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arXiv:quant-ph/0109002

Experimental realization of 7-qubit universal perfect controlled-NOT and controlled square-root NOT gates

Daxiu Wei, Xiaodong Yang, Jun Luo, Xianping Sun, Xizhi Zeng, Liu, Maili, Shangwu Ding

Published Sep 1, 2001• 1 citation
arXivHTMLPDF

Abstract

The controlled-NOT gate and controlled square-root NOT gate play an important role in quantum algorithm. This article reports the experimental results of these two universal quantum logic gates (controlled square-root NOT gate and controlled-NOT gate) on a 7-qubit NMR quantum computer. Further, we propose a simple experimental method to measure and correct the error in the controlled phase-shift gate, which is helpful to construct a more perfect phase-shift gate experimentally and can also be used in more qubits discrete Fourier transformation.

DOI
10.48550/arxiv.quant-ph/0109002

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The controlled-NOT gate and controlled square-root NOT gate play an important role in quantum algorithm. This article reports the experimental results of these two universal quantum logic gates (controlled square-root NOT gate and controlled-NOT gate) on a 7-qubit NMR quantum computer. Further, we propose a simple experimental method to measure and correct the error in the controlled phase-shift gate, which is helpful to construct a more perfect phase-shift gate experimentally and can also be used in more qubits discrete Fourier transformation.
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The Quantum Fourier transform (QFT) is a key ingredient in most quantum algorithms. We have compared various spin-based quantum computing schemes to implement the QFT from the point of view of their actual time-costs and the accuracy of the implementation. We focus here on an interesting decomposition of the QFT as a product of the non-selective Hadamard transformation followed by multiqubit gates corresponding to square- and higher-roots of controlled-NOT gates. This decomposition requires only O(n) operations and is thus linear in the number of qubits n. The schemes were implemented on a two-qubit NMR quantum information processor and the resultant density matrices reconstructed using standard quantum state tomography techniques. Their experimental fidelities have been measured and compared.
With the technique of opposite phases, the sequence pulse for exact controlled not gate was designed, and the controlled controlled phase shift gate, which is the key gate in Grovers algorithm, and the double controlled not gate were also constructed by employing only two body interaction. The symmetric operators of quantum states were made up. All the above are the tools of the quantum state engineering, therefore, theyare very useful for both theoretic and experimental investigations of quantum computation.
A quantum circuit network is a set of circuits that implements a certain computation task. Being at the centre of the quantum circuit network, the multi-qubit controlled phase shift is one of the most important quantum gates. In this paper, we apply the method of modular structuring in classical computer architecture to the quantum computer and give a recursive realization of the multi-qubit phase gate. This realization of the controlled phase shift gate is convenient in realizing certain quantum algorithms. We have experimentally implemented this modularized multi-qubit controlled phase gate in a three-qubit nuclear magnetic resonance (NMR) quantum system. The network is demonstrated experimentally using line selective pulses in the NMR technique. The procedure has the advantage of being simple and easy to implement.
Quantum computers promise great improvements in solving problems such as factoring large integers, simulating quantum systems, and database searching. Using a photon as a quantum bit (qubit) is one of the most promising ways to realize a universal quantum computer because the coherent superposition state of a photon is very robust against various sources of decoherence. However, it is too difficult to realize two-qubit (photon) gates because it requires huge nonlinearity between photons. Here we show the realization of a controlled-NOT (CNOT) gate, the most important and elemental two-qubit gate for quantum computation, by extending our previous research. The heart of our experiment is the conditional measurement of two-photon coincidences in the Franson-type experiment[7]. The photon counting measurement plays the same role as the nonlinearity required for the two-qubit gate, and our system reproduces the truth table of the CNOT gate. Furthermore, we create an entangled state from the superposition state by our gate, which is clear evidence that our gate works as a quantum logic gate. Our results make it possible to manipulate the quantum state of photons including entanglement and represent significant progress in the operation of various algorithms in quantum computation.