The measurement of a quantum system is often performed by encoding its state in a single observable of a light field. The measurement efficiency of this observable can be reduced by loss or excess noise on the way to the detector. Even a quantum-limited detector that simultaneously measures a second noncommuting observable would double the output noise, therefore limiting the efficiency to $50\mathrm{%}$. At microwave frequencies, an ideal measurement efficiency can be achieved by noiselessly amplifying the information-carrying quadrature of the light field but this has remained an experimental challenge. Indeed, while state-of-the-art Josephson-junction-based parametric amplifiers can perform an ideal single-quadrature measurement, they require lossy ferrite circulators in the signal path, drastically decreasing the overall efficiency. In this paper, we present a nonreciprocal parametric amplifier that combines single-quadrature measurement and directionality without the use of strong external magnetic fields. We extract a measurement efficiency of ${62}_{\ensuremath{-}9}^{+17}\mathrm{%}$ that exceeds the quantum limit and that is not limited by fundamental factors. The amplifier can be readily integrated with superconducting devices, creating a path for ideal measurements of quantum bits and mechanical oscillators.
The measurement of a quantum system is often performed by encoding its state in a single observable of a light field. The measurement efficiency of this observable can be reduced by loss or excess noise on the way to the detector. Even a quantum-limited detector that simultaneously measures a second noncommuting observable would double the output noise, therefore limiting the efficiency to 50\mathrm{%}. At microwave frequencies, an ideal measurement efficiency can be achieved by noiselessly amplifying the information-carrying quadrature of the light field but this has remained an experimental challenge. Indeed, while state-of-the-art Josephson-junction-based parametric amplifiers can perform an ideal single-quadrature measurement, they require lossy ferrite circulators in the signal path, drastically decreasing the overall efficiency. In this paper, we present a nonreciprocal parametric amplifier that combines single-quadrature measurement and directionality without the use of strong external magnetic fields. We extract a measurement efficiency of {62}_{\ensuremath{-}9}^{+17}\mathrm{%} that exceeds the quantum limit and that is not limited by fundamental factors. The amplifier can be readily integrated with superconducting devices, creating a path for ideal measurements of quantum bits and mechanical oscillators.
The measurement of a quantum system is often performed by encoding its state in a single observable of a light field. The measurement efficiency of this observable can be reduced by loss or excess noise on the way to the detector. Even a quantum-limited detector that simultaneously measures a second noncommuting observable would double the output noise, therefore limiting the efficiency to 50%. At microwave frequencies, an ideal measurement efficiency can be achieved by noiselessly amplifying the information-carrying quadrature of the light field but this has remained an experimental challenge. Indeed, while state-of-the-art Josephson-junction-based parametric amplifiers can perform an ideal single-quadrature measurement, they require lossy ferrite circulators in the signal path, drastically decreasing the overall efficiency. In this paper, we present a nonreciprocal parametric amplifier that combines single-quadrature measurement and directionality without the use of strong external magnetic fields. We extract a measurement efficiency of 62+17−9% that exceeds the quantum limit and that is not limited by fundamental factors. The amplifier can be readily integrated with superconducting devices, creating a path for ideal measurements of quantum bits and mechanical oscillators.
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.
Nonreciprocal microwave routing plays a crucial role in measuring quantum circuits, and allows for realizing cascaded quantum systems for generating and stabilizing entanglement between noninteracting qubits. The most commonly used tools for implementing directionality are ferrite-based circulators. These devices are versatile, but suffer from excess loss, a large footprint, and fixed directionality. For utilizing nonreciprocity in scalable quantum circuits it is desirable to develop efficient integration of low-loss and controllable directional elements. Here, we report the design and experimental realization of a minimal controllable directional interface that can be directly coupled to superconducting qubits. In the device presented, nonreciprocity is realized through a combination of interference and phase-controlled parametric pumping. We have achieved a maximum directionality of around 30 dB, and the performance of the device is predicted quantitatively from independent calibration measurements. Using the excellent agreement of model and experiment, we predict that the circuit will be useable as a chiral qubit interface with inefficiencies at the 1 % level or below. Our work offers a promising route for realizing high-fidelity signal routing and entanglement generation in all-to-all connected microwave quantum networks, and provides a path for isolator-free qubit readout schemes. Published by the American Physical Society 2024
High fidelity qubit readout is a cornerstone for quantum information protocols. In traditional superconducting qubit readout, a chain of microwave amplifiers and nonreciprocal components aid in detecting the qubit's state with tolerable added noise and backaction. However, the loss, size, and magnetic field of standard nonreciprocal components have sparked a decades-long search for more efficient and scalable alternatives. One prominent approach employs networks of parametrically coupled modes to achieve nonreciprocity. While this class of devices can be directly integrated with the qubit's readout cavity, current understanding of the resulting single quantum system is substantially lacking. Here we provide a first-principles theoretical tool to understand and design networks of linear modes integrated with embedded qubits. We utilize this theory to inform and analyze the experimental implementation of a qubit readout with an integrated three-mode nonreciprocal system. In doing so, we achieve excellent agreement between the experimental and theoretical qubit measurement and dephasing rates. We then theoretically analyze the same system operated as an integrated nonreciprocal amplifier, predicting high efficiency for reasonable experimental parameters.
One of the primary requirements for superconducting quantum information processors is high-fidelity, quantum non-demolition qubit readout. In superconducting circuits, we perform measurements with quantum-limited microwave amplifiers. These amplifiers are based on microwave cavities and powered by Josephson-junction based nonlinearities, which we drive to parametrically modulate the circuit and generate gain. However, cavity-based amplifiers generally suffer from a fixed gain-bandwidth product, a limited dynamic range, and the absence of directionality, and so they must be operated with external lossy microwave commercial components such as circulators. Many of these limitations can be circumvented by combining multiple parametric processes in a few-mode device, in particular by combining parametric drives which produce gain and those which produce gainless photon conversion. By combining balanced gain and conversion processes between a pair of modes, we have demonstrated transmission-only, phase-sensitive, gain-bandwidth-free amplification. We have also used measurements of transmon qubits with this mode of amplification to demonstrate its practical utility. More, by combining multiple instances of imbalanced gain and conversion processes among three modes, we have realized devices with non-reciprocal, transmission-only amplification, matched ports, and a large, gain-independent bandwidth. One of the biggest challenges in tuning multiple parametric processes is both inherent and dynamically-generated higher order nonlinearities in the device, which shift mode frequencies and parametric coupling strengths with pump power, preventing accurate balancing of the parametric processes. These can be controlled through engineering the Hamiltonian of the nonlinear element, in this thesis either a linearly-shunted Josephson Ring Modulator or SNAIL (Superconducting Nonlinear Asymmetric Inductive eLements), which for certain applied flux values can minimize or even change the sign of higher-order even nonlinearities. Additionally, we have explored a range of circuit parameters, allowing us to also control the relative size of odd-order nonlinearities. We have developed a series of prototypes which implement these concepts, and have achieved both high-dynamic range singly pumped amplifiers, and a promising platform for multi-parametric devices. We conclude by presenting recent progress towards implementing multiple parametric schemes that generates a practical directional amplifier, and discuss the remaining obstacles to a truly ideal parametric amplifiers.
The authors program a superconducting circuit $i\phantom{\rule{0}{0ex}}n$ $s\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}u$ to operate as a microwave circulator, or a directional amplifier. The compact lumped element can be directly integrated with other superconducting circuitry for nearly lossless routing and measurement of quantum microwave signals. This work combines advanced understanding of parametric-coupling physics with innovative design and engineering, for fundamental impact on quantum measurements plus direct technological impact on current efforts to build scalable, on-chip infrastructure for quantum computing.