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arXiv:cond-mat/0308560 · Physical Review Letters

One-Shot Quantum Measurement Using a Hysteretic dc SQUID

O. Buisson, Franck Balestro, Jukka P Pekola, F. W. J. Hekking

Published Jun 13, 2003• 40 citations
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Abstract

We propose a single shot quantum measurement to determine the state of a Josephson charge quantum bit (qubit). The qubit is a Cooper pair box and the measuring device is a two junction superconducting quantum interference device (dc SQUID). This coupled system exhibits a close analogy with a Rydberg atom in a high Q cavity, except that in the present device we benefit from the additional feature of escape from the supercurrent state by macroscopic quantum tunneling, which provides the final readout. We test the feasibility of our idea against realistic experimental circuit parameters and by analyzing the phase fluctuations of the qubit.

DOI
10.1103/physrevlett.90.238304

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We propose a single shot quantum measurement to determine the state of a Josephson charge quantum bit (qubit). The qubit is a Cooper pair box and the measuring device is a two junction superconducting quantum interference device (dc SQUID). This coupled system exhibits a close analogy with a Rydberg atom in a high Q cavity, except that in the present device we benefit from the additional feature of escape from the supercurrent state by macroscopic quantum tunneling, which provides the final readout. We test the feasibility of our idea against realistic experimental circuit parameters and by analyzing the phase fluctuations of the qubit.
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.
We present a new configuration concept in which two similar Josephson junctions are coupled through a capacitor placed in parallel to a dc-superconducting quantum interference device (SQUID) to improve the characteristics of phase qubits. In real coupled quantum systems, because of mutual effects such as crosstalk, entangled quantum states cannot be independently measured. The proposed two-qubit system is demonstrated to have a negligible crosstalk, obtained from the application of a single measurement pulse and an appropriate external flux to one of the junctions and the dc-SQUID, respectively. Surprisingly, the theoretically predicted fidelity for a single-qubit design increases to 99.99% for typical Josephson junction parameters. The high-fidelity measurement is reached even with pulse times less than 1 ns, while the highest fidelities reported so far are obtained by wide temporal pulses through single-shot current pulse measurements. This is accomplished by proper coupling capacitance, which determines the coupling time, the measurement time, and their proportion. Furthermore, the ratio of decoherence time for this structure with respect to the one belonging to a typical qubit is found to be more than 1.42.
The flux states of a rf superconducting quantum interference device (SQUID) can be used to investigate macroscopic quantum effects, the most challenging of which is the detection of quantum coherent oscillations, and are promising candidates for the implementation of quantum computing. The use of a proper readout system is of utmost importance for these purposes. In this letter we present experimental evidence of the possibility of using an underdamped, hysteretic dc SQUID to read out stroboscopically the flux states of a rf SQUID, allowing a single shot discrimination with an efficiency of 98%. The devices are all integrated on chip.
We propose a scheme for entangled state measurement at flux qubits (quantum bits) depending on the sensitivity measurement of a dc SQUID (superconducting quantum interference device). The dc SQUID is used as a flux qubit readout device. The switching current distribution of the dc SQUID is sufficiently narrow to distinguish between two ground states of three Josephson junction qubits with a large mutual inductance between a qubit and the dc SQUID. However, discrimination between two ground states becomes difficult with the smaller mutual inductance that is preferable for qubit coherence. We employed averaging to increase the effective sensitivity. However the averaging smears out the entanglement over two qubits. We found that a Bell-pair measurement can be performed with flux qubits to prove the existence of an entangled state over two qubits. The pre-ensembled measurement scheme, in which our flux qubit readouts work, is preferable to entangled state measurement.
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.
We have realized a hysteretic dc SQUID to measure the flux states of a rf SQUID inductively coupled to the hysteretic dc SQUID. This type of measurement is required whenever is necessary to make a non invasive measure of the state of the rf SQUID. This is the case of measurements of macroscopic quantum coherence or measurements on q-bits systems. With the proposed set up the hysteretic dc SQUID can switch from the superconducting to the normal state depending on the total applied magnetic flux. On this system we measured at 4.2 K the change on the switching probability of the dc SQUID by varying the flux state of the rf SQUID. The experimental results agree very well with the theoretical predictions showing that this device can be used to perform non invasive measurements of the rf SQUID flux state.