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Pulse and Hold Switching Current Readout of Superconducting Quantum Circuits

Jochen Walter

Published Jan 1, 2006• 1 citation
OpenAlex

Abstract

Josephson junction qubits are promising candidates for a scalable quantum processor. Such qubits are commonly manipulated by means of sequences of rf-pulses and different methods are used to determine their quantum state. The readout should be able to distinguish the two qubit states with high accuracy and be faster than the relaxation time of the qubit. We discuss and experiment with a readout method based on the switching of a Josephson junction from the zero voltage state to a finite voltage state. The Josephson junction circuit has a non-linear dynamics and when it is brought to a bifurcation point, it can be made arbitrarily sensitive to small perturbations. This extreme sensitivity at a bifurcation point can be used to distinguish the two quantum states if the topology of the phase space of the circuit leads to a quick separation into the final states where re-crossings of the bifurcation point are negligible. We optimize a switching current detector by analyzing the phase space of a Josephson junction circuit with frequency dependent damping. A pulse and hold technique is used where an initial current pulse brings the junction close to its bifurcation point and the subsequent hold level is used to give the circuit enough time to evolve until the two states can be distinguished by the measuring instrument. We generate the pulse and hold waveform by a new technique where a voltage step with following linear voltage rise is applied to a bias capacitor. The frequency dependent damping is realized by an on-chip RC-environment fabricated with optical lithography. Josephson junction circuits are added on by means of e-beam lithography. Measurements show that switching currents can be detected with pulses as short as 5 ns and a resolution of 2.5% for a sample directly connected to the measurement leads of the cryostat. Detailed analysis of the switching currents in the RC-environment show that pulses with a duration of 20 us can be explained by a generalization of Kramers' escape theory, whereas switching the same sample with 25 ns pulses occurs out of thermal equilibrium, with sensitivity and speed adequate for qubit readout.

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Pulse and hold strategy for switching current measurements

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We investigate by theory and experiment, the Josephson junction switching current detector in an environment with frequency-dependent damping. Analysis of the circuit's phase space shows that a favorable topology for switching can be obtained with overdamped dynamics at high frequencies. A pulse-and-hold method is described, where a fast switch pulse brings the circuit close to an unstable point in the phase space when biased at the hold level. Experiments are performed on Cooper pair transistors and quantronium circuits, which are overdamped at high frequencies with an on-chip RC shunt. For $20\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$ switch pulses the switching process is well described by thermal equilibrium escape, based on a generalization of the Kramers formula to the case of frequency-dependent damping. A capacitor bias method is used to create very rapid, $25\phantom{\rule{0.3em}{0ex}}\mathrm{ns}$ switch pulses, where it is observed that the switching process is not governed by thermal equilibrium noise.

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Josephson junction qubits are promising candidates for a scalable quantum processor. Such qubits are commonly manipulated by means of sequences of rf-pulses and different methods are used to determine their quantum state. The readout should be able to distinguish the two qubit states with high accuracy and be faster than the relaxation time of the qubit. We discuss and experiment with a readout method based on the switching of a Josephson junction from the zero voltage state to a finite voltage state. The Josephson junction circuit has a non-linear dynamics and when it is brought to a bifurcation point, it can be made arbitrarily sensitive to small perturbations. This extreme sensitivity at a bifurcation point can be used to distinguish the two quantum states if the topology of the phase space of the circuit leads to a quick separation into the final states where re-crossings of the bifurcation point are negligible. We optimize a switching current detector by analyzing the phase space of a Josephson junction circuit with frequency dependent damping. A pulse and hold technique is used where an initial current pulse brings the junction close to its bifurcation point and the subsequent hold level is used to give the circuit enough time to evolve until the two states can be distinguished by the measuring instrument. We generate the pulse and hold waveform by a new technique where a voltage step with following linear voltage rise is applied to a bias capacitor. The frequency dependent damping is realized by an on-chip RC-environment fabricated with optical lithography. Josephson junction circuits are added on by means of e-beam lithography. Measurements show that switching currents can be detected with pulses as short as 5 ns and a resolution of 2.5% for a sample directly connected to the measurement leads of the cryostat. Detailed analysis of the switching currents in the RC-environment show that pulses with a duration of 20 us can be explained by a generalization of Kramers' escape theory, whereas switching the same sample with 25 ns pulses occurs out of thermal equilibrium, with sensitivity and speed adequate for qubit readout.
We investigate by theory and experiment, the Josephson junction switching current detector in an environment with frequency-dependent damping. Analysis of the circuit's phase space shows that a favorable topology for switching can be obtained with overdamped dynamics at high frequencies. A pulse-and-hold method is described, where a fast switch pulse brings the circuit close to an unstable point in the phase space when biased at the hold level. Experiments are performed on Cooper pair transistors and quantronium circuits, which are overdamped at high frequencies with an on-chip RC shunt. For $20\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$ switch pulses the switching process is well described by thermal equilibrium escape, based on a generalization of the Kramers formula to the case of frequency-dependent damping. A capacitor bias method is used to create very rapid, 25ns25\phantom{\rule{0.3em}{0ex}}\mathrm{ns}25ns switch pulses, where it is observed that the switching process is not governed by thermal equilibrium noise.
We examine in theory and by numerical simulation, the dynamic process of switching from a zero voltage to a finite voltage state in a Josephson junction circuit. The theoretical model describes small capacitance Josephson junctions which are overdamped at high frequencies, and can be applied to detection of the quantum state of a qubit circuit. We show that the speed and fidelity of the readout are strongly influenced by the topology of the phase space attractors. The readout will be close to optimal when choosing the circuit parameters so as to avoid having an unstable limiting cycle which separates the two basins of attraction.
Measuring the dynamics of a quantum bit (qubit) relies on the accurate detection of the quantum state of the system. A widely used method to measure the state of a solid state Josephson junction qubit is to measure the switching current of a Josephson device. This work investigates the measurement of the switching current of SQUID samples by means of fast current pulses. The response of a SQUID to a square current pulse has to be measured at the top of a dilution refrigerator through long cables, resulting in bandwidth limitations. A switch in the last instance of a pulse will not be detected, resulting in uncertainties in the detection. We explain how a square bias pulse that is directly followed by a hold level of lower amplitude can be used to circumvent the bandwidth limitations by latching the state of the system it was in after the bias pulse. This corresponds to a sample and hold measurement. Every single measurement in a quantum mechanical probability measurement has to be statistically independent. We show correlation measurements for di erent settings of the pulse parameters and at di erent magnitudes of the switching current. A gure of merit for a quantum detector is its resolution. The measurements show that with the sample and hold technique good current resolutions can be obtained, even at very small magnitudes and short pulse durations. In order to make a fast measurement of the switching current, the switching process must occur during the bias pulse. We show in both measurements and computer simulations that a fast switch pulse can induce switching by the hold level,even when the hold level was initially adjusted to a value where it never switched the sample. The computer simulations show that by choosing the hold amplitude low enough, switching occurs rapidly, determined by the bias pulse alone.
We report on measurements of macroscopic quantum states in superconducting Josephson circuits using a highly sensitive hybrid quantum interferometer as the readout probe. The investigated Josephson circuit is one of the leading candidates as solid-state qubits (persistent current qubit), which are known to exhibit macroscopic quantum states with atomic-like properties. The readout device is a modified Andreev interferometer with semi-metallic normal segment in a “folded" geometry, and is designed to reduce the back action during measurement, as well as minimising the electromagnetic coupling between the circuit and the environment.\n A pulsed lock-in technique has been developed to perform continuous readout of the superconductor phase difference using pulse lengths down to 10 ns. The technique enables to control the energy of the probing quasiparticles in the normal segment of the interferometer, which in turn allows to control of the supercurrent owing in the SNS junction and prevents electron heating of the normal segment.\n An experimental set-up was designed and installed in a dilution fridge consisting of shielded wiring, magnetic screens, RF tight sample holder and printed circuit board to allow the injection of high frequency excitation signals, while minimising the environment effect on the qubit through careful electrical filtering. The effect of strong RF irradiation on Andreev interferometers allowed us to estimate the response time of the readout device to be less than 40 ps.\n The measurements show that two macroscopically distinct metastable states exist when the device is biased at the qubit degeneracy point, between which the system makes transitions that can be continuously monitored. Real time kinetics of the system has been investigated at different magnetic fluxes, pulse parameters, temperature and RF radiation. Based on statistical analysis of the transitions, we argue that the metastability is connected with macroscopic quantum tunnelling effects rather than thermal excitation. The experimental data support the hypothesis of a large low frequency noise causing low transition rates.
Dispersive readouts for superconducting qubits have the advantage of speed and minimal invasiveness. We have developed such an amplifier, the cavity bifurcation amplifier (CBA), and applied it to the readout of the quantronium qubit. It consists of a Josephson junction embedded in a microwave on-chip resonator. In contrast with the Josephson bifurcation amplifier, which has an on-chip capacitor shunting a junction, the resonator is based on a simple coplanar waveguide imposing a predetermined frequency and whose other rf characteristics such as the quality factor are easily controlled and optimized. Under proper microwave irradiation conditions, the CBA has two metastable states. Which state is adopted by the CBA depends on the state of a quantronium qubit coupled to the CBA's junction. Due to the megahertz repetition rate and large signal to noise ratio, we can show directly that the coherence is limited by 1∕f1∕f1∕f gate charge noise when biased at the ``sweet spot''---a point insensitive to first order gate charge fluctuations. This architecture lends itself to scalable quantum computing using a multiresonator chip with multiplexed readouts.
We present a systematic study of the phase coherent dynamics of a superconducting three-Josephson-junction flux qubit. The qubit state is detected with the integrated-pulse method, which is a variant of the pulsed switching-dc-superconducting quantum interference device (SQUID) method. In this scheme, the dc SQUID bias current pulse is applied via a capacitor instead of a resistor, giving rise to a narrow bandpass instead of a pure low-pass filter configuration of the electromagnetic environment. Measuring one and the same qubit with both setups allows a direct comparison. With the capacitive method about four times faster switching pulses and an increased visibility are achieved. Furthermore, the deliberate engineering of the electromagnetic environment, which minimizes the noise due to the bias circuit, is facilitated. Right at the degeneracy point, the qubit coherence is limited by energy relaxation. We find two main noise contributions. White noise limits the energy relaxation and contributes to the dephasing far from the degeneracy point. 1∕f1∕f1∕f noise is the dominant source of dephasing in the direct vicinity of the optimal point. The influence of 1∕f1∕f1∕f noise is also supported by nonrandom beatings in the Ramsey and spin echo decay traces. Numeric simulations of a coupled qubit-oscillator system indicate that these beatings are due to the resonant interaction of the qubit with at least one pointlike fluctuator, coupled especially strongly to the qubit.