NMR Quantum Information Processing

Ramanathan, Chandrasekhar; Boulant, Nicolas; Chen, Zhiying; Cory, David G.; Chuang, Isaac L.; Steffen, Matthias

doi:10.1002/chin.200503278

Cited by 5 publications

(6 citation statements)

References 72 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In the following, we present an experiment which demonstrates the quantum algorithm for a ququart. Historically, many quantum algorithms were implemented in NMR systems 8 9 10 11 12 13 , especially those algorithms where entanglement is not required 14 15 16 17 . The implementation of the algorithm using a ququart is achieved using a spin– nuclei, which has been extensively used in NMR-QIP applications as exemplified in 18 19 20 21 22 23 24 25 26 27 28 29 30 and reviewed in 31 .…”

Section: Resultsmentioning

confidence: 99%

Computational speed-up with a single qudit

Gedik

Silva

Çakmak

et al. 2015

Sci Rep

112

114

View full text Add to dashboard Cite

Quantum algorithms are known for providing more efficient solutions to certain computational tasks than any corresponding classical algorithm. Here we show that a single qudit is sufficient to implement an oracle based quantum algorithm, which can solve a black-box problem faster than any classical algorithm. For 2d permutation functions defined on a set of d elements, deciding whether a given permutation is even or odd, requires evaluation of the function for at least two elements. We demonstrate that a quantum circuit with a single qudit can determine the parity of the permutation with only one evaluation of the function. Our algorithm provides an example for quantum computation without entanglement since it makes use of the pure state of a qudit. We also present an experimental realization of the proposed quantum algorithm with a quadrupolar nuclear magnetic resonance using a single four-level quantum system, i.e., a ququart.

show abstract

Section: Resultsmentioning

confidence: 99%

Computational speed-up with a single qudit

Gedik

Silva

Çakmak

et al. 2015

Sci Rep

112

114

View full text Add to dashboard Cite

show abstract

“…This results in a signal, proportional to the pseudopure parameter α (see Subsection 1.3.2), from which the logical state can be extracted. This process does not result in projective measurement, but still allows universal computation including full state tomography [28]. In addition, the expectation value of any Hermitian operator can be obtained in a single shot, allowing the measurement of arbitrary operators by quadrature detection [23].…”

Section: Measurement: Free Induction Decaymentioning

confidence: 99%

Few‐Qubit Magnetic Resonance Quantum Information Processors: Simulating Chemistry and Physics

Criger¹,

Park²,

Baugh³

2014

Advances in Chemical Physics

View full text Add to dashboard Cite

“…The goal of quantum control is to implement a nontrivial dynamical map on a quantum system as a means to achieve a desired task. Historically, the major developments in quantum control protocols have been motivated by applications in physical chemistry whereby shaped laser pulses excite molecular vibrations and rotations [1,2], and in nuclear magnetic resonance whereby shaped rf pulses cause desired spin rotations in magneticresonance-imaging [3,4,5]. More recently, quantum control theory has been considered in the development of quantum information processors in order to tackle the challenges of extreme precision and robustness to noise and environmental perturbations [5,6,7,8,9].…”

Section: Introductionmentioning

confidence: 99%

Constructing general unitary maps from state preparations

et al. 2009

View full text Add to dashboard Cite

We present an efficient algorithm for generating unitary maps on a d-dimensional Hilbert space from a time-dependent Hamiltonian through a combination of stochastic searches and geometric construction. The protocol is based on the eigen-decomposition of the map. A unitary matrix can be implemented by sequentially mapping each eigenvector to a fiducial state, imprinting the eigenphase on that state, and mapping it back to the eigenvector. This requires the design of only d state-to-state maps generated by control waveforms that are efficiently found by a gradient search with computational resources that scale polynomially in d. In contrast, the complexity of a stochastic search for a single waveform that simultaneously acts as desired on all eigenvectors scales exponentially in d. We extend this construction to design maps on an n-dimensional subspace of the Hilbert space using only n stochastic searches. Additionally, we show how these techniques can be used to control atomic spins in the ground electronic hyperfine manifold of alkali atoms in order to implement general qudit logic gates as well to perform a simple form of error correction on an embedded qubit.

show abstract

NMR Quantum Information Processing

Cited by 5 publications

References 72 publications

Computational speed-up with a single qudit

Computational speed-up with a single qudit

Few‐Qubit Magnetic Resonance Quantum Information Processors: Simulating Chemistry and Physics

Constructing general unitary maps from state preparations

Contact Info

Product

Resources

About