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arXiv:cond-mat/0407299

Single-Shot Readout of Macroscopic Quantum Superposition State in a Superconducting Flux Qubit

Hirotaka Tanaka, Shiro Saito, Hayato Nakano, Kouichi Semba, Masahito Ueda, Hideaki Takayanagi

Published Jul 12, 2004• 8 citations
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Abstract

Single-shot readout experiments were performed on the two lowest-energy states of a superconducting qubit with three Josephson junctions embedded in a superconducting loop. We measured the qubit state via switching current Isw of a current-biased dc-SQUID, a quantum detector surrounding the qubit loop. The qubit signals were measured in a small Isw regime of the SQUID, typically less than 100 nA, where the Isw distribution is particularly narrow. The obtained single-shot data indicate that the qubit state is readout, through the flux generated by the qubit persistent-current, as energy eigenstates rather than current eigenstates.

DOI
10.48550/arxiv.cond-mat/0407299

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arXiv:cond-mat/0305461•Science•Mar 20, 2003•1,216 citations
Single-shot readout experiments were performed on the two lowest-energy states of a superconducting qubit with three Josephson junctions embedded in a superconducting loop. We measured the qubit state via switching current Isw of a current-biased dc-SQUID, a quantum detector surrounding the qubit loop. The qubit signals were measured in a small Isw regime of the SQUID, typically less than 100 nA, where the Isw distribution is particularly narrow. The obtained single-shot data indicate that the qubit state is readout, through the flux generated by the qubit persistent-current, as energy eigenstates rather than current eigenstates.
The readout process of a superconducting flux-qubit is theoretically analyzed in terms of the quantum dynamics of a qubit-SQUID coupled system during measurement. The quantity directly observed by the measurement is the switching current (Isw) of the dc-SQUID placed around the qubit ring. In order to clarify the relation between the Isw and the qubit state, we calculated the time evolution of the density operator of the qubit-SQUID system while increasing the SQUID bias current until switching events occur and obtained the switching current distributions. This clarifies what information of the qubit is obtained by a dc-SQUID switching current measurement under specific conditions, for example, when the qubit eigenstate is a superposition of two different flux states.
Abstract. Superconducting circuits with Josephson tunnel junctions are interesting systems for research on quantummechanical behavior of macroscopic degrees of freedom. A particular realization is a small superconducting loop containing three Josephson junctions. Close to magnetic frustration 1=2, the physics of this system corresponds to a double well, whose minima correspond to persistent currents of opposite sign. We present DC measurements of the flux indicating a smooth transition close to the degeneracy point even at very low temperatures. Furthermore, microwavespectroscopy experiments allow for the excitation to the next excited state. The dependence of the energy of the resonance on the applied flux clearly indicates the nature of these states as tunneling-splitted superpositions of flux states. We theoretically analyze the system using a generalized master-equation formulation of the spin-boson model. We address the nature of the measuring process by a switching DC SQUID and the possible interpretation of the spectroscopy data in terms of quantum coherence. We discuss these aspects in the context of further applications as a quantum bit.
Two states of a flux qubit with three Josephson junctions were shown in a single measurement with a dc-SQUID. The qubit is an aluminum superconductor loop surrounded by a dc-SQUID for readout. It has two states, which have persistent currents flowing in opposite directions. The readout data for three samples with different junction sizes suggest that the probability distribution for the double-well potential depends on the ratio of E J / E C , where E J is the Josephson energy and E C is the charging energy. The probability distribution was estimated by calculating the wavefunctions and energy levels for the measured samples. We measured the retrapping current of a dc-SQUID without the qubit as a function of the magnetic field. It was found that the relative phase relation for the magnetic field dependence of the retrapping current jumped from 0 to π at E J ≈ E C . This jump can be explained phenomenologically by taking into account the two kinds of dissipation arising from ac currents flowing through the lead and along the SQUID loop. The fact that the jump occurred at E J ≈ E C strongly suggests that the quantum nature of the electromagnetic environment needs to be taken into account in order to understand the origin of the dissipation.
We present a readout method for superconducting flux qubits. The qubit quantum flux state can be measured by determining the Josephson inductance of an inductively coupled dc superconducting quantum interference device (dc-SQUID). We determine the response function of the dc-SQUID and its back-action on the qubit during measurement. Due to driving, the qubit energy relaxation rate depends on the spectral density of the measurement circuit noise at sum and difference frequencies of the qubit Larmor frequency and SQUID driving frequency. The qubit dephasing rate is proportional to the spectral density of circuit noise at the SQUID driving frequency. These features of the back-action are qualitatively different from the case when the SQUID is used in the usual switching mode. For a particular type of readout circuit with feasible parameters we find that single shot readout of a superconducting flux qubit is possible.
The states of superconducting quantum bits, as the Josephson phase qubits and flux qubits, are distinguished by magnetic flux generated by a persistent current in a superconducting loop. As the readout circuit contributes decoherence, its coupling to the qubit should be made as weak as possible. We demonstrate a method to maximize the measurement contrast of the two qubit states, thus allowing to significantly decrease the coupling to the readout. This technique is promising for multiqubit circuits since it allows to read out the states of several qubits by using a single readout circuit.
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.