Fast Accurate State Measurement with Superconducting Qubits

Evan Jeffrey, Daniel Sank, J. Y. Mutus, T. C. White, J. Kelly, R. Barends, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, A. Megrant, P. J. J. O’Malley, C. Neill, P. Roushan, A. Vainsencher, J. Wenner, A. N. Cleland, and John M. Martinis

Phys. Rev. Lett. 112, 190504 – Published 15 May 2014

Abstract

Faster and more accurate state measurement is required for progress in superconducting qubit experiments with greater numbers of qubits and advanced techniques such as feedback. We have designed a multiplexed measurement system with a bandpass filter that allows fast measurement without increasing environmental damping of the qubits. We use this to demonstrate simultaneous measurement of four qubits on a single superconducting integrated circuit, the fastest of which can be measured to 99.8% accuracy in 140 ns. This accuracy and speed is suitable for advanced multiqubit experiments including surface-code error correction.

Received 19 December 2013

DOI:https://doi.org/10.1103/PhysRevLett.112.190504

Authors & Affiliations

Evan Jeffrey, Daniel Sank, J. Y. Mutus, T. C. White, J. Kelly, R. Barends, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, A. Megrant, P. J. J. O’Malley, C. Neill, P. Roushan, A. Vainsencher, J. Wenner, A. N. Cleland, and John M. Martinis¹

Department of Physics, University of California, Santa Barbara, California 93106-9530, USA

^*martinis@physics.ucsb.edu

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Vol. 112, Iss. 19 — 16 May 2014

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Images

Figure 1
Device layout and frequency response. (a) Micrograph of the device with lumped element model (inset). The qubits $q$ are coupled through a capacitor $C_{g}$ to the voltage antinode of the $λ / 4$ measurement resonator $r$ . The resonators are coupled via capacitors $C_{κ}$ to the filter resonator $F$ . The red arrow indicates the path by which photons leave the filter through a wire bond (not shown) and enter an amplification chain. (b) Transmission spectrum $S_{21}$ of the detector. Transmission measured on a test chip is shown by the heavy (black) curve, and a Lorentzian fit is shown by the thin (green) curve. The measurement resonators are in the passband where the transmission is large, whereas the qubits are off resonance and thus protected from the environment. The inset shows a detail of the spectrum from the chip used in this experiment. Each dip in the transmission curve comes from one measurement resonator. Values for $S_{21}$ are plotted with an arbitrary offset in the vertical scale.
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Figure 2
Measurement pulse shape and resonator photon occupation. (a) Measurement pulse produced by the arbitrary waveform generator for a single qubit (real quadrature). (b) Time dependent population of the measurement resonator as measured by the ac Stark shift. This shows the initial 25 ns strong drive, which quickly rings up the resonator, the sustain pulse, and the free ringdown with time constant $1 / κ_{r} = 37 ns$ . This corresponds to a resonator $Q_{r}$ of 1561.
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Figure 3
Single shot measurement events for one qubit after 140 ns pulse integration. Points in the wrong cluster are due to unwanted qubit transitions. The inset shows histograms of the IQ points projected onto line connecting the $| 0 ⟩$ and $| 1 ⟩$ clouds. Heavy lines are Gaussian fits to the histograms and are used for computing the separation fidelity.
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Figure 4
Measurement errors versus pulse integration time for one qubit. Large (green) circles show the separation errors $ε_{s} = 1 - F_{s} (t)$ while the dark (blue) and light (red) small circles show $ε_{| 0 ⟩} (t)$ and $ε_{| 1 ⟩} (t)$ , respectively. The vertical arrow indicates the time slice at 140 ns represented in Fig. 3.
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Figure 5
Simultaneous measurement of four qubits. Separation and actual state fidelities are shown as in Fig. 4. All four qubits exhibit fast measurement, with three of them reaching 99% fidelity in 200 ns. Small ripples on qubits $Q_{1}$ and $Q_{3}$ were caused by spectral leakage.
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