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Chinese Physics

Quantization of the double-qubit structure and quantum computation

Liang Bao-Long, Ji‐Suo Wang

Published Oct 1, 2007• 6 citations
Publisher

Abstract

The quantization scheme of a double-qubit structure with superconducting quantum interference devices (SQUIDs) is given. By introducing unitary matrices and using spectral decompositions, the Hamiltonian operator of the system is exactly formulated in compact forms in spin-1/2 notation. A scheme of designing controlled-phase-shift (CPS) gates is also proposed by using this circuit system.

DOI
10.1088/1009-1963/16/10/046

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The quantization scheme of a double-qubit structure with superconducting quantum interference devices (SQUIDs) is given. By introducing unitary matrices and using spectral decompositions, the Hamiltonian operator of the system is exactly formulated in compact forms in spin-1/2 notation. A scheme of designing controlled-phase-shift (CPS) gates is also proposed by using this circuit system.
In this paper, the number-phase quantization scheme of the mesoscopic circuit, which consists of a single-qubit structure with superconducting quantum interference device coupled with a super-conducting resonator, is given. By introducing a unitary matrix and by means of spectral decomposition, the Hamiltonian operator of the system is exactly formulated in compact forms in spin-1/2 notation. The eigenvalues and the eigenstates of the system are investigated. It is found that using this system the entangled states can not only be prepared, but also be manipulated by tuning the magnetic flux through the super-conducting loop.
In the system with superconducting quantum interference devices (SQUID) in cavity,a scheme for con- structing two-qubit quantum phase gate via a conventional geometric phase-shift is proposed by using a quantized cavity field and classical microwave pulses.In this scheme,the gate operation is realized in the subspace spanned by the two lower flux states of the SQUID system and the population operator of the excited state has no effect on it.Thus the effect of decoherence caused from the levels of the SQUID system is possible to minimize.Under cavity decay,our strictly numerical simulation shows that it is also possible to realize the unconventional geometric phase gate.The experimental feasibility is discussed in detail.
We present a scheme to realize the basic two-qubit logic gates such as the quantum phase gate and SWAP gate using a detuned microwave cavity interacting with three-level superconducting-quantum-interference-device (SQUID) qubit(s), by placing SQUID(s) in a two-mode microwave cavity and using adiabatic passage methods. In this scheme, the two logical states of the qubit are represented by the two lowest levels of the SQUID and the cavity fields are treated as quantized. Compared with the previous method, the complex procedures of adjusting the level spacing of the SQUID and applying the resonant microwave pulse to the SQUID to create transformation are not required. Based on superconducting device with relatively long decoherence time and simplified operation procedure, the gates operate at a high speed, which is important in view of decoherence.
In the system with superconducting quantum interference devices (SQUID) in cavity, a scheme for constructing two-qubit quantum phase gate via a conventional geometric phase-shift is proposed by using a quantized cavity field and classical microwave pulses. In this scheme, the gate operation is realized in the subspace spanned by the two lower flux states of the SQUID system and the population operator of the excited state has no effect on it. Thus the effect of decoherence caused from the levels of the SQUID system is possible to minimize. Under cavity decay, our strictly numerical simulation shows that it is also possible to realize the unconventional geometric phase gate. The experimental feasibility is discussed in detail.
Two classes of superconducting devices have been proposed as quantum bits (qubits) for realizing quantum logic operations. The flux qubits based on a superconducting quantum interference device (SQUID) appear to be particularly promising owing to the macroscopic nature of the qubit and potential integration with high-speed control circuitry in the form of rapid single-flux quantum electronics. Recent progress is discussed and near-term challenges mentioned. The radio frequency SQUID-based qubit offers a prospect for a reliably manufacturable scalable approach.