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arXiv:quant-ph/0104127 · Physical review. B, Condensed matter

Nonadiabatic detection of the geometric phase of the macroscopic quantum state with a symmetric SQUID

Xiang‐Bin Wang, Matsumoto Keiji

Published May 2, 2002• 32 citations
arXivHTMLPDF

Abstract

We propose a type of nonadiabatic scheme to detect the geometric phase for the macroscopic state of a Josephson-junction system. After extending the scheme to the two-qubit cases, we provide a type of nonadiabatic geometric C-NOT gate that can play an important role in quantum computation.
DOI
10.1103/physrevb.65.172508

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The nonadiabatic geometric quantum computation may be achieved using coupled low-capacitance Josephson junctions. We show that the nonadiabatic effects as well as the adiabatic condition are very important for these systems. Moreover, we find that it may be hard to detect the adiabatic Berry's phase in this kind of superconducting nanocircuits; but the nonadiabatic phase may be measurable with current techniques. Our results may provide useful information for the implementation of geometric quantum computation.
We propose an experimentally feasible scheme to achieve quantum computation based on nonadiabatic geometric phase shifts, in which a cyclic geometric phase is used to realize a set of universal quantum gates. Physical implementation of this set of gates is designed for Josephson junctions and for NMR systems. Interestingly, we find that the nonadiabatic phase shift may be independent of the operation time under appropriate controllable conditions. A remarkable feature of the present nonadiabatic geometric gates is that there is no intrinsic limitation on the operation time.
Abstract When a quantum-mechanical system undergoes an adiabatic cyclic evolution, it acquires a geometrical phase factor1 in addition to the dynamical one; this effect has been demonstrated in a variety of microscopic systems2. Advances in nanotechnology should enable the laws of quantum dynamics to be tested at the macroscopic level3, by providing controllable artificial two-level systems (for example, in quantum dots4 and superconducting devices5, 6). Here we propose an experimental method to detect geometric phases in a superconducting device. The setup is a Josephson junction nanocircuit consisting of a superconducting electron box. We discuss how interferometry based on geometrical phases may be realized, and show how the effect may be applied to the design of gates for quantum computation.
Nonadiabatic geometric phases have important applications in quantum computation, as they depend only on the global properties of the evolution paths, and thus are robust against certain types of local noise. Experimental implementation is challenging, though, due to the need for complex control of multilevel or multiple quantum systems. This study proposes a delicate gate implementation to solve the problem, based on parametrically tunable resonant coupling between two superconducting transmon qubits, without introducing any auxiliary state. This approach is promising for high-fidelity geometric manipulation and robust solid-state quantum computing.
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