Bulk Spin-Resonance Quantum Computation

Geometric phases have stimulated researchers for its potential applications in many areas of science. One of them is fault-tolerant quantum computation. A preliminary requisite of quantum computation is the implementation of controlled logic gates by controlled dynamics of qubits. In controlled dynamics, one qubit undergoes coherent evolution and acquires appropriate phase, depending on the state of other qubits. If the evolution is geometric, then the phase acquired depend only on the geometry of the path executed, and is robust against certain types of errors. This phenomenon leads to an inherently fault-tolerant quantum computation. Here we suggest a technique of using non-adiabatic geometric phase for quantum computation, using selective excitation. In a two-qubit system, we selectively evolve a suitable subsystem where the control qubit is in state |1 , through a closed circuit. By this evolution, the target qubit gains a phase controlled by the state of the control qubit. Using these geometric phase gates we demonstrate implementation of Deutsch-Jozsa algorithm and Grover's search algorithm in a two-qubit system.

mentioning

confidence: 99%

Use of non-adiabatic geometric phase for quantum computing by NMR

Das

Kumar

2005

“…Many applications in NMR spectroscopy (6,7) and NMR quantum computing (10,11,12) require unitary transformations of the form…”

Section: Theorymentioning

confidence: 99%

Broadband geodesic pulses for three spin systems: time-optimal realization of effective trilinear coupling terms and indirect SWAP gates

Reiss

Khaneja

Glaser

2003

Broadband implementations of time-optimal geodesic pulse elements are introduced for the efficient creation of effective trilinear coupling terms for spin systems consisting of three weakly coupled spins 1/2. Based on these pulse elements, the time-optimal implementation of indirect SWAP operations is demonstrated experimentally. The duration of indirect SWAP gates based on broadband geodesic sequence is reduced by 42.3% compared to conventional approaches.

“…Nuclear magnetic resonance (NMR) has played a leading role for practical demonstration of quantum algorithms and quantum gates . Deutsch-Jozsa algorithm [9][10][11][12], Grover's search algorithm [13][14][15], quantum Fourier transform [16] and the Shor's factorization algorithm [17] have been implemented by liquid-state NMR. The unitary operators needed for implementation of these algorithms by NMR, have mostly been realized using spin selective radio frequency (r.f) pulses and coupling evolution, utilizing indirect spin-spin(J) or dipolar couplings among the spins.…”

Section: Introductionmentioning

confidence: 99%

Implementation of conditional phase-shift gate for quantum information processing by NMR, using transition-selective pulses

Das

Mahesh

Kumar

2002

Experimental realization of quantum information processing in the field of nuclear magnetic resonance (NMR) has been well established. Implementation of conditional phase shift gate has been a significant step, which has lead to realization of important algorithms such as Grover's search algorithm and quantum Fourier transform. This gate has so far been implemented in NMR by using coupling evolution method. We demonstrate here the implementation of the conditional phase shift gate using transition selective pulses. As an application of the gate, we demonstrate Grover's search algorithm and quantum Fourier transform by simulations and experiments using transition selective pulses.