We propose a low noise, triply-resonant, electro-optic (EO) scheme for quantum microwave-tooptical conversion based on coupled nanophotonics resonators integrated with a superconducting qubit. Our optical system features a split resonance -a doublet -with a tunable frequency splitting that matches the microwave resonance frequency of the superconducting qubit. This is in contrast to conventional approaches where large optical resonators with free-spectral range comparable to the qubit microwave frequency are used. In our system, EO mixing between the optical pump coupled into the low frequency doublet mode and a resonance microwave photon results in an up-converted optical photon on resonance with high frequency doublet mode. Importantly, the down-conversion process, which is the source of noise, is suppressed in our scheme as the coupled-resonator system does not support modes at that frequency. Our device has at least an order of magnitude smaller footprint than the conventional devices, resulting in large overlap between optical and microwave fields and large photon conversion rate (g/2π) in the range of ∼5-15 kHz. Owing to large g factor and doubly-resonant nature of our device, microwave-to-optical frequency conversion can be achieved with optical pump powers in the range of tens of microwatts, even with moderate values for optical Q (∼ 10 6 ) and microwave Q (∼ 10 4 ). The performance metrics of our device, with substantial improvement over the previous EO-based approaches, promise a scalable quantum microwave-tooptical conversion and networking of superconducting processors via optical fiber communication.arXiv:1711.00346v1 [quant-ph] 1 Nov 2017

Fast, high-fidelity measurement is a key ingredient for quantum error correction. Conventional approaches to the measurement of superconducting qubits, involving linear amplification of a microwave probe tone followed by heterodyne detection at room temperature, do not scale well to large system sizes. Here we introduce an alternative approach to measurement based on a microwave photon counter. We demonstrate raw single-shot measurement fidelity of 92%. Moreover, we exploit the intrinsic damping of the counter to extract the energy released by the measurement process, allowing repeated high-fidelity quantum non-demolition measurements. Crucially, our scheme provides access to the classical outcome of projective quantum measurement at the millikelvin stage. In a future system, counter-based measurement could form the basis for a scalable quantum-to-classical interface.

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We describe a microwave amplifier based on the Superconducting Low-inductance Undulatory Galvanometer (SLUG). The SLUG is embedded in a microstrip resonator, and the signal current is injected directly into the device loop. Measurements at 30 mK show gains of 25 dB at 3 GHz and 15 dB at 9 GHz. Amplifier performance is well described by a simple numerical model based on the Josephson junction phase dynamics. We expect optimized devices based on high critical current junctions to achieve gain greater than 15 dB, bandwidth of several hundred MHz, and added noise of order one quantum in the frequency range of 5-10 GHz.PACS numbers: 85.25. Am, 85.25.Dq, 84.30.Le, 84.40.Lj Recent progress in the superconducting quantum circuit community has motivated a search for ultralow-noise microwave amplifiers for the readout of qubits and linear cavity resonators [1,2]. It has long been recognized that the dc Superconducting QUantum Interference Device (SQUID) can achieve noise performance approaching the standard quantum limit of half a quantum [3]. While in principle the SQUID should be able to amplify signals approaching the Josephson frequency (typically several tens of GHz), it remains challenging to integrate the SQUID into a 50 Ω environment and to provide for efficient coupling of the microwave signal to the device. In one arrangement, a multiturn input coil has been configured as a microstrip resonator, with the SQUID washer acting as a groundplane [4]. This so-called microstrip SQUID amplifier has achieved noise performance within a factor of two of the standard quantum limit at 600 MHz [5,6]; however, performance degrades at higher frequencies due to the reduced coupling associated with the shorter microstrip input line [7]. An alternative approach accesses the GHz regime by integrating a high-gain SQUID gradiometer into a coplanar transmission line resonator at a current antinode [8,9]. In other work, Jospehson circuits have been driven by an external microwave tone to enable ultralow-noise parametric amplification of microwave frequency signals [10][11][12]; however, Josephson parametric amplifiers provide limited bandwidth and dynamic range, and the external microwave bias circuitry introduces an additional layer of complexity.In this Letter we describe a new device configuration that provides efficient coupling of a GHz-frequency signal to a compact Superconducting Low-inductance Undulatory Galvanometer (SLUG). In contrast to the dc SQUID, which relies on a separate inductive element to transform the input signal into a magnetic flux, the SLUG samples the magnetic flux generated by a current that is directly injected into the device loop [13]. The compact geometry of the SLUG makes the device straightforward to model at microwave frequencies and * Electronic address: rfmcdermott@wisc.edu easy to integrate into a microwave transmission line. Moreover, it is simple to decouple the SLUG modes from the input modes, allowing for separate optimization of the gain element and the matching network.The layer stackup of ...

We describe a novel scheme for low-noise phase-insensitive linear amplification at microwave frequencies based on the superconducting low-inductance undulatory galvanometer (SLUG). Direct integration of the junction equations of motion provides access to the full scattering matrix of the SLUG. We discuss the optimization of SLUG amplifiers and calculate amplifier gain and noise temperature in both the thermal and quantum regimes. Loading of the SLUG element by the finite input admittance is taken into account, and strategies for decoupling the SLUG from the higher-order modes of the input circuit are discussed. The microwave SLUG amplifier is expected to achieve noise performance approaching the standard quantum limit in the frequency range from 5-10 GHz, with gain around 15 dB for a single-stage device and instantaneous bandwidths of order 1 GHz. V

Quantum process tomography has become increasingly critical as the need grows for robust verification and validation of candidate quantum processors. Here, we present an approach for efficient quantum process tomography that uses a physically motivated ansatz for an unknown quantum process. Our ansatz bootstraps to an effective description for an unknown process on a multi-qubit processor from pairwise two-qubit tomographic data. Further, our approach can inherit insensitivity to system preparation and measurement error from the two-qubit tomography scheme. We benchmark our approach using numerical simulation of noisy three-qubit gates, and show that it produces highly accurate characterizations of quantum processes. Further, we demonstrate our approach experimentally, building three-qubit gate reconstructions from two-qubit tomographic data.

The promise of quantum computing with imperfect qubits relies on the ability of a quantum computing system to scale cheaply through error correction and fault tolerance. While fault tolerance requires relatively mild assumptions about the nature of qubit errors, the overhead associated with coherent and non-Markovian errors can be orders of magnitude larger than the overhead associated with purely stochastic Markovian errors. One proposal to address this challenge is to randomize the circuits of interest, shaping the errors to be stochastic Pauli errors but leaving the aggregate computation unaffected. The randomization technique can also suppress couplings to slow degrees of freedom associated with non-Markovian evolution. Here, we demonstrate the implementation of Pauli-frame randomization in a superconducting circuit system, exploiting a flexible programming and control infrastructure to achieve this with low effort. We use high-accuracy gate-set tomography to characterize in detail the properties of the circuit error, with and without the randomization procedure, which allows us to make rigorous statements about Markovianity as well as the nature of the observed errors. We demonstrate that randomization suppresses signatures of non-Markovian evolution to statistically insignificant levels, from a Markovian model violation ranging from 43σ to 1987σ , down to violations between 0.3σ and 2.7σ under randomization. Moreover, we demonstrate that, under randomization, the experimental errors are well described by a Pauli error model, with model violations that are similarly insignificant (between 0.8σ and 2.7σ ). Importantly, all these improvements in the model accuracy were obtained without degradation to fidelity, and with some improvements to error rates as quantified by the diamond norm. This demonstrates the ability of Pauli-frame randomization to shape noise into forms that are more benign for quantum error correction and fault tolerance.

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