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arXiv:cond-mat/0108231 · Superconductor Science and Technology

Dc SQUID sensitivity for readout of entangled state quantum bits

H Tanaka, Y Sekine, S Saito, H Takayanagi

Published Nov 21, 2001• 5 citations
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Abstract

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.

DOI
10.1088/0953-2048/14/12/339

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Physica Scripta•Jan 1, 2002•29 citations
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.
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 flux state quantum bit (qubit) is promising for a solid state implementation of scalable quantum computing. The simplest flux state qubit consists of an rf SQUID with two fluxoid states, which can be readout with a dc SQUID - the most sensitive magnetic flux detector. Efficient readout with less back-action is desirable for quantum computing. In this work, we report measurements of the switching flux and switching current distributions of under damped dc SQUIDs. The data show that single shot readout of flux qubit with very high efficiency (>99%) can be realized using underdamped hysteretic dc SQUIDs.
Recent experiments on superconducting flux qubits, consisting of a superconducting loop interrupted by Josephson junctions, have demonstrated quantum coherence between two different quantum states. The state of the qubit is measured with a superconducting quantum interference device (SQUID). Such measurements require the SQUID to have high resolution while exerting minimal backaction on the qubit. By designing shunts across the SQUID junctions appropriately, one can improve the measurement resolution without increasing the backaction significantly. Using a path-integral approach to analyze the Caldeira-Leggett model, we calculate the narrowing of the distribution of the switching events from the zero-voltage state of the SQUID for arbitrary shunt admittances, focusing on shunts consisting of a capacitance Cs{C}_{s}Cs​ and resistance Rs{R}_{s}Rs​ in series. To test this model, we fabricated a dc SQUID in which each junction is shunted with a thin-film interdigitated capacitor in series with a resistor, and measured the switching distribution as a function of temperature and applied magnetic flux. After accounting for the damping due to the SQUID leads, we found good agreement between the measured escape rates and the predictions of our model. We analyze the backaction of a shunted symmetric SQUID on a flux qubit. For the given parameters of our SQUID and realistic parameters for a flux qubit, at the degeneracy point we find a relaxation time of $113\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$, which limits the decoherence time to $226\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$. Based on our analysis of the escape process, we determine that a SQUID with purely capacitive shunts should have narrow switching distributions and no dissipation.
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.
In flux qubits, qubit states are commonly read out by a dc superconducting quantum interference device (SQUID), which is inductively coupled to the qubit and works as a persistent current detector. However, neither the bottom nor the top regions of the critical current modulation curve of the SQUID can be used for the readout. In this paper, we show that a flux-trap loop inserted to the readout SQUID provides the ability to adjust the working point, which helps to avoid this constraint. This improvement is useful for some complicated flux qubit experiments.
The INSQUID (INductive Superconducting QUantum Interference Device) can measure the flux state of a superconducting qubit rapidly, while allowing the quantum state of the qubit to evolve with low levels of back action. The INSQUID consists of a dc SQUID with unshunted junctions connected in parallel with a superconducting inductor; the qubit is placed inside the SQUID loop. The inductor is coupled to a readout dc SQUID with resistively-shunted junctions. By applying appropriate fluxes to the input SQUID and the inductor, the INSQUID can be turned "off", so that virtually no flux noise is coupled from the readout SQUID to the qubit. Different flux biases turn the INSQUID "on", enabling the readout SQUID to measure the flux state of the qubit. The INSQUID can also be used to turn on and off the coupling between two or more qubits.