64 research outputs found
Spectral implementation of some quantum algorithms by one- and two-dimensional nuclear magnetic resonance
Quantum information processing has been effectively demonstrated on a small
number of qubits by nuclear magnetic resonance. An important subroutine in any
computing is the readout of the output. ``Spectral implementation'' originally
suggested by Z.L. Madi, R. Bruschweiler and R.R. Ernst,
[J. Chem. Phys. 109, 10603 (1999)], provides an elegant method of readout
with the use of an extra `observer' qubit. At the end of computation, detection
of the observer qubit provides the output via the multiplet structure of its
spectrum. In "spectral implementation" by two-dimensional experiment the
observer qubit retains the memory of input state during computation, thereby
providing correlated information on input and output, in the same spectrum.
"Spectral implementation" of Grover's search algorithm, approximate quantum
counting, a modified version of Berstein-Vazirani problem, and Hogg's algorithm
is demonstrated here in three and four-qubit systems.Comment: 39 pages,11 figure
Programmable quantum state discriminator by Nuclear Magnetic Resonance
In this paper a programmable quantum state discriminator is implemented by
using nuclear magnetic resonance. We use a two qubit spin-1/2 system, one for
the data qubit and one for the ancilla (programme) qubit. This device does the
unambiguous (error free) discrimination of pair of states of the data qubit
that are symmetrically located about a fixed state. The device is used to
discriminate both, linearly polarized states and elliptically polarized states.
The maximum probability of the successful discrimination is achieved by
suitably preparing the ancilla qubit. It is also shown that, the probability of
discrimination depends on angle of unitary operator of the protocol and
ellipticity of the data qubit state.Comment: 22 pages and 9 figure
Quantum Information processing by NMR: Implementation of Inversion-on-equality gate, Parity gate and Fanout gate
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.Comment: 24 pages, 7 figure
Efficient Quantum State Tomography for Quantum Information Processing using a two-dimensional Fourier Transform Technique
A new method of quantum state tomography for quantum information processing
is described. The method based on two-dimensional Fourier transform technique
involves detection of all the off-diagonal elements of the density matrix in a
two-dimensional experiment. All the diagonal elements are detected in another
one-dimensional experiment. The method is efficient and applicable to a wide
range of spin systems. The proposed method is explained using a 2 qubit system
and demonstrated by tomographing arbitrary complex density matrices of 2 and 4
qubit systems using simulations.Comment: 11 pages and 2 figure
Search for optimum labeling schemes in qubit systems for Quantum Information processing by NMR
Optimal labeling schemes lead to efficient experimental protocols for quantum
information processing by nuclear magnetic resonance (NMR). A systematic
approach of finding optimal labeling schemes for a given computation is
described here. The scheme is described for both quadrupolar systems and
spin-1/2 systems. Finally, one of the optimal labeling scheme has been used to
experimentally implement a quantum full-adder in a 4-qubit system by NMR, using
the technique of transition selective pulses.Comment: 24 pages, 6 figure
Quantum Information processing by NMR: Preparation of pseudopure states and implementation of unitary operations in a single-qutrit system
Theoretical Quantum Information Processing (QIP) has matured from the use of
qubits to the use of qudits (systems having states> 2). Where as most of the
experimental implementations have been performed using qubits, little
experimental work has been carried out using qudits as yet. In this paper we
demonstrate experimental realization of a qutrit system by nuclear magnetic
resonance (NMR), utilizing deuterium (spin-1) nuclei partially oriented in
liquid crystalline phase. Preparation of pseudopure states and implementation
of unitary operations are demonstrated in this single-qutrit system, using
transition selective pulses.Comment: 11 pages, 2 figure
Use of non-adiabatic geometric phase for quantum computing by nuclear magnetic resonance
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
Experimental implementation of local adiabatic evolution algorithms by an NMR quantum information processor
Quantum adiabatic algorithm is a method of solving computational problems by
evolving the ground state of a slowly varying Hamiltonian. The technique uses
evolution of the ground state of a slowly varying Hamiltonian to reach the
required output state. In some cases, such as the adiabatic versions of
Grover's search algorithm and Deutsch-Jozsa algorithm, applying the global
adiabatic evolution yields a complexity similar to their classical algorithms.
However, using the local adiabatic evolution, the algorithms given by J. Roland
and N. J. Cerf for Grover's search [ Phys. Rev. A. {\bf 65} 042308(2002)] and
by Saurya Das, Randy Kobes and Gabor Kunstatter for the Deutsch-Jozsa algorithm
[Phys. Rev. A. {\bf 65}, 062301 (2002)], yield a complexity of order
(where N=2 and n is the number of qubits). In this paper we report
the experimental implementation of these local adiabatic evolution algorithms
on a two qubit quantum information processor, by Nuclear Magnetic Resonance.Comment: Title changed, Adiabatic Grover's search algorithm added, error
analysis modifie
Quantum information processing by NMR using a 5-qubit system formed by dipolar coupled spins in an oriented molecule
Quantum Information processing by NMR with small number of qubits is well
established. Scaling to higher number of qubits is hindered by two major
requirements (i) mutual coupling among qubits and (ii) qubit addressability. It
has been demonstrated that mutual coupling can be increased by using residual
dipolar couplings among spins by orienting the spin system in a liquid
crystalline matrix. In such a case, the heteronuclear spins are weakly coupled
but the homonuclear spins become strongly coupled. In such circumstances, the
strongly coupled spins can no longer be treated as qubits. However, it has been
demonstrated elsewhere, that the energy levels of a strongly coupled N
spin-1/2 system can be treated as an N-qubit system. For this purpose the
various transitions have to be identified to well defined energy levels. This
paper consists of two parts. In the first part, the energy level diagram of a
heteronuclear 5-spin system is obtained by using a newly developed
heteronuclear z-cosy (HET-Z-COSY) experiment. In the second part,
implementation of logic gates, preparation of pseudopure states, creation of
entanglement and entanglement transfer is demonstrated, validating the use of
such systems for quantum information processing.Comment: 23 pages, 8 figure
Use of Quadrupolar Nuclei for Quantum Information processing by Nuclear Magnetic Resonance: Implementation of a Quantum Algorithm
Physical implementation of Quantum Information Processing (QIP) by
liquid-state Nuclear Magnetic Resonance (NMR), using weakly coupled spin-1/2
nuclei of a molecule, is well established. Nuclei with spin1/2 oriented in
liquid crystalline matrices is another possibility. Such systems have multiple
qubits per nuclei and large quadrupolar couplings resulting in well separated
lines in the spectrum. So far, creation of pseudopure states and logic gates
have been demonstrated in such systems using transition selective
radio-frequency pulses. In this paper we report two novel developments. First,
we implement a quantum algorithm which needs coherent superposition of states.
Second, we use evolution under quadrupolar coupling to implement multi qubit
gates. We implement Deutsch-Jozsa algorithm on a spin-3/2 (2 qubit) system. The
controlled-not operation needed to implement this algorithm has been
implemented here by evolution under the quadrupolar Hamiltonian. This method
has been implemented for the first time in quadrupolar systems. Since the
quadrupolar coupling is several orders of magnitude greater than the coupling
in weakly coupled spin-1/2 nuclei, the gate time decreases, increasing the
clock speed of the quantum computer.Comment: 16 pages, 3 figure
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