quantum hardware. By practical, we mean adapting the circuit to particulars of the physical environment which restricts/complicates the establishment of certain direct interactions between qubits. This is a quantum version of the classical circuit placement problem. We study the theoretical aspects of the problem and also present empirical results that match the best known solutions that have been developed by experimentalists. Finally, we discuss the efficiency of the approach and scalability of its implementation with regards to the future development of quantum hardware.

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Section: Resultsmentioning

confidence: 99%

Section: Example 1 Illustrated In Figure 1(a) Is the Acetyl Chloridementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quantum Circuit Placement

Maslov

Falconer

Mosca

2008

IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.

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“…The cost definition must reflect how difficult it is to implement the gate and, therefore, will depend on the details of the physical device considered to implement the circuit. For example, for nuclear magnetic resonance (NMR) techniques, the cost of the gate must take into account the number of RF pulses, as well as the duration of the interaction periods necessary to implement the gate [4]. In a setting guided by the Ising-type Hamiltonian in a weak coupling regime (such as liquid NMR [4] and superconductors [6]), a controlled-V and its complex conjugate must be associated with approximately half the cost of a CNOT gate each.…”

Section: Introductionmentioning

confidence: 99%

“…ESEARCH in quantum circuit synthesis is motivated by the growing interest in quantum computation [19] and advances in experimental implementations [4], [7], [8], [25]. In realistic devices, experimental errors and decoherence introduce errors during computation.…”

mentioning

confidence: 99%

Quantum Circuit Simplification and Level Compaction

Maslov

Dueck

Miller

et al. 2008

IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.

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227

246

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Abstract-Quantum circuits are time-dependent diagrams describing the process of quantum computation. Usually, a quantum algorithm must be mapped into a quantum circuit. Optimal synthesis of quantum circuits is intractable, and heuristic methods must be employed. With the use of heuristics, the optimality of circuits is no longer guaranteed. In this paper, we consider a local optimization technique based on templates to simplify and reduce the depth of nonoptimal quantum circuits. We present and analyze templates in the general case and provide particular details for the circuits composed of NOT, CNOT, and controlled-sqrt-of-NOT gates. We apply templates to optimize various common circuits implementing multiple control Toffoli gates and quantum Boolean arithmetic circuits. We also show how templates can be used to compact the number of levels of a quantum circuit. The runtime of our implementation is small, whereas the reduction in the number of quantum gates and number of levels is significant.

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