While quantum information processing by nuclear magnetic resonance (NMR) with small number of qubits is well established, implementation of lengthy computations have proved to be difficult due to decoherence/relaxation. In such circumstances, shallow circuits (circuits using parallel computation) may prove to be realistic. Parity and fanout gates are essential to create shallow circuits. In this article we implement inversion-on-equality gate, followed by parity gate and fanout gate in 3-qubit systems by NMR, using evolution under indirect exchange coupling Hamiltonian.While quantum information processing by nuclear magnetic resonance (NMR) with small number of qubits is well established, implementation of lengthy computations have proved to be difficult due to decoherence/relaxation. In such circumstances, shallow circuits (circuits using parallel computation) may prove to be realistic. Parity and fanout gates are essential to create shallow circuits. In this article we implement inversion-on-equality gate, followed by parity gate and fanout gate in 3-qubit systems by NMR, using evolution under indirect exchange coupling Hamiltonian.

arXiv:quant-ph/0404036Apr 6, 20041 citation

Classical model for bulk-ensemble NMR quantum computation

Rüdiger Schack, Carlton M. Caves

We present a classical model for bulk-ensemble NMR quantum computation: the quantum state of the NMR sample is described by a probability distribution over the orientations of classical tops, and quantum gates are described by classical transition probabilities. All NMR quantum computing experiments performed so far with three quantum bits can be accounted for in this classical model. After a few entangling gates, the classical model suffers an exponential decrease of the measured signal, whereas there is no corresponding decrease in the quantum description. We suggest that for small numbers of quantum bits, the quantum nature of NMR quantum computation lies in the ability to avoid an exponential signal decrease.We present a classical model for bulk-ensemble NMR quantum computation: the quantum state of the NMR sample is described by a probability distribution over the orientations of classical tops, and quantum gates are described by classical transition probabilities. All NMR quantum computing experiments performed so far with three quantum bits can be accounted for in this classical model. After a few entangling gates, the classical model suffers an exponential decrease of the measured signal, whereas there is no corresponding decrease in the quantum description. We suggest that for small numbers of quantum bits, the quantum nature of NMR quantum computation lies in the ability to avoid an exponential signal decrease.

arXiv:quant-ph/9903101Physical Review ADec 1, 199976 citations

Quantum computing with NMR

Jonathan A. Jones

arXiv:1011.1382Progress in Nuclear Magnetic Resonance SpectroscopyNov 9, 2010188 citations

Quantum and classical parallelism in parity algorithms for ensemble quantum computers

Ralf Stadelhofer, Dieter Suter, Wolfgang Banzhaf

The determination of the parity of a string of $N$ binary digits is a well-known problem in classical as well as quantum information processing, which can be formulated as an oracle problem. It has been established that quantum algorithms require at least $N∕2$ oracle calls. We present an algorithm that reaches this lower bound and is also optimal in terms of additional gate operations required. We discuss its application to pure and mixed states. Since it can be applied directly to thermal states, it does not suffer from signal loss associated with pseudo-pure-state preparation. For ensemble quantum computers, the number of oracle calls can be further reduced by a factor ${2}^{k}$ , with $k∊{1,2,\dots{},{\mathrm{log}}_{2}(N∕2)}$ , provided the signal-to-noise ratio is sufficiently high. This additional speed-up is linked to (classical) parallelism of the ensemble quantum computer. Experimental realizations are demonstrated on a liquid-state NMR quantum computer.The determination of the parity of a string of $N$ binary digits is a well-known problem in classical as well as quantum information processing, which can be formulated as an oracle problem. It has been established that quantum algorithms require at least $N∕2$ oracle calls. We present an algorithm that reaches this lower bound and is also optimal in terms of additional gate operations required. We discuss its application to pure and mixed states. Since it can be applied directly to thermal states, it does not suffer from signal loss associated with pseudo-pure-state preparation. For ensemble quantum computers, the number of oracle calls can be further reduced by a factor ${2}^{k}$, with $k∊{1,2,\dots{},{\mathrm{log}}_{2}(N∕2)}$, provided the signal-to-noise ratio is sufficiently high. This additional speed-up is linked to (classical) parallelism of the ensemble quantum computer. Experimental realizations are demonstrated on a liquid-state NMR quantum computer.

Physical Review AMar 28, 200520 citations

NMR quantum computation

Jonathan A. Jones

Progress in Nuclear Magnetic Resonance SpectroscopyJun 1, 2001177 citations

The determination of the parity of a string of

N

binary digits is a well-known problem in classical as well as quantum information processing, which can be formulated as an oracle problem. It has been established that quantum algorithms require at least

N∕2

oracle calls. We present an algorithm that reaches this lower bound and is also optimal in terms of additional gate operations required. We discuss its application to pure and mixed states. Since it can be applied directly to thermal states, it does not suffer from signal loss associated with pseudo-pure-state preparation. For ensemble quantum computers, the number of oracle calls can be further reduced by a factor

{2}^{k}

, with

k∊{1,2,\dots{},{\mathrm{log}}_{2}(N∕2)}

, provided the signal-to-noise ratio is sufficiently high. This additional speed-up is linked to (classical) parallelism of the ensemble quantum computer. Experimental realizations are demonstrated on a liquid-state NMR quantum computer.