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arXiv:1003.2065 · Physical Review A

Preparing pseudopure states with controlled-transfer gates

Minaru Kawamura, Benjamin C. Rowland, Jonathan A. Jones

Published Sep 17, 2010• 12 citations
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Abstract

The preparation of pseudopure states plays a central role in the implementation of quantum information processing in high-temperature ensemble systems, such as nuclear magnetic resonance. Here we describe a simple approach based on controlled-transfer gates which permits pseudopure states to be prepared efficiently using spatial averaging techniques.

DOI
10.1103/physreva.82.032315

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The preparation of pseudopure states plays a central role in the implementation of quantum information processing in high-temperature ensemble systems, such as nuclear magnetic resonance. Here we describe a simple approach based on controlled-transfer gates which permits pseudopure states to be prepared efficiently using spatial averaging techniques.
The use of nuclear magnetic resonance (NMR) to carry out quantum information processing (QIP) often requires the preparation, transformation, and detection of pseudopure states. In our previous work, it was shown that the use of pairs of pseudopure states (POPS) as a basis for QIP is very convenient because of the simplicity in experimental execution. It is now further demonstrated that the product of the NMR spectra corresponding to two sets of POPS that share a common pseudopure state has the same peak frequencies as those of the common (single) pseudopure state. Examples of applying two different quantum logic gates to a 5-qubit system are given.
Quantum-information processing by liquid-state NMR spectroscopy uses pseudopure states to mimic the evolution and observations on true pure states. A new method of preparing pseudopure states is described, which involves the selection of spatially labeled states of an ancilla spin with which the spin system of interest is correlated. This permits a general procedure to be given for the preparation of pseudopure states on any number of spins, subject to the limitations imposed by the loss of signal from the selected subensemble. The preparation of a single pseudopure state is demonstrated by carbon and proton NMR of 13C{}^{13}\mathrm{C}13C-labeled alanine. With a judicious choice of magnetic-field gradients, the method further allows encoding of up to 2N{2}^{N}2N pseudopure states in independent spatial modes in an N+1N+1N+1 spin system. Fast encoding and decoding schemes are demonstrated for the preparation of four such spatially labeled pseudopure states.
Nuclear magnetic resonance (NMR) is one of the experimental schemes for quantum computation. Most initial state of quantum algorithm in NMR computation is the pseudopure state. Until now, there are several methods to prepare pseudopure state. This note, based on the idea of controlled-not (CNOT) gates combination, has analyzed the characteristics of this method in the odd- and even-qubit system. Also, we have designed the pulse sequence for a 4-qubit sample to obtain pseudopure state, and realized it in the experiment. This method reduces the complexity of experiment and gives a high signal-to-noise (S/N) ratio.
A method for creating pseudopure states in NMR is described that combines spatial averaging and logical labeling techniques. This method uses one labeling qubit and any desired pseudopure state of any number of qubits can be created in the subsystem manifolds of the labeling qubit. The method uses a nonselective $\ensuremath{\pi}/2$ radio frequency pulse on all the nonlabeling qubits to equalize the populations of all the states within each subsystem, followed by a single transition-selective $\ensuremath{\pi}$ pulse on one of the transitions of the labeling qubit. The transverse magnetization created during the process is destroyed by a magnetic field gradient pulse, yielding a subsystem pseudopure state. The method is demonstrated experimentally on a system of three qubits.
Quantum-information processing is carried out using dipolar coupled spins and high-resolution nuclear magnetic resonance (NMR). The systems chosen are the dipolar coupled methyl protons of CH3CN{\mathrm{CH}}_{3}\mathrm{CN}CH3​CN partially oriented in a liquid crystalline matrix yielding a two-qubit system and dipolar coupled 13C{}^{13}\mathrm{C}13C and methyl protons of 13CH3CN{}^{13}{\mathrm{CH}}_{3}\mathrm{CN}13CH3​CN also partially oriented in the liquid crystalline matrix, yielding a three-qubit system. The dipolar coupled protons of oriented CH3{\mathrm{CH}}_{3}CH3​ group are chemically and magnetically identical and their eigenstates can be divided into a set of quartet states (symmetric A) and a pair of doublet (E) states. We describe here a method for selectively retaining the magnetization of the symmetric states, yielding two and three qubit systems. We create pseudopure states using single-quantum-transition selective pulses and implement two- and three-qubit gates using one- and two-dimensional NMR.
The premise of nuclear magnetic resonance (NMR) quantum computing is that pseudopure quantum states, for which the populations of all energy levels but one are equal, can be used instead of pure quantum states. However, for systems with a large number of quantum bits (qubits), it would require elaborate pulse sequences with many steps to prepare these pseudopure states. To overcome this problem, a method using pairs of pseudopure states (POPS) instead of individual pseudopure states as the basis for NMR quantum computing is introduced here. The POPS approach has a significant advantage over the existing methods that, regardless of the number of qubits, only a single step is needed to prepare each pair of pseudopure states. A detailed analysis of a 16-level spin system is given, and the results of applying a c2{c}^{2}c2-NOT quantum logic gate (a controlled-NOT gate conditional upon the state of two other qubits) to all the POPS in the system are presented.