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arXiv:cond-mat/0507709 · Physical Review B

Detection of geometric phases in flux qubits with coherent pulses

Zhihui Peng, M. J. Zhang, Dongning Zheng

Published Jan 23, 2006• 13 citations
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Abstract

We propose a feasible experimental scheme to demonstrate the geometric phase in flux qubits by means of a detuning coherent microwave pulse technique. Through measuring the probability of the persistent current state in the flux qubits, one can detect the Berry phase that is acquired with the system's Hamiltonian adiabatical circular evolution in the parameter space. Furthermore, we show that one could choose an appropriate amplitude of pulses in an experiment to obtain high readout resolution when the detuning frequency of the pulses is fixed, and controlled phase shift gates can be implemented based on the geometric phases by inductance coupling of two flux qubits.

DOI
10.1103/physrevb.73.020502

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We propose a feasible experimental scheme to demonstrate the geometric phase in flux qubits by means of a detuning coherent microwave pulse technique. Through measuring the probability of the persistent current state in the flux qubits, one can detect the Berry phase that is acquired with the system's Hamiltonian adiabatical circular evolution in the parameter space. Furthermore, we show that one could choose an appropriate amplitude of pulses in an experiment to obtain high readout resolution when the detuning frequency of the pulses is fixed, and controlled phase shift gates can be implemented based on the geometric phases by inductance coupling of two flux qubits.
To achieve robust gate operations on superconducting charge qubits, we theoretically propose a feasible scheme to realize geometric quantum computation via coherent pulses. Only by adiabatically tuning the microwave pulses applied to the gate capacitance can the Berry phases associated with the system be acquired, from which we construct a universal set of geometric gates. Combining the geometric approach with the coherent pulse technique, robust quantum operations aimed at combating noise errors may be implemented experimentally.
We propose an experimentally realizable method to control the coupling between two flux qubits. In our proposal, the bias fluxes are always fixed for these two inductively coupled qubits. The detuning of these two qubits can be initially chosen to be sufficiently large, so that their initial interbit coupling is almost negligible. When a variable frequency or time-dependent magnetic flux (TDMF) is applied to one of the qubits, a well-chosen frequency of the TDMF can be used to compensate the initial detuning and to couple two qubits. This proposed method avoids fast changes of either qubit frequencies or the amplitudes of the bias magnetic fluxes through the qubit loops, and also offers a remarkable way to implement any logic gate, as well as tomographically measure flux qubit states.
We experimentally demonstrate coherent oscillations of a tunable superconducting flux qubit by manipulating its energy potential with a nanosecond-long pulse of magnetic flux. The occupation probabilities of two persistent current states oscillate at a frequency ranging from 6 GHz to 21 GHz, tunable by changing the amplitude of the flux pulse. The demonstrated operation mode could allow quantum gates to be realized in less than 100 ps, which is much shorter than gate times attainable in other superconducting qubits. Another advantage of this type of qubit is its immunity to both thermal and magnetic field fluctuations.
We present an adiabatic geometric quantum computation strategy based on the non-degenerate energy eigenstates in (but not limited to) superconducting phase qubit systems. The fidelity of the designed quantum gate was evaluated in the presence of simulated thermal fluctuations in a superconducting phase qubits circuit and was found to be quite robust against random errors. In addition, it was elucidated that the Berry phase in the designed adiabatic evolution may be detected directly via the quantum state tomography developed for superconducting qubits. We also analyze the effects of control parameter fluctuations on the experimental detection of the Berry phase.
The Berry phase is a geometric phase acquired during adiabatic evolution over a closed loop in parameter space. It plays an essential role in geometric quantum gates and other phase-based protocols. In non-Hermitian systems, the Berry phase is complex, introducing fundamentally new geometric effects, including state amplification. In this work, we report experimental measurement of both the real and imaginary components of a Berry phase in a fully quantum system using a superconducting transmon circuit with engineered dissipation. We also demonstrate the path-dependent effects of the imaginary part on the dissipation and its utility in the implementation of non-unitary quantum control. These findings establish a clear geometric distinction between the real and imaginary components of the Berry phase and experimentally confirm the unique adiabatic behavior of non-Hermitian quantum systems.
We have observed coherent time evolution between two quantum states of a superconducting flux qubit comprising three Josephson junctions in a loop. The superposition of the two states carrying opposite macroscopic persistent currents is manipulated by resonant microwave pulses. Readout by means of switching-event measurement with an attached superconducting quantum interference device revealed quantum-state oscillations with high fidelity. Under strong microwave driving, it was possible to induce hundreds of coherent oscillations. Pulsed operations on this first sample yielded a relaxation time of 900 nanoseconds and a free-induction dephasing time of 20 nanoseconds. These results are promising for future solid-state quantum computing.