Low-noise cryogenic microwave amplifier characterization with a calibrated noise source.

Parametric amplifiers have become a workhorse in superconducting quantum computing; however, research and development of these devices has been hampered by inconsistent and, sometimes, misleading noise performance characterization methodologies. The concepts behind noise characterization are deceptively simple, and there are many places where one can make mistakes, either in measurement or in interpretation and analysis. In this article, we cover the basics of noise performance characterization and the special problems it presents in parametric amplifiers with limited power handling capability. We illustrate the issues with three specific examples: a high-electron mobility transistor amplifier, a Josephson traveling-wave parametric amplifier, and a Josephson parametric amplifier. We emphasize the use of a 50-Ω shot noise tunnel junction (SNTJ) as a broadband noise source, demonstrating its utility for cryogenic amplifier amplifications. These practical examples highlight the role of loss as well as the additional parametric amplifier "idler" input mode.

Nonlinear Sideband Cooling to a Cat State of Motion.

The ability to prepare a macroscopic mechanical resonator into a quantum superposition state is an outstanding goal of cavity optomechanics. Here, we propose a technique to generate cat states of motion using the intrinsic nonlinearity of a dispersive optomechanical interaction. By applying a bichromatic drive to an optomechanical cavity, our protocol enhances the inherent second-order processes of the system, inducing the requisite two-phonon dissipation. We show that this nonlinear sideband cooling technique can dissipatively engineer a mechanical resonator into a cat state, which we verify using the full Hamiltonian and an adiabatically reduced model. While the fidelity of the cat state is maximized in the single-photon, strong-coupling regime, we demonstrate that Wigner negativity persists even for weak coupling. Finally, we show that our cat state generation protocol is robust to significant thermal decoherence of the mechanical mode, indicating that such a procedure may be feasible for near-term experimental systems.

Control and readout of a superconducting qubit using a photonic link.

Delivering on the revolutionary promise of a universal quantum computer will require processors with millions of quantum bits (qubits)1-3. In superconducting quantum processors4, each qubit is individually addressed with microwave signal lines that connect room-temperature electronics to the cryogenic environment of the quantum circuit. The complexity and heat load associated with the multiple coaxial lines per qubit limits the maximum possible size of a processor to a few thousand qubits5. Here we introduce a photonic link using an optical fibre to guide modulated laser light from room temperature to a cryogenic photodetector6, capable of delivering shot-noise-limited microwave signals directly at millikelvin temperatures. By demonstrating high-fidelity control and readout of a superconducting qubit, we show that this photonic link can meet the stringent requirements of superconducting quantum information processing7. Leveraging the low thermal conductivity and large intrinsic bandwidth of optical fibre enables the efficient and massively multiplexed delivery of coherent microwave control pulses, providing a path towards a million-qubit universal quantum computer.

Efficient Qubit Measurement with a Nonreciprocal Microwave Amplifier.

The act of observing a quantum object fundamentally perturbs its state, resulting in a random walk toward an eigenstate of the measurement operator. Ideally, the measurement is responsible for all dephasing of the quantum state. In practice, imperfections in the measurement apparatus limit or corrupt the flow of information required for quantum feedback protocols, an effect quantified by the measurement efficiency. Here, we demonstrate the efficient measurement of a superconducting qubit using a nonreciprocal parametric amplifier to directly monitor the microwave field of a readout cavity. By mitigating the losses between the cavity and the amplifier, we achieve a measurement efficiency of (72±4)%. The directionality of the amplifier protects the readout cavity and qubit from excess backaction caused by amplified vacuum fluctuations. In addition to providing tools for further improving the fidelity of strong projective measurement, this work creates a test bed for the experimental study of ideal weak measurements, and it opens the way toward quantum feedback protocols based on weak measurement such as state stabilization or error correction.

Ultrastrong Parametric Coupling between a Superconducting Cavity and a Mechanical Resonator.

We present a new optomechanical device where the motion of a micromechanical membrane couples to a microwave resonance of a three-dimensional superconducting cavity. With this architecture, we realize ultrastrong parametric coupling, where the coupling not only exceeds the dissipation in the system but also rivals the mechanical frequency itself. In this regime, the optomechanical interaction induces a frequency splitting between the hybridized normal modes that reaches 88% of the bare mechanical frequency, limited by the fundamental parametric instability. The coupling also exceeds the mechanical thermal decoherence rate, enabling new applications in ultrafast quantum state transfer and entanglement generation.

[Pharmacotherapy of Vestibular Disorders, Nystagmus and Cerebellar Disorders]. / Medikamentöse Therapiemöglichkeiten bei vestibulären Störungen, Nystagmus und zerebellären Ataxien.

There are currently different groups of drugs for the pharmacotherapy of vertigo, nystagmus and cerebellar disorders: antiemetics; anti-inflammatories, antimenieres, and antimigraineous medications and antidepressants, anticonvulsants, aminopyridines as well as acetyl-DL-leucine. In acute unilateral vestibulopathy, corticosteroids improve the recovery of peripheral vestibular function, but currently there is not sufficient evidence for a general recommendation. There is insufficient evidence to support the view that 16 mg t. i. d. or 48 mg t. i. d. betahistine has an effect in Menière's disease. Therefore, higher dosages are recommended. In animal studies, it was shown that betahistine increases cochlear blood flow. In vestibular paroxysmia, oxcarbazepine was effective (one randomized controlled trial (RCT)). Aminopyridines are recommended for the treatment of downbeat nystagmus (two RCTs) and episodic ataxia type 2 (EA2, one RCT). There has been no RCT on the efficacy of beta-blockers or topiramate but one RCT on flunarizine in vestibular migraine. Based on clinical experience, a treatment analogous to that for migraine without aura can be recommended. Acetyl-DL-leucine improved cerebellar ataxia (two observational studies); it also accelerated central compensation in an animal model of acute unilateral lesion, but RCTs were negative. There are ongoing RCTs on treatment of vestibular paroxysmia with carbamazepine (VESPA), acute unilateral vestibulopathy with betahistine (BETAVEST), vestibular migraine with metoprolol (PROVEMIG), benign paroxysmal positional vertigo with vitamin D (VitD@BPPV), EA2 with 4-aminopyridine versus acetazolamide (EAT-2-TREAT), and cerebellar ataxias with acetyl-DL-leucine (ALCAT).

Nonreciprocal Microwave Signal Processing with a Field-Programmable Josephson Amplifier.

We report on the design and implementation of a field-programmable Josephson amplifier (FPJA)-a compact and lossless superconducting circuit that can be programmed in situ by a set of microwave drives to perform reciprocal and nonreciprocal frequency conversion and amplification. In this work, we demonstrate four modes of operation: frequency conversion (transmission of -0.5 dB, reflection of -30 dB), circulation (transmission of -0.5 dB, reflection of -30 dB, isolation of 30 dB), phase-preserving amplification (gain > 20 dB, one photon of added noise) and directional phase-preserving amplification (reflection of -10 dB, forward gain of 18 dB, reverse isolation of 8 dB, one photon of added noise). The system exhibits quantitative agreement with the theoretical prediction. Based on a gradiometric superconducting quantum-interference device with Nb/Al-AlOx/Nb Josephson junctions, the FPJA is first-order insensitive to flux noise and can be operated without magnetic shielding at low temperature. Owing to its flexible design and compatibility with existing superconducting fabrication techniques, the FPJA offers a straightforward route toward on-chip integration with superconducting quantum circuits such as qubits and microwave optomechanical systems.

Mechanically Mediated Microwave Frequency Conversion in the Quantum Regime.

We report the observation of efficient and low-noise frequency conversion between two microwave modes, mediated by the motion of a mechanical resonator subjected to radiation pressure. We achieve coherent conversion of more than 10^{12} photons/s with a 95% efficiency and a 14 kHz bandwidth. With less than 10^{-1} photons·s^{-1}·Hz^{-1} of added noise, this optomechanical frequency converter is suitable for quantum state transduction. We show the ability to operate this converter as a tunable beam splitter, with direct applications for photon routing and communication through complex quantum networks.

Overwhelming Thermomechanical Motion with Microwave Radiation Pressure Shot Noise.

We measure the fundamental noise processes associated with a continuous linear position measurement of a micromechanical membrane incorporated in a microwave cavity optomechanical circuit. We observe the trade-off between the two fundamental sources of noise that enforce the standard quantum limit: the measurement imprecision and radiation pressure backaction from photon shot noise. We demonstrate that the quantum backaction of the measurement can overwhelm the intrinsic thermal motion by 24 dB, entering a new regime for cavity optomechanical systems.

Quantum-enabled temporal and spectral mode conversion of microwave signals.

Electromagnetic waves are ideal candidates for transmitting information in a quantum network as they can be routed rapidly and efficiently between locations using optical fibres or microwave cables. Yet linking quantum-enabled devices with cables has proved difficult because most cavity or circuit quantum electrodynamics systems used in quantum information processing can only absorb and emit signals with a specific frequency and temporal envelope. Here we show that the temporal and spectral content of microwave-frequency electromagnetic signals can be arbitrarily manipulated with a flexible aluminium drumhead embedded in a microwave circuit. The aluminium drumhead simultaneously forms a mechanical oscillator and a tunable capacitor. This device offers a way to build quantum microwave networks using separate and otherwise mismatched components. Furthermore, it will enable the preparation of non-classical states of motion by capturing non-classical microwave signals prepared by the most coherent circuit quantum electrodynamics systems.

[Pharmacotherapy of Vestibular Disorders, Nystagmus and Cerebellar Disorders]. / Medikamentöse Therapiemöglichkeiten bei vestibulären Störungen, Nystagmus und zerebellären Ataxien.

There are currently different groups of drugs for the pharmacotherapy of vertigo, nystagmus and cerebellar disorders: antiemetics; anti-inflammatories, antimenieres, and antimigraineous medications and antidepressants, anticonvulsants, aminopyridines as well as acetyl-DL-leucine. In acute unilateral vestibulopathy, corticosteroids improve the recovery of peripheral vestibular function, but currently there is not sufficient evidence for a general recommendation. There is insufficient evidence to support the view that 16 mg t. i. d. or 48 mg t. i. d. betahistine has an effect in Menière's disease. Therefore, higher dosages are recommended. In animal studies, it was shown that betahistine increases cochlear blood flow. In vestibular paroxysmia, oxcarbazepine was effective (one randomized controlled trial (RCT)). Aminopyridines are recommended for the treatment of downbeat nystagmus (two RCTs) and episodic ataxia type 2 (EA2, one RCT). There has been no RCT on the efficacy of beta-blockers or topiramate but one RCT on flunarizine in vestibular migraine. Based on clinical experience, a treatment analogous to that for migraine without aura can be recommended. Acetyl-DL-leucine improved cerebellar ataxia (two observational studies); it also accelerated central compensation in an animal model of acute unilateral lesion, but RCTs were negative. There are ongoing RCTs on treatment of vestibular paroxysmia with carbamazepine (VESPA), acute unilateral vestibulopathy with betahistine (BETAVEST), vestibular migraine with metoprolol (PROVEMIG), benign paroxysmal positional vertigo with vitamin D (VitD@BPPV), EA2 with 4-aminopyridine versus acetazolamide (EAT-2-TREAT), and cerebellar ataxias with acetyl-DL-leucine (ALCAT).

Quantum Nondemolition Measurement of a Nonclassical State of a Massive Object.

By coupling a macroscopic mechanical oscillator to two microwave cavities, we simultaneously prepare and monitor a nonclassical steady state of mechanical motion. In each cavity, correlated radiation pressure forces induced by two coherent drives engineer the coupling between the quadratures of light and motion. We, first, demonstrate the ability to perform a continuous quantum nondemolition measurement of a single mechanical quadrature at a rate that exceeds the mechanical decoherence rate, while avoiding measurement backaction by more than 13 dB. Second, we apply this measurement technique to independently verify the preparation of a squeezed state in the mechanical oscillator, resolving quadrature fluctuations 20% below the quantum noise.

Tunable resonant and nonresonant interactions between a phase qubit and LC resonator.

We use a flux-biased radio frequency superconducting quantum interference device (rf SQUID) with an embedded flux-biased direct current SQUID to generate strong resonant and nonresonant tunable interactions between a phase qubit and a lumped-element resonator. The rf SQUID creates a tunable magnetic susceptibility between the qubit and resonator providing resonant coupling strengths from zero to near the ultrastrong coupling regime. By modulating the magnetic susceptibility, nonresonant parametric coupling achieves rates >100 MHz. Nonlinearity of the magnetic susceptibility also leads to parametric coupling at the subharmonics of the qubit-resonator detuning.

Consensus paper: management of degenerative cerebellar disorders.

Treatment of motor symptoms of degenerative cerebellar ataxia remains difficult. Yet there are recent developments that are likely to lead to significant improvements in the future. Most desirable would be a causative treatment of the underlying cerebellar disease. This is currently available only for a very small subset of cerebellar ataxias with known metabolic dysfunction. However, increasing knowledge of the pathophysiology of hereditary ataxia should lead to an increasing number of medically sensible drug trials. In this paper, data from recent drug trials in patients with recessive and dominant cerebellar ataxias will be summarized. There is consensus that up to date, no medication has been proven effective. Aminopyridines and acetazolamide are the only exception, which are beneficial in patients with episodic ataxia type 2. Aminopyridines are also effective in a subset of patients presenting with downbeat nystagmus. As such, all authors agreed that the mainstays of treatment of degenerative cerebellar ataxia are currently physiotherapy, occupational therapy, and speech therapy. For many years, well-controlled rehabilitation studies in patients with cerebellar ataxia were lacking. Data of recently published studies show that coordinative training improves motor function in both adult and juvenile patients with cerebellar degeneration. Given the well-known contribution of the cerebellum to motor learning, possible mechanisms underlying improvement will be outlined. There is consensus that evidence-based guidelines for the physiotherapy of degenerative cerebellar ataxia need to be developed. Future developments in physiotherapeutical interventions will be discussed including application of non-invasive brain stimulation.

Entangling mechanical motion with microwave fields.

When two physical systems share the quantum property of entanglement, measurements of one system appear to determine the state of the other. This peculiar property is used in optical, atomic, and electrical systems in an effort to exceed classical bounds when processing information. We extended the domain of this quantum resource by entangling the motion of a macroscopic mechanical oscillator with a propagating electrical signal and by storing one half of the entangled state in the mechanical oscillator. This result demonstrates an essential requirement for using compact and low-loss micromechanical oscillators in a quantum processor, can be extended to sense forces beyond the standard quantum limit, and may enable tests of quantum theory.

[Cardinal symptom vertigo from the neurologist's perspective]. / Leitsymptom Schwindel aus Sicht des Neurologen.

In most patients with vertigo, the first and clinically most important question posed to neurologists is whether it is a central or a peripheral syndrome. In more than 90 % of cases, this differentiation is made possible by systematically recording the patient history (asking about the type of vertigo, the duration, triggers and accompanying symptoms) and conducting a physical examination. Particularly in the case of acute vertigo disorders, a five-step procedure has proven useful: 1. A cover test to look for vertical divergence (skew deviation) as a central sign and component of the ocular tilt reaction (OTR); 2. Examination with and without Frenzel goggles to differentiate between peripheral vestibular spontaneous nystagmus and central fixation nystagmus; 3. Examination of smooth pursuit; 4. Examination of the gaze-holding function (particularly gaze-evoked nystagmus beating in the opposite direction to spontaneous nystagmus); 5. The head impulse test to look for a deficit in the vestibulo-ocular reflex (VOR). Considerable advances have been made in the pharmacotherapy of vertigo disorders during the last 10 years, including cortisone for the treatment of acute vestibular neuritis, betahistine as a high-dose long-term treatment for Menière's disease, carbamazepine to treat vestibular paroxysmia and aminopyridine for down- and upbeat nystagmus and episodic ataxia type 2.

Signatures of nonlinear cavity optomechanics in the weak coupling regime.

We identify signatures of the intrinsic nonlinear interaction between light and mechanical motion in cavity optomechanical systems. These signatures are observable even when the cavity linewidth exceeds the optomechanical coupling rate. A strong laser drive red detuned by twice the mechanical frequency from the cavity resonance frequency makes two-phonon processes resonant, which leads to a nonlinear version of optomechanically induced transparency. This effect provides a new method of measuring the average phonon number of the mechanical oscillator. Furthermore, we show that if the strong laser drive is detuned by half the mechanical frequency, optomechanically induced transparency also occurs due to resonant two-photon processes. The cavity response to a second probe drive is in this case nonlinear in the probe power. These effects should be observable with optomechanical coupling strengths that have already been realized in experiments.

Coherent state transfer between itinerant microwave fields and a mechanical oscillator.

Macroscopic mechanical oscillators have been coaxed into a regime of quantum behaviour by direct refrigeration or a combination of refrigeration and laser-like cooling. This result supports the idea that mechanical oscillators may perform useful functions in the processing of quantum information with superconducting circuits, either by serving as a quantum memory for the ephemeral state of a microwave field or by providing a quantum interface between otherwise incompatible systems. As yet, the transfer of an itinerant state or a propagating mode of a microwave field to and from a storage medium has not been demonstrated, owing to the inability to turn on and off the interaction between the microwave field and the medium sufficiently quickly. Here we demonstrate that the state of an itinerant microwave field can be coherently transferred into, stored in and retrieved from a mechanical oscillator with amplitudes at the single-quantum level. Crucially, the time to capture and to retrieve the microwave state is shorter than the quantum state lifetime of the mechanical oscillator. In this quantum regime, the mechanical oscillator can both store quantum information and enable its transfer between otherwise incompatible systems.