Session F25: Superconducting Qubits: Read-out, Feedback and Stabilization

Non-linear processes in thin titanium nitride transmission lines for parametric amplification

Nitride superconductors, such as titanium nitride and niobium titanium nitride, are a non-linear, low dissipation medium at microwave frequencies. The lossless nonlinearity may be probed and utilized. Important applications include generation of higher harmonics , e.g. 3f, and a microwave version of the optical paramagnetic amplifier, i.e. the degenerate-pump case of four-photon mixing (FPM). An amplifier based on these principles should allow for very wide bandwidth, low noise (quantum limited) and high dynamic range devices. These measurements are performed via a single layer, 3 meter long TiN spiral and measured at temperatures below 100 mK. Initial results of the design, fabrication, testing, and impedance optimization of a titanium nitride based parametric amplifier are presented.   

Efficiency of a microwave photon detector based on a current-biased Josephson junction

In this talk we discuss the efficiency of a microwave photon detector based on a current-biased Josephson junction driven by a classical microwave source. We consider the evolution of the junction in the presence of the environment and tunneling events to the voltage state. We calculate the switching time distribution to the voltage state and evaluate the efficiency of the photon detector as a function of input power and the junction parameters. We present conditions for the optimal power matching between the detector and the microwave source.   

Optimization of single shot readout of a transmon qubit using a SLUG microwave amplifier

We report on measurement of a superconducting transmon qubit using a number of optimization techniques and a low noise amplifier. ~Optimization is performed over power and frequency, and a genetic algorithm is employed to optimize the readout fidelity as a function of the measurement pulse shape. ~In addition, a superconducting low-inductance undulatory galvanometer (SLUG), a SQUID-based microwave amplifier, is used to reduce system noise. ~The SLUG amplifier has very high dynamic range and low noise over a relatively wide frequency range. ~Both the SLUG amplifier and genetic algorithm lead to improved readout fidelity over analytic pulse shaping and HEMT amplification.   

Large gain quantum-limited qubit state measurement using a two mode nonlinear cavity

A single nonlinear cavity dispersively coupled to a qubit functions as a large gain detector near a bifurcation, but also has an unavoidable large backaction that prevents QND measurement at weak couplings~[1]. We show theoretically that a modified setup involving two cavities (one linear, one nonlinear) and a dispersively coupled qubit allows for a far more optimal measurement. In particular, operating near a point of bifurcation, one is able to both achieve a large gain as well as a near quantum-limited backaction. We present analytic results for the gain and noise of this detector and a heuristic understanding of the physics, thus presenting a complete description of this new way of performing weak qubit state measurements. The setup we describe can easily be realised in experiments with superconducting circuits involving Josephson junctions~[2,3].\\[4pt] [1] C. LaFlamme, A.A. Clerk, Phys. Rev. A \textbf{83}, 033803 (2011)\\[0pt] [2] F.R. Ong \emph{et al.}, Phys. Rev. Lett. \textbf{106}, 167002 (2011)\\[0pt] [3] M. Hatridge \emph{et al.}, Phys. Rev. B \textbf{83}, 134501 (2011)   

A $>$10 GHz JPC with Trans-Gain for Qubit Readout

For multi-qubit circuit QED experiments, it is desirable to work with cavities at frequencies $>$10 GHz to allow for design flexibility. However, performance of following electronics can be best optimized at low frequencies (3-5 GHz). These seemingly contradictory requirements can be naturally reconciled using the Josephson Parametric Converter (JPC). The JPC is a quantum limited amplifier comprised of two non-degenerate resonators coupled via a ring of Josephson junctions. It can bridge frequency ranges separated by more than an octave via its trans-gain, a process in which a signal incident on one port is frequency converted and transmitted with gain on the other port. Here we present data on the trans-gain of a JPC with one resonator at 11.5 GHz and the other at 4.5 GHz which could be used in such a readout scheme without any significant compromise on gain, dynamic range, or bandwidth.   

Characterization of a Multi-Layer Parametric Amplifier with On-Chip Bias Line

Single shot dispersive readout of superconducting qubits requires a near quantum limited microwave amplifier. Based on the parametric amplifier design from UC Berkeley, we have developed a parametric amplifier using the UCSB multilayer fabrication with a single ended input and an on-chip flux bias line. These changes enable us to use a smaller and simpler chip mount with separate signal and flux ports. The high bandwidth of the flux port allows us to flux pump the amplifier and should allow dynamic frequency tuning on ns timescales. Flux pumping also requires fewer components in the measurement line, reducing signal loss. With this design we have achieved parametric amplification using two kinds of input pumping and three kinds of flux pumping; for each mode we have characterized gain bandwidth product, saturation power, and noise temperature.   

Increasing dynamic range in microwave parametric amplifiers

Parametric amplifiers have long been of interest in quantum information due to their high gain and near quantum limited performance. In collaboration with UC Berkeley, we are improving upon their proven parametric amplifier design, which consists of a lumped element LC resonator, with a SQUID providing a tunable nonlinear inductance. In order to improve the dynamic range of these amplifiers, multiple SQUIDs are used in series in order to distribute the non-linearity across many junctions. We report on the design of a single-ended amplifier using our 7-layer fabrication process, combining photo and electron beam lithography. We explore the experimental optimization of such a design, specifically the impact of adding additional SQUIDs on overall device performance.   

Improved JPC performance via a low inductance, lumped element design

The Josephson Parametric Converter (JPC), a linear, non-degenerate, nearly quantum-limited amplifier, is a promising tool for quantum information applications. We propose a new JPC design characterized by the use of multi-pF parallel-plate capacitors. By decreasing the geometric inductance of the system, higher critical-current Josephson junctions can be used. Both the bandwidth and dynamic range can thus be increased by a factor of two relative to existing microstrip devices. When integrated with a shunted ring of Josephson junctions [1], these devices should also be tunable over more than a GHz. We present simulations of the circuit behavior and preliminary measurements of a proof-of-concept device. \\[4pt] [1] N. Roch et al., Phys. Rev. Lett. 108, 147701, 2012   

Optimizing bandwidth and dynamic range of lumped Josephson parametric amplifiers

Superconducting parametric amplifiers have revolutionized the field of quantum measurement by providing high gain, ultra-low noise amplification. They have been used successfully for high-fidelity qubit state measurements, probing nano-mechanical resonators, quantum feedback, and for microwave quantum optics experiments. Though several designs exist, a simple and robust architecture is the Lumped Josephson Parametric Amplifier (LJPA). This device consists of a capacitively shunted SQUID directly coupled to a transmission line to form a low quality factor (Q) nonlinear resonator. We discuss amplifiers which can be tuned over the full 4-8 GHz band with 20-25 dB of gain and 10 - 50 MHz of signal bandwidth. However, similar to other parametric amplifiers employing a resonant circuit, the LJPA suffers from low dynamic range and has a -1 dB gain compression point of order -130 dBm. We explore new designs comprised of an array of SQUIDs to improve the dynamic range. We will present the results of numerical simulations and preliminary experiments. We will also briefly discuss improvements obtained from different biasing methods and packaging.   

Real-time digital processing of qubit readout and feedback control

Rapid progress in high fidelity readout of superconducting qubits paves the way for measurement-based feedback control of quantum systems and error correction protocols. A traditional data acquisition and processing setup, consisting of separate digitizer card for qubit readout, PC for processing and commercial arbitrary waveform generator (AWG) for qubit control, however, can have latency of at least several milliseconds and cannot meet the timing requirement of quantum feedback experiments. We have implemented an all-in-one system that contains a digitizer, a demodulator, a qubit-state estimator and an AWG on a commercial field-programmable-gate-array (FPGA) board. The FPGA system shows superior performance in terms of throughput, timing stability and on-the-fly programmability compared to traditional technology. Latency of the FPGA system can be on the order of only hundreds of nanoseconds. Results from our project of integrating the real-time processing power of the FPGA with a qubit + amplifier system will be shown.   

Stabilizer quantum error correction toolbox for superconducting qubits

Rudimentary quantum error correction (QEC) has been achieved in a superconducting qubit circuit [1]. Realization of topological protection and QEC based on stabilizer codes will require protocols for QND measurement of multi-qubit Pauli operators on arbitrary selected subsets of qubits. Initial progress towards this goal has been achieved with four-qubit stabilizer pumping in a trapped ion system [2]. We present a general protocol for stabilizer measurement and pumping in a system of $N$ superconducting qubits. We assume always-on, fixed dispersive couplings $\chi$ to a single mode of a high-$Q$ microwave resonator in the strong-dispersive limit defined by $\chi\gg 1/T_2,\kappa$, where $T_2$ is the qubit coherence time and $\kappa$ is the cavity line width. In this limit, we show how to measure an arbitrary weight $M\leq N$ Pauli operator, by entangling the multi-qubit state with two distinguishable coherent states of the cavity. Together with a fast cavity readout ($T_{\rm meas}\ll 1/\kappa$), which can be achieved by tunable coupling to a low-$Q$ cavity mode, this enables the efficient measurement of mulit-qubit Pauli operators.\newline [1] M. D. Reed et al. Nature 2012, {\bf 482}, 382-385\newline [2] J. T. Barreiro et al. Nature 2011, {\bf 470}, 486   

Autonomous stabilization of an entangled state of two transmon qubits

Recent circuit QED (cQED) experiments on superconducting transmon qubits have shown good progress towards measurement-based quantum feedback, that should allow the stabilization of interesting quantum states, such as an entangled state of two qubits. These experiments crucially depend on fast, high-fidelity, quantum non-demolition qubit readout using superconducting parametric amplifiers as well as high-speed room-temperature electronics. We describe an alternate autonomous-feedback strategy to stabilize two qubits dispersively coupled to a single cavity into an entangled state, while obviating the need for an optimized measurement chain. The system Hamiltonian is designed to be in the strong dispersive cQED regime where the dispersive shifts of the two qubits are tuned to be equal ($\chi/2\pi = 5$~MHz) and larger than the cavity linewidth ($\kappa/2\pi = 1.5$~MHz). By applying continuous microwave drives at the cavity and qubit frequencies, the system is forced into the desired quantum state. The stabilization rate of this scheme is of order $\kappa$ which can be made much faster than all decoherence rates 1/T$_1$, 1/T$_\phi$ that take the system out of the entangled state. We will discuss initial experimental progress towards the goal of autonomous high-fidelity entanglement.   

Efficient Experimental Characterization of a Feedback Scheme for Qubit Initialization

Quantum feedback based on high-efficiency projective measurements has a variety of potential applications such as active qubit initialization and quantum teleportation. Here, we experimentally investigate active initialization of a single transmon qubit in circuit quantum electrodynamics using parametric amplification similar to the experiment by Rist\`e \emph{et. al.} [1]. We implement the feedback scheme using field-programmable gate array (FPGA) electronics which conditions a $\pi$-pulse on the outcome of a prior quantum nondemolition measurement. Our processing unit also records multi-dimensional histograms which reveal the correlations between the initial and final state of the feedback process. We use these histograms to characterize the efficiency of our feedback implementation without the necessity of storing all individual single-shot measurement traces. The presented histogram-based measurement technique has potential applications in other experiments which involve feedback such as quantum teleportation. \newline [1] D.~Rist\`e, C.~C. Bultink, K.~W. Lehnert, L.~DiCarlo, arXiv:1207.2944v1.   

Superconducting qubit parameter optimization for remote entanglement

The combination of coherent lifetimes in excess of 100 microseconds and robust operation of low noise parametric amplifiers has enabled experiments in which high fidelity continuous measurement can be performed, opening the door for measurement based quantum feedback. The first experiment realized in this regime aimed at stabilizing a dynamical state of a superconducting qubit using a closed feedback loop [1]. We explore the prospects of extending this unprecedented control to engineered networks comprised of several superconducting qubits and microwave cavities, with the particular goal of stabilizing a central feature of quantum mechanics: the entanglement. We will discuss the optimal choice of hardware---qubit, cavity, and circuitry---as well as measurement protocols for maximizing entanglement. \\[4pt] [1] R. Vijay et al., Nature 490, 77-80 (2012)   

Progress towards measurement-induced entanglement of remote superconducting qubits

Generation and distribution of entanglement are critical capabilities for quantum computation and simulation. In superconducting qubits, entanglement can be achieved via direct qubit-qubit coupling on chip. In contrast to this type of local interaction, we present experiments and simulations targeted at generating entanglement between remote (non-coupled) 3D transmons. Entanglement is achieved via joint measurement in a basis that does not project, and thus does not dephase, the odd-parity Bell manifold (\textbar 01\textgreater /\textbar 10\textgreater ). The experiments rely on coherent state detection, rather than photon-counting, and are a step towards deterministic feedback stabilization of remote qubit entanglement. We also model the effects of experimental realities, including excess amplifier noise, cable insertion loss, and finite qubit coherence times.