Session B27: Focus Session: Superconducting Qubits - Measurement

Quantum Noise in a Chirped Superconducting Nonlinear Resonator

A nonlinear Josephson junction oscillator driven near resonance can exhibit bistability, forming the basis for sensitive, digital quantum state readout. We consider the case of a high-Q resonator embedded with a Josephson junction excited with a chirped frequency signal. For sufficient drive amplitude, the resonator phase locks with the drive signal and enters the high amplitude oscillation state, a phenomenon known as autoresonance. The probability of capture in a given chirped pulse depends on the initial phase difference between the drive signal and of the fluctuation induced oscillations of the resonator. We find that the width of this threshold is in agreement with recent theoretical predictions and is set by zero-point fluctuations of the resonator. Autoresonant capture forms the basis for fast readout of a superconducting qubit coupled to a high-Q resonator.   

Measurement backaction and the quantum Zeno effect in a superconducting qubit

Strong measurement of a quantum system can inhibit quantum state evolution, a phenomenon known as the quantum Zeno effect. If the measurement is not perfectly quantum non-demolition, it can also cause spurious transitions between states. We study these effects in a transmon qubit dispersively coupled to a superconducting microwave readout cavity. We use a fast, ultralow-noise parametric amplifier to amplify the microwave photons used to probe the qubit state, enabling continuous high-fidelity monitoring of the qubit. This arrangement allows us to observe quantum jumps between the qubit states in real time. We examine the dependence of the jump times on measurement strength and the qubit excitation protocol.   

Investigation of the measurement dynamics of a flux qubit inductively coupled to a readout dc-SQUID

In this paper we investigate the measurement dynamics of a flux qubit inductively coupled to a capacitively shunted, readout dc-SQUID. We study how the measurement induced dephasing and relaxation rates scale as a function of the qubit operation point and measurement strength. We find analytical solutions when the measurement is quantum-non-demolition (QND) and provide a numerical investigation for non-QND operation. This is of importance as the measurement of the flux qubit when operated at its sweet spot is inherently non-QND. We conclude this with a discussion of the measurement efficiency and signal-to-noise ratio.   

Optimization of SQUID-based microwave parametric amplifiers for qubit readout

We present recent experimental and theoretical results on the optimization of SQUID-based parametric microwave amplifiers for ultra low noise readout of superconducting and spin-based qubits. The devices consist of an unshunted two-junction SQUID in parallel with an on-chip capacitor, forming a non-linear microwave resonator. The SQUID is operated in a non-linear regime below the critical current, thus producing no local dissipation. These amplifiers have gain exceeding 20 dB, 10 MHz of broadly tunable bandwidth, and quantum-limited noise performance. We present measurements on amplifiers with tunnel type and weak link Josephson junctions. We discuss the use of array structures to optimize dynamic range as well as a resonant flux-coupled input capable of operation in a transmission configuration and potentially suitable for on-chip integration.   

Fluxonium qubit readout with the Josephson parametric converter

Rapid, single shot quantum-non demolition readout is a prerequisite for proposed active quantum feedback and error correction experiments in superconducting qubit systems. The fluxonium qubit, an artificial atom comprised of a Josephson junction array inductively shunting a Cooper-pair box, is a non- Purcell limited system with excellent coherence times, making it a natural candidate for such experiments. The largest obstacle towards achieving single shot fluxonium readout is the severe signal-to-noise ratio degradation of the qubit readout by the microwave frequency amplification chain. This degradation can be minimized through the addition of a quantum- limited pre-amplifier to the chain. We have designed and constructed such an amplifier, the Josephson Parametric Converter (JPC), which achieves nearly quantum limited amplification with a bandwidth and dynamic range suitable for readout of our current fluxonium design, and are currently integrating the JPC and fluxonium. We will discuss experimental requirements of the combined JPC and fluxonium system and anticipated improvements in measurement fidelity and speed.   

Dispersive Readout of a Superconducting Flux Qubit Using a Microstrip SQUID Amplifier

Dispersive techniques for the readout of superconducting qubits offer the possibility of high repetition-rate, quantum non-demolition measurement by avoiding dissipation close to the qubit. To achieve dispersive readout, we couple our three-junction aluminum flux qubit inductively to a 1-2 GHz non-linear oscillator formed by a capacitively shunted DC SQUID. The frequency of this resonator is modulated by the state of the qubit via the flux-dependent inductance of the SQUID. Readout is performed by probing the resonator in the linear (weak drive) regime with a microwave tone and monitoring the phase of the reflected signal. A microstrip SQUID amplifier (MSA) is used to increase the sensitivity of the measurement over that of a HEMT (high electron mobility transistor) amplifier. We report measurements of the performance of our amplification chain. Increased fidelity and reduced measurement backaction resulting from the implementation of the MSA will also be discussed.   

SQUID-tunable microwave lumped-element oscillators and distributed resonators

We have fabricated lumped-element microwave oscillators and coplanar waveguide resonators consisting of a dc SQUID using submicron Al-AlOx-Al junctions with resonance frequencies in the range of several GHz. The SQUID oscillators consist of a dc SQUID shunted with a capacitor formed from superconducting layers. The CPW resonators are formed from Nb $\lambda $/2 coplanar transmission lines with a center conductor interrupted by an Al dc SQUID at the current anti-node of the fundamental mode. The resonance frequency can be varied by tuning the Josephson inductance of the SQUID with on-chip flux and bias-current lines. We discuss applications employing these devices, including a new readout scheme for superconducting flux qubits and for the detection of microwave cavity photons.   

Multiplexing Readout of a Qubit Array via a Single Transmission Line

A resonant circuit coupled to a qubit displays a shift of its resonance frequency depending on the quantum state of the qubit. The qubit state can be thus measured by probing the resonator near its resonance frequency. By coupling every qubit to its individual resonator of distinct frequency, one can read out the state of an array of many qubits through a single microwave line coupled to all resonators. Moreover, this readout can be performed simultaneously by using a multi-tone microwave pulse with frequency-division multiplexing. We will present measurements on an ensemble of 7 superconducting flux qubits located on one chip and each coupled to an individual transmission-line resonator. We performed spectroscopy of all qubits and determined their parameters in a single measurement run. Our latest experiments on simultaneous preparation and readout of the 7-qubit array will be presented.   

Multiplexed dispersive readout of superconducting phase qubits

A dispersive readout scheme is being developed for superconducting phase qubits. By inductively coupling to a LC resonator, the measured state of the qubit (left or right side of the potential well) can be read out as a shift of the resonance frequency. Compared to our current SQUID readout, this method eliminates the generation of quasiparticles, increases the reliability by reducing the junction count per qubit from 4 to 1, and reduces the chip wire count since the readout can be frequency multiplexed.   

Non-linear dispersive interaction in superconducting circuit QED

In circuit quantum electrodynamics, the strong coupling between superconducting qubits and a coplanar waveguide resonator (CPW) has been utilized to study the light-atom interaction. When the qubit is detuned far away from the resonator in frequency, linear dispersive interaction has been used for the readout of qubit states by measuring the pulling frequency of the resonator. Alternatively, we investigate dispersive interaction in a broader regime by measuring the accumulated dynamic phase with Wigner tomography. In the quasi-adiabatic process of tuning the qubit frequency, the dynamic phase measurement can be pushed to the case of zero detuning with up to the five-photon Fock state in the CPW resonator. The exotic non-linear behaviors of the qubit on resonator cat state and coherent state have been revealed, strongly depending on the strength of dispersive interaction. Our experimental data are consistent with the numerical calculation using the Jaynes-Cumming model.   

Circuit QED with a Nonlinear Resonator: ac-Stark Shift and Dephasing

Coupling a superconducting qubit to a superconducting resonator enables to investigate the interaction between light and matter with a unique flexibility of design, and allows to reach coupling regimes hardly accessible otherwise [Wallraff Nature 2004]. In this talk, we discuss the ac-Stark shift and the measurement induced dephasing of a qubit embedded in a \emph{nonlinear} resonator, an architecture that has demonstrated high fidelity single-shot qubit state readout [Mallet Nat. Phys. 2009]. In our experiment, a transmon qubit [Koch PRA 2007] is capacitively coupled to a coplanar waveguide resonator incorporating a Josephson junction that provides a Kerr nonlinearity. We have measured the qubit spectrum while pumping the nonlinear resonator with a microwave tone. Measurements of the qubit frequency shift provide a sensitive probe of the intracavity field, yielding a precise characterization of the resonator nonlinearity. The qubit linewidth has a complex dependence on the pump frequency and amplitude, which is correlated with the gain of the nonlinear resonator operated as a small-signal amplifier. The corresponding dephasing rate is found to be close to the quantum limit for most pump parameters.   

Improved Superconducting Qubit Readout by Qubit-Induced Nonlinearities in the Straddling Regime

In dispersive readout schemes, qubit-induced nonlinearities have typically limited the measurement fidelities by reducing the signal-to-noise ratio (SNR) when the measurement power is increased [1]. However, it has been recently shown that these nonlinearities, together with the many-level system (MLS) nature of superconducting qubits, can be used to improve qubit readout in some regimes [2]. Moreover, for the transmon qubit [3], it has been shown that when the resonator's frequency sits between two of the MLS' transition frequencies -- the so-called straddling regime -- contributions of higher levels add constructively to improve the SNR [4]. In this talk, we explore the advantages of using both the qubit-induced nonlinearties and the straddling regime for qubit readout.\\[4pt] [1] Boissonneault et al, PRA 77, 060305(R) (2007)\\[0pt] [2] Reed et al, PRL 105, 173601 (2010), Bishop et al, PRL 105, 100505 (2010), Boissonneault et al, PRL 105, 100504 (2010)\\[0pt] [3] Koch et al, PRA 76, 042319 (2007)\\[0pt] [4] Srinivasan et al, V26.00006, 2010 March Meeting.   

Purcell Protection and Cycling Transition Measurement with a Superconducting V-system

We perform time-domain experiments on a superconducting qubit with a V-level energy structure coupled to a superconducting, coplanar waveguide resonator. Quantum interference and the V-level energy scheme allow independent control of the qubit energy and dipole via two on-chip fast flux bias lines [1]. The tunable dipole is predicted to protect the qubit from cavity-induced spontaneous emission. We probe this ``Purcell protection'' by measuring the qubit lifetime at constant cavity-qubit detuning for a range of coupling strengths. We also show how the coupled cavity-qubit energy spectrum allows for a cycling-type measurement that is predicted to improve the signal to noise ratio of qubit state readout by as much as an order of magnitude.\\[4pt] [1] J.M. Gambetta et al., arXiv:1009.4470v1   

Quantum State Tomography of a Cooper-pair Box

A 4-8 GHz microwave pulse shaping system with 3 ns Gaussian pulse rise time, arbitrary pulse envelope and phase control has been implemented. The system utilizes a two-channel 1 GSa/s DAC board\footnote{Designed by J. Martinis at UCSB and fabricated by HSCC.} to supply control voltages to an IQ mixer. The signals to the mixer have been optimized to obtain an on-off ratio of $>85\mbox{ dB}$ and phase deviations $<5\%$. The setup has been used to manipulate an $Al/AlO_{x}/Al$ Cooper-pair box (CPB) qubit coupled to a lumped-element microwave resonator ($f_0 = 5.446 \mbox{ GHz}$). The CPB has a charging energy $E_C/h = 6.25\mbox{ GHz}$ and a maximum $E_J/h = 19\mbox{ GHz}$ which was decreased to an effective $E_J/h = 6.1\mbox{ GHz}$ by an external magnetic field. By measuring the microwave transmission at $f_0$ in a pulsed-probe scheme, we perform a dispersive readout of the qubit. We present tomography data on the $\vert g \rangle$, $\vert e \rangle$, $(\vert g \rangle + \vert e \rangle)/\sqrt{2}$ and $(\vert g \rangle + i \vert e \rangle)/\sqrt{2}$ states. We find good agreement with theory, confirming that we have achieved the desired microwave pulse control.   

A phase qubit coupled to an RF-SQUID resonator

We have coupled a tunable cavity (an RF-SQUID resonator) to a phase qubit. The resonator can be used both for state transfer experiments as well as a measurement/readout device for the qubit. Specifically, it can be used in three different ways to help interrogate the state of the qubit. First, changes in the resonator frequency can be monitored in order to read out the qubit state after a conventional fast measure pulse is applied to the qubit bias flux. Second, we can perform a linear dispersive measurement of the qubit state using the coupled interaction between the qubit and the resonator. Here, the resonator will have a qubit-state dependent frequency shift. Finally, we can exploit the nonlinearity of the resonator by driving it into the bifurcated regime and performing a single- shot measurement of the state of the qubit. I will discuss the design, fabrication, and operation of this system.