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arXiv:cond-mat/0507548 · Physical Review B

Dispersive measurements of superconducting qubit coherence with a fast latching readout

Irfan A. Siddiqi, Rajamani Vijay, Michael Metcalfe, Etienne Boaknin, Luigi Frunzio, Robert J. Schoelkopf, Michel Devoret

Published Feb 23, 2006• 151 citations
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Abstract

The ``quantronium'' is a superconducting qubit consisting of a split Cooper pair box in which a large tunnel junction is inserted. This circuit has a special bias point where the Larmor frequency is, to first order, insensitive to fluctuations in the bias parameters---the charge of the box island and the phase of the large junction. At this optimal working point, the state of the qubit can be determined by dispersive measurements that probe the second derivative of the state energy with respect to these bias parameters. We use the quantronium phase degree of freedom to perform a nonlinear, dispersive measurement of its inductive response using bifurcation amplification. This dispersive readout projects the state of the qubit in a few nanoseconds, and its latching property allows us to record the resulting information in a few hundred nanoseconds. We have measured, using this technique, Rabi oscillations and Ramsey fringes with an improved signal-to-noise ratio and contrast. The speed of this readout scheme also opens the door for a class of experiments that would characterize the relaxation processes associated with the measurement protocol.

DOI
10.1103/physrevb.73.054510

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The ``quantronium'' is a superconducting qubit consisting of a split Cooper pair box in which a large tunnel junction is inserted. This circuit has a special bias point where the Larmor frequency is, to first order, insensitive to fluctuations in the bias parameters---the charge of the box island and the phase of the large junction. At this optimal working point, the state of the qubit can be determined by dispersive measurements that probe the second derivative of the state energy with respect to these bias parameters. We use the quantronium phase degree of freedom to perform a nonlinear, dispersive measurement of its inductive response using bifurcation amplification. This dispersive readout projects the state of the qubit in a few nanoseconds, and its latching property allows us to record the resulting information in a few hundred nanoseconds. We have measured, using this technique, Rabi oscillations and Ramsey fringes with an improved signal-to-noise ratio and contrast. The speed of this readout scheme also opens the door for a class of experiments that would characterize the relaxation processes associated with the measurement protocol.
During this grant, we have invented, designed and successfully operated a new type of readout for charge-phase superconducting qubits. This new readout is based on the bifurcation of an RF-driven Josephson junction inserted in the loop of a split Cooper pair box. When the amplitude of the RF drive is in the vicinity of the bifurcation points a small change in the effective critical current of the junction is amplified into a large phase change in the reflected signal. The performance reached by the device is in agreement with theoretical predictions. The speed of this readout is unprecedented: we measure in 20ns the critical current increment corresponding to the transition between the 2 states of the qubit. The repetition rate is 10Mz. We have performed a series of experiments showing that the amplification mechanism behaves as expected. No quasiparticles are produced during the readout and the back-action on the qubit when the readout is OFF is minimal. We have performed decoherence measurements at dilution refrigerator temperatures on the quantronium qubit integrated with RF readout. These measurements involve all possible 1-qubit gate operations. Compared with the DC readout method we have gained in repetition rate (factor of 100), signal-to-noise ration on all coherence signals (factor of 10) but most importantly, on readout fidelity which now attains more than 60% (compared to 15%). This last improvement is very important for showing the entanglement produced by two-bit gate operations. The T1 has also been improved by 250%. We still have comparable T2 as before but we suspect this is due to insufficient filtering on the listening lines of our measurement apparatus and this problem is technically solvable. In parallel with this work on readout and decoherence of the quantronium qubit, we have designed a new 2-bit gate based on capacitive coupling between qubits and worked out the complete protocol of pulses.
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.
During this thesis, we have used superconducting circuits with Josephson junctions, derived from the Cooper pair box, in order to implement quantum bits (qubits). To implement two-qubit gates, we have developed a new circuit, the quantroswap, which consists in two capacitively coupled Cooper pair box, each of them being manipulated and read separately. We have demonstrated coherent exchange of energy between them, but we have also observed a problem of qubit instability. In order to avoid this spurious effect, we have implemented another circuit based on a charge insensitive split Cooper pair box coupled to a non-linear resonator for readout-out purpose. We have measured large coherence time, and obtained large readout fidelity (90%) using the bifurcation phenomenon. For metrological purpose, microwave reflectometry measurement on a quantronium also allowed us to relate an applied current I to the frequency f=I/2e of induced Bloch oscillations.
In this work we consider measurements on quantum systems emphasizing\non read-out of superconducting qubits. The qubit is always coupled to an\nenvironment, containing a macroscopic number of degrees of freedom. This\nperturbs the qubit and destroys the phase coherence of the quantum state.\nOne tries to minimize this destructive effect by encoding the quantum information in quantum states which do not couple strongly to the dominant\nnoise sources. It is therefore necessary to design read-out methods that can\ndistinguish these states.\n\nWe focus primarily on the single Cooper-pair box (SCB) charge qubit, whose\nproperties are based on the Josephson effect and Coulumb blockade in superconducting electrical circuits. By encoding the information in the qubit\nenergy eigenstates, it is possible to protect it from the most dangerous decoherence source - charge fluctuations in the environment. We investigate\nthe measurement setup, where the SCB is coupled to a lumped element LCoscillator whose resonance frequency is orders of magnitude smaller than the qubit energy splitting. In this regime the SCB will act as an effective positive or negative capacitance, depending on the quantum state. This quantum capacitance then shifts the oscillator resonance frequency, which can be detected in a homodyne phase measurement.\n\nWe have found that reading out a charge qubit by measuring its quantum\ncapacitance in this manner is quantum limited, independently of the oscillator\nquality factor Q. Moreover, we have found that the low-Q oscillator\nis advantageous for the measurement in two ways: first, such an oscillator\nbetter protects the qubit from thermal dephasing, and, second, it allows to\nincrease the speed of the read-out, making it possible to distinguish the qubit states in a single shot measurement.
Designing quantum systems with the measurement speed and accuracy needed for quantum error correction using superconducting qubits requires iterative design and testing informed by accurate models and characterization tools. We introduce a single protocol, with few prerequisite calibrations, to measure the dispersive shift, resonator linewidth, and drive power used in the dispersive readout of superconducting qubits. We find that the resonator linewidth is poorly controlled, with a factor of 2 variation between the maximum and minimum measured values, and this variation is likely to require focused attention in future quantum error correction experiments. We also introduce a protocol for measuring the efficiency of the readout system using the same power levels as are used in typical qubit readout, and without the need to measure the qubit dephasing. We routinely run these protocols on chips with tens of qubits to a hundred qubits, driven by automation software with little human interaction. Using the extracted system parameters, we find that a model based on these parameters predicts the readout signal-to-noise ratio to within 10% over a device with 54 qubits.
The superconducting charge-phase ``quantronium'' qubit is considered in order to develop a model for the measurement process used in the experiment of Vion et al. [Science 296, 886 (2002)]. For this model we propose a method for including the bias current in the readout process in a fundamentally irreversible way, which to first order is approximated by the Josephson junction tilted-washboard potential phenomenology. The decohering bias current is introduced in the form of a Lindblad operator and the Wigner function for the current-biased readout Josephson junction is derived and analyzed. During the readout current pulse used in the quantronium experiment we find that the coherence of the qubit initially prepared in a symmetric superposition state is lost at a time of 0.2ns0.2\phantom{\rule{0.3em}{0ex}}\mathrm{ns}0.2ns after the bias current pulse has been applied, a time scale that is much shorter than the experimental readout time. Additionally we look at the effect of Johnson-Nyquist noise with zero mean from the current source during the qubit manipulation and show that the decoherence due to the irreversible bias current description is an order of magnitude smaller than that found through adding noise to the reversible tilted-washboard potential model. Our irreversible bias current model is also applicable to persistent-current-based qubits where the state is measured according to its flux via a small-inductance direct-current superconducting quantum interference device.