Search

Engineering the Hamiltonian of a quantum system is fundamental to the design of quantum systems. Automating Hamiltonian design through gradient-based optimization can dramatically accelerate this process. However, computing the gradients of eigenvalues and eigenvectors of a Hamiltonian--a large, sparse matrix--relative to system properties poses a significant challenge, especially for arbitrary systems. Superconducting quantum circuits offer substantial flexibility in Hamiltonian design, making them an ideal platform for this task. In this work, we present a comprehensive framework for the gradient-based optimization of superconducting quantum circuits, leveraging the SQcircuit software package. By addressing the challenge of calculating the gradient of the eigensystem for large, sparse Hamiltonians and integrating automatic differentiation within SQcircuit, our framework enables efficient and precise computation of gradients for various circuit properties or custom-defined metrics, streamlining the optimization process. We apply this framework to the qubit discovery problem, demonstrating its effectiveness in identifying qubit designs with superior performance metrics. The optimized circuits show improvements in a heuristic measure of gate count, upper bounds on gate speed, decoherence time, and resilience to noise and fabrication errors compared to existing qubits. While this methodology is showcased through qubit optimization and discovery, it is versatile and can be extended to tackle other optimization challenges in superconducting quantum hardware design., Comment: 23 pages, 10 figures. Accompanying SQcircuit package on https://sqcircuit.org/

We propose networking superconducting quantum circuits by transducing their excitations (typically 4-8 GHz) to 100-500 MHz photons for transmission via cryogenic coaxial cables. Counter-intuitively, this frequency downconversion reduces noise and transmission losses. We introduce a multi-octave asymmetrically threaded SQUID circuit (MOATS) capable of the required efficient, high-rate transduction. For a 100-meter cable with $Q_i = 10^5$ at 10 mK, our approach achieves single-photon fidelities of 0.962 at 200 MHz versus 0.772 at 8 GHz, and triples the lower bound on quantum channel capacity. This method enables kilometer-scale quantum links while maintaining high fidelities, combining improved performance with the practical advantages of flexible, compact coaxial cables., Comment: 8 pages, 3 figures

Photonic addressing of superconducting circuits has been proposed to overcome wiring complexity and heat load challenges, but superconducting-photonic links suffer from an efficiency-noise trade-off that limits scalability. This trade-off arises because increasing power conversion efficiency requires reducing optical power, which makes the converted signal susceptible to shot noise. We analyze this trade-off and find the infidelity of qubit gates driven by photonic signals scales inversely with the number of photons used, and therefore the power efficiency of the converter. While methods like nonlinear detection or squeezed light could mitigate this effect, we consider generating higher frequency electrical signals, such as millimeter-waves (100 GHz), using laser light. At these higher frequencies, circuits have higher operating temperatures and cooling power budgets. We demonstrate an optically-driven cryogenic millimeter-wave source with a power efficiency of $10^{-4}$ that can generate ${1}~\mathrm{\mu W}$ of RF power at 80 GHz with 1500 thermal photons of added noise at 4 K. Using this source, we perform frequency-domain spectroscopy of superconducting NbTiN resonators at 80-90 GHz. Our results show a promising approach to alleviate the efficiency-noise constraints on optically-driven superconducting circuits while leveraging the benefits of photonic signal delivery. Further optimization of power efficiency and noise at high frequencies could make photonic control of superconducting qubits viable at temperatures exceeding 1 kelvin., Comment: 14 pages, 8 figures

Integrated optomechanical systems are one of the leading platforms for manipulating, sensing, and distributing quantum information. The temperature increase due to residual optical absorption sets the ultimate limit on performance for these applications. In this work, we demonstrate a two-dimensional optomechanical crystal geometry, named \textbf{b-dagger}, that alleviates this problem through increased thermal anchoring to the surrounding material. Our mechanical mode operates at 7.4 GHz, well within the operation range of standard cryogenic microwave hardware and piezoelectric transducers. The enhanced thermalization combined with the large optomechanical coupling rates, $g_0/2\pi \approx 880~\mathrm{kHz}$, and high optical quality factors, $Q_\text{opt} = 2.4 \times 10^5$, enables the ground-state cooling of the acoustic mode to phononic occupancies as low as $n_\text{m} = 0.35$ from an initial temperature of 3 kelvin, as well as entering the optomechanical strong-coupling regime. Finally, we perform pulsed sideband asymmetry of our devices at a temperature below 10 millikelvin and demonstrate ground-state operation ($n_\text{m} < 0.45$) for repetition rates as high as 3 MHz. Our results extend the boundaries of optomechanical system capabilities and establish a robust foundation for the next generation of microwave-to-optical transducers with entanglement rates overcoming the decoherence rates of state-of-the-art superconducting qubits., Comment: 13 pages, 4 main figures

Delay lines that store quantum information are crucial for advancing quantum repeaters and hardware efficient quantum computers. Traditionally, they are realized as extended systems that support wave propagation but provide limited control over the propagating fields. Here, we introduce a parametrically addressed delay line for microwave photons that provides a high level of control over the stored pulses. By parametrically driving a three-wave mixing circuit element that is weakly hybridized with an ensemble of resonators, we engineer a spectral response that simulates that of a physical delay line, while providing fast control over the delay line's properties. We demonstrate this novel degree of control by choosing which photon echo to emit, translating pulses in time, and even swapping two pulses, all with pulse energies on the order of a single photon. We also measure the noise added from our parametric interactions and find it is much less than one photon., Comment: 15 pages, 11 figures; v3: more update

The vacuum beam guide (VBG) presents a completely different solution for quantum channels to overcome the limitations of existing fiber and satellite technologies for long-distance quantum communication. With an array of aligned lenses spaced kilometers apart, the VBG offers ultra-high transparency over a wide range of optical wavelengths. With realistic parameters, the VBG can outperform the best fiber by three orders of magnitude in terms of attenuation rate. Consequently, the VBG can enable long-range quantum communication over thousands of kilometers with quantum channel capacity beyond $10^{13}$ qubit/sec, orders of magnitude higher than the state-of-the-art quantum satellite communication rate. Remarkably, without relying on quantum repeaters, the VBG can provide a ground-based, low-loss, high-bandwidth quantum channel that enables novel distributed quantum information applications for computing, communication, and sensing.

Quantum optical technologies promise advances in sensing, computing, and communication. A key resource is squeezed light, where quantum noise is redistributed between optical quadratures. We introduce a monolithic, chip-scale platform that exploits the $\chi^{(2)}$ nonlinearity of a thin-film lithium niobate (TFLN) resonator device to efficiently generate squeezed states of light. Our system integrates all essential components -- except for the laser and two detectors -- on a single chip with an area of one square centimeter, significantly reducing the size, operational complexity, and power consumption associated with conventional setups. Our work addresses challenges that have limited previous integrated nonlinear photonic implementations that rely on either $\chi^{(3)}$ nonlinear resonators or on integrated waveguide $\chi^{(2)}$ parametric amplifiers. Using the balanced homodyne measurement subsystem that we implemented on the same chip, we measure a squeezing of 0.55 dB and an anti-squeezing of 1.55 dB. We use 20 mW of input power to generate the parametric oscillator pump field by employing second harmonic generation on the same chip. Our work represents a substantial step toward compact and efficient quantum optical systems posed to leverage the rapid advances in integrated nonlinear and quantum photonics., Comment: 21 pages; 4 figures in main body, 8 supplementary figures

In situ tunable photonic filters and memories are important for emerging quantum and classical optics technologies. However, most photonic devices have fixed resonances and bandwidths determined at the time of fabrication. Here we present an in situ tunable optical resonator on thin-film lithium niobate. By leveraging the linear electro-optic effect, we demonstrate widely tunable control over resonator frequency and bandwidth on two different devices. We observe up to $\sim50\times$ tuning in the bandwidth over $\sim50$ V with linear frequency control of $\sim230$ MHz/V. We also develop a closed-form model predicting the tuning behavior of the device. This paves the way for rapid phase and amplitude control over light transmitted through our device., Comment: 22 pages, 11 figure, 2 tables

Optical frequency combs have revolutionized precision measurement, time-keeping, and molecular spectroscopy. A substantial effort has developed around "microcombs": integrating comb-generating technologies into compact, reliable photonic platforms. Current approaches for generating these microcombs involve either the electro-optic (EO) or Kerr mechanisms. Despite rapid progress, maintaining high efficiency and wide bandwidth remains challenging. Here, we introduce a new class of microcomb -- an integrated optical frequency comb generator that combines electro-optics and parametric amplification to yield a frequency-modulated optical parametric oscillator (FM-OPO). In stark contrast to EO and Kerr combs, the FM-OPO microcomb does not form pulses but maintains operational simplicity and highly efficient pump power utilization with an output resembling a frequency-modulated laser. We outline the working principles of FM-OPO and demonstrate them by fabricating the complete optical system in thin-film lithium niobate (LNOI). We measure pump to comb internal conversion efficiency exceeding 93% (34% out-coupled) over a nearly flat-top spectral distribution spanning approximately 1,000 modes (approximately 6 THz). Compared to an EO comb, the cavity dispersion rather than loss determines the FM-OPO bandwidth, enabling broadband combs with a smaller RF modulation power. The FM-OPO microcomb, with its robust operational dynamics, high efficiency, and large bandwidth, contributes a new approach to the field of microcombs and promises to herald an era of miniaturized precision measurement, and spectroscopy tools to accelerate advancements in metrology, spectroscopy, telecommunications, sensing, and computing., Comment: 8 pages, 4 figures main text; another 19 pages and 9 figures in methods and supplementary

Mid-infrared spectroscopy, an important and widespread technique for sensing molecules, has encountered barriers stemming from sources either limited in tuning range or excessively bulky for practical field use. We present a compact, efficient, and broadly tunable optical parametric oscillator (OPO) device surmounting these challenges. Leveraging a dispersion-engineered singly-resonant OPO implemented in thin-film lithium niobate-on-sapphire, we achieve broad and controlled tuning over an octave, from 1.5 to 3.3 microns by combining laser and temperature tuning. The device generates > 25 mW of mid-infrared light at 3.2 microns, offering a power conversion efficiency of 15% (45% quantum efficiency). We demonstrate the tuning and performance of the device by successfully measuring the spectra of methane and ammonia, verifying our approach's relevance for gas sensing. Our device signifies an important advance in nonlinear photonics miniaturization and brings practical field applications of high-speed and broadband mid-infrared spectroscopy closer to reality., Comment: 19 pages, 11 figures

On-chip photonic quantum circuits with integrated quantum memories have the potential to radically progress hardware for quantum information processing. In particular, negatively charged group-IV color centers in diamond are promising candidates for quantum memories, as they combine long storage times with excellent optical emission properties and an optically-addressable spin state. However, as a material, diamond lacks many functionalities needed to realize scalable quantum systems. Thin-film lithium niobate (TFLN), in contrast, offers a number of useful photonic nonlinearities, including the electro-optic effect, piezoelectricity, and capabilities for periodically-poled quasi-phase matching. Here, we present highly efficient heterogeneous integration of diamond nanobeams containing negatively charged silicon-vacancy (SiV) centers with TFLN waveguides. We observe greater than 90\% transmission efficiency between the diamond nanobeam and TFLN waveguide on average across multiple measurements. By comparing saturation signal levels between confocal and integrated collection, we determine a $10$-fold increase in photon counts channeled into TFLN waveguides versus that into out-of-plane collection channels. Our results constitute a key step for creating scalable integrated quantum photonic circuits that leverage the advantages of both diamond and TFLN materials.

Lithium niobate is a promising material for developing quantum acoustic technologies due to its strong piezoelectric effect and availability in the form of crystalline thin films of high quality. However, at radio frequencies and cryogenic temperatures, these resonators are limited by the presence of decoherence and dephasing due to two-level systems. To mitigate these losses and increase device performance, a more detailed picture of the microscopic nature of these loss channels is needed. In this study, we fabricate several lithium niobate acoustic wave resonators and apply different processing steps that modify their surfaces. These treatments include argon ion sputtering, annealing, and acid cleans. We characterize the effects of these treatments using three surface-sensitive measurements: cryogenic microwave spectroscopy measuring density and coupling of TLS to mechanics, x-ray photoelectron spectroscopy and atomic force microscopy. We learn from these studies that, surprisingly, increases of TLS density may accompany apparent improvements in the surface quality as probed by the latter two approaches. Our work outlines the importance that surfaces and fabrication techniques play in altering acoustic resonator coherence, and suggests gaps in our understanding as well as approaches to address them., Comment: 10 pages, 7 figures

We demonstrate strong coupling of gigahertz-frequency nanomechanical resonators to a frequency-tunable superconducting microwave resonator via a galvanically bonded flip-chip method. By tuning the microwave resonator with an external magnetic field, we observe a series of hybridized microwave-mechanical modes and report coupling strengths of $\sim {15}~\text{MHz}$ at cryogenic temperatures. The demonstrated multi-chip approach provides flexible rapid characterization and simplified fabrication, and could potentially enable coupling between a variety of quantum systems. Our work represents a step towards a plug-and-play architecture for building more complex hybrid quantum systems., Comment: 10 pages, 8 figures. First three authors contributed equally to this work

We demonstrate strong dispersive coupling between a fluxonium superconducting qubit and a 690 megahertz mechanical oscillator, extending the reach of circuit quantum acousto-dynamics (cQAD) experiments into a new range of frequencies. We have engineered a qubit-phonon coupling rate of $g\approx2\pi\times14~\text{MHz}$, and achieved a dispersive interaction that exceeds the decoherence rates of both systems while the qubit and mechanics are highly nonresonant ($\Delta/g\gtrsim10$). Leveraging this strong coupling, we perform phonon number-resolved measurements of the mechanical resonator and investigate its dissipation and dephasing properties. Our results demonstrate the potential for fluxonium-based hybrid quantum systems, and a path for developing new quantum sensing and information processing schemes with phonons at frequencies below 700 MHz to significantly expand the toolbox of cQAD., Comment: 22 pages, 12 figures

Time-periodic systems allow engineering new effective Hamiltonians from limited physical interactions. For example, the inverted position of the Kapitza pendulum emerges as a stable equilibrium with rapid drive of its pivot point. In this work, we propose the $\textit{Kapitzonium}$: a Floquet qubit that is the superconducting circuit analog of a mechanical Kapitza pendulum. Under periodic driving, the emerging qubit states are exponentially protected against bit and phase flips caused by dissipation, which is the primary source of decoherence of current qubits. However, we find that dissipation causes leakage out of the Floquet qubit subspace. We engineer a passive cooling scheme to stabilize the qubit subspace, which is crucial for high fidelity quantum control under dissipation. Furthermore, we introduce a hardware-efficient fluorescence-based method for qubit measurement and discuss the experimental implementation of the Floquet qubit. The proposed Kapitzonium is one of the simplest Floquet qubits that can be realized with current technology -- and it already has many intriguing features and capabilities. Our work provides the first steps to develop more complex Floquet quantum systems from the ground up to realize large-scale protected engineered dynamics.

In the field of quantum technology, nanomechanical oscillators offer a host of useful properties given their compact size, long lifetimes, and ability to detect force and motion. Their integration with superconducting quantum circuits shows promise for hardware-efficient computation architectures and error-correction protocols based on superpositions of mechanical coherent states. One limitation of this approach is decoherence processes affecting the mechanical oscillator. Of particular interest are two-level system (TLS) defects in the resonator host material, which have been widely studied in the classical domain, primarily via measurements of the material loss tangent. In this manuscript, we use a superconducting qubit as a quantum sensor to perform phonon number-resolved measurements on a phononic crystal cavity. This enables a high-resolution study of mechanical dissipation and dephasing in coherent states of variable size (mean phonon number $\navg\simeq1-10$). We observe nonexponential energy decay and a state size-dependent reduction of the dephasing rate, which we attribute to interactions with TLS. Using a numerical model, we reproduce the energy decay signatures (and to a lesser extent, the dephasing signatures) via mechanical emission into a small ensemble ($N=5$) of saturable and rapidly dephasing TLS. Our findings comprise a detailed examination of TLS-induced phonon decoherence in the quantum regime., Comment: 13 pages, 4 figures, 4 supplemental figures, 1 supplemental table

The quantum noise of light fundamentally limits optical phase sensors. A semiclassical picture attributes this noise to the random arrival time of photons from a coherent light source such as a laser. An engineered source of squeezed states suppresses this noise and allows sensitivity beyond the standard quantum limit (SQL) for phase detection. Advanced gravitational wave detectors like LIGO have already incorporated such sources, and nascent efforts in realizing quantum biological measurements have provided glimpses into new capabilities emerging in quantum measurement. We need ways to engineer and use quantum light within deployable quantum sensors that operate outside the confines of a lab environment. Here we present a photonic integrated circuit fabricated in thin-film lithium niobate that provides a path to meet these requirements. We use the second-order nonlinearity to produce a squeezed state at the same frequency as the pump light and realize circuit control and sensing with electro-optics. Using a 26.2 milliwatts of optical power, we measure (2.7 $\pm$ 0.2 )$\%$ squeezing and apply it to increase the signal-to-noise ratio of phase measurement. We anticipate that on-chip photonic systems like this, which operate with low power and integrate all of the needed functionality on a single die, will open new opportunities for quantum optical sensing., Comment: 14 pages, 3+3 figures

A quantum network that distributes and processes entanglement would enable powerful new computers and sensors. Optical photons with a frequency of a few hundred terahertz are perhaps the only way to distribute quantum information over long distances. Superconducting qubits on the other hand, which are one of the most promising approaches for realizing large-scale quantum machines, operate naturally on microwave photons that have roughly $40,000$ times less energy. To network these quantum machines across appreciable distances, we must bridge this frequency gap and learn how to generate entanglement across widely disparate parts of the electromagnetic spectrum. Here we implement and demonstrate a transducer device that can generate entanglement between optical and microwave photons, and use it to show that by detecting an optical photon we add a single photon to the microwave field. We achieve this by using a gigahertz nanomechanical resonance as an intermediary, and efficiently coupling it to optical and microwave channels through strong optomechanical and piezoelectric interactions. We show continuous operation of the transducer with $5\%$ frequency conversion efficiency, and pulsed microwave photon generation at a heralding rate of $15$ hertz. Optical absorption in the device generates thermal noise of less than two microwave photons. Joint measurements on optical photons from a pair of transducers would realize entanglement generation between distant microwave-frequency quantum nodes. Improvements of the system efficiency and device performance, necessary to realize a high rate of entanglement generation in such networks are within reach., Comment: 18 pages, 12 figures, 1 table

Many attractive photonics platforms still lack integrated photodetectors due to inherent material incompatibilities and lack of process scalability, preventing their widespread deployment. Here we address the problem of scalably integrating photodetectors in a photonic platform-independent manner. Using a thermal evaporation and deposition technique developed for nanoelectronics, we show that tellurium (Te), a quasi-2D semi-conductive element, can be evaporated at low temperature directly onto photonic chips to form air-stable, high-responsivity, high-speed, ultrawide-band photodetectors. We demonstrate detection at visible, telecom, and mid-infrared wavelengths, a bandwidth of more than 40 GHz, and platform-independent scalable integration with photonic structures in silicon, silicon nitride and lithium niobate.

Superconducting quantum circuits are a promising hardware platform for realizing a fault-tolerant quantum computer. Accelerating progress in this field of research demands general approaches and computational tools to analyze and design more complex superconducting circuits. We develop a framework to systematically construct a superconducting quantum circuit's quantized Hamiltonian from its physical description. As is often the case with quantum descriptions of multicoordinate systems, the complexity rises rapidly with the number of variables. Therefore, we introduce a set of coordinate transformations with which we can find bases to diagonalize the Hamiltonian efficiently. Furthermore, we broaden our framework's scope to calculate the circuit's key properties required for optimizing and discovering novel qubits. We implement the methods described in this work in an open-source Python package SQcircuit. In this manuscript, we introduce the reader to the SQcircuit environment and functionality. We show through a series of examples how to analyze a number of interesting quantum circuits and obtain features such as the spectrum, coherence times, transition matrix elements, coupling operators, and the phase coordinate representation of eigenfunctions., Comment: 23 pages, 6 figures. Accompanying SQcircuit package on https://sqcircuit.org/

Thin-film lithium niobate (TFLN) is an emerging platform for compact, low-power nonlinear-optical devices, and has been used extensively for near-infrared frequency conversion. Recent work has extended these devices to mid-infrared wavelengths, where broadly tunable sources may be used for chemical sensing. To this end, we demonstrate efficient and broadband difference frequency generation between a fixed 1-micron pump and a tunable telecom source in uniformly-poled TFLN-on-sapphire by harnessing the dispersion-engineering available in tightly-confining waveguides. We show a simultaneous 1-2 order-of-magnitude improvement in conversion efficiency and ~5-fold enhancement of operating bandwidth for mid-infrared generation when compared to conventional lithium niobate waveguides. We also examine the effects of mid-infrared loss from surface-adsorbed water on the performance of these devices., Comment: 5 pages, 4 figures

The capability to modulate the intensity of an optical beam has scientific and practical significance. In this work, we demonstrate Y-Z cut lithium niobate acousto-optic modulators with record-high modulation efficiency, requiring only $1.5~\text{W}/\text{cm}^2$ for 100% modulation at 7 MHz. These modulators use a simple fabrication process; coating the top and bottom surfaces of a thin lithium niobate wafer with transparent electrodes. The fundamental shear acoustic mode of the wafer is excited through the transparent electrodes by applying voltage with frequency corresponding to the resonant frequency of this mode, confining an acoustic standing wave to the electrode region. Polarization of light propagating through this region is modulated at the applied frequency. Polarization modulation is converted to intensity modulation by placing the modulator between polarizers. To showcase an important application space for this modulator, we integrate it with a standard image sensor and demonstrate 4 megapixel time-of-flight imaging, Comment: 18 pages, 8 figures

Integrated photonics operating at visible-near-infrared (VNIR) wavelengths offer scalable platforms for advancing optical systems for addressing atomic clocks, sensors, and quantum computers. The complexity of free-space control optics causes limited addressability of atoms and ions, and this remains an impediment on scalability and cost. Networks of Mach-Zehnder interferometers can overcome challenges in addressing atoms by providing high-bandwidth electro-optic control of multiple output beams. Here, we demonstrate a VNIR Mach-Zehnder interferometer on lithium niobate on sapphire with a CMOS voltage-level compatible full-swing voltage of 4.2 V and an electro-optic bandwidth of 2.7 GHz occupying only 0.35 mm$^2$. Our waveguides exhibit 1.6 dB/cm propagation loss and our microring resonators have intrinsic quality factors of 4.4 $\times$ 10$^5$. This specialized platform for VNIR integrated photonics can open new avenues for addressing large arrays of qubits with high precision and negligible cross-talk., Comment: 10 pages, 4 figures

Precisely engineered mechanical oscillators keep time, filter signals, and sense motion, making them an indispensable part of today's technological landscape. These unique capabilities motivate bringing mechanical devices into the quantum domain by interfacing them with engineered quantum circuits. Proposals to combine microwave-frequency mechanical resonators with superconducting devices suggest the possibility of powerful quantum acoustic processors. Meanwhile, experiments in several mechanical systems have demonstrated quantum state control and readout, phonon number resolution, and phonon-mediated qubit-qubit interactions. Currently, these acoustic platforms lack processors capable of controlling multiple mechanical oscillators' quantum states with a single qubit, and the rapid quantum non-demolition measurements of mechanical states needed for error correction. Here we use a superconducting qubit to control and read out the quantum state of a pair of nanomechanical resonators. Our device is capable of fast qubit-mechanics swap operations, which we use to deterministically manipulate the mechanical states. By placing the qubit into the strong dispersive regime with both mechanical resonators simultaneously, we determine the resonators' phonon number distributions via Ramsey measurements. Finally, we present quantum tomography of the prepared nonclassical and entangled mechanical states. Our result represents a concrete step toward feedback-based operation of a quantum acoustic processor., Comment: 13 pages, 4+5 figures

Integrated circulators and isolators are important for developing on-chip optical technologies, such as laser cavities, communication systems, and quantum information processors. These devices appear to inherently require mirror symmetry breaking to separate backwards from forwards propagation, so existing implementations rely upon magnetic materials, or interactions driven by propagating waves. In contrast to previous work, we demonstrate a mirror symmetric nonreciprocal device. Our device comprises three coupled photonic resonators implemented in thin-film lithium niobate. Applying radio frequency modulation, we drive conversion between the frequency eigenmodes of this system. We measure nearly 40 dB of isolation for approximately 75 mW of RF power near 1550 nm. We simultaneously generate nonreciprocal conversion between all of the eigenmodes in order to demonstrate circulation. Mirror symmetric circulation significantly simplifies the fabrication and operation of nonreciprocal integrated devices. Finally, we consider applications of such on-chip isolators and circulators, such as full-duplex isolation within a single waveguide., Comment: 7 pages, 4 figures (main body)

We demonstrate second harmonic generation of blue light on an integrated thin-film lithium niobate waveguide and observe a conversion efficiency of $\eta_0= 33000\%/\text{W-cm}^2$, significantly exceeding previous demonstrations., Comment: 3 pages, 2 figures, 6 references

We can encode a qubit in the energy levels of a quantum system. Relaxation and other dissipation processes lead to decay of the fidelity of this stored information. Is it possible to preserve the quantum information for a longer time by introducing additional drives and dissipation? The existence of autonomous quantum error correcting codes answers this question in the positive. Nonetheless, discovering these codes for a real physical system, i.e., finding the encoding and the associated driving fields and bath couplings, remains a challenge that has required intuition and inspiration to overcome. In this work, we develop and demonstrate a computational approach based on adjoint optimization for discovering autonomous quantum error correcting codes given a description of a physical system. We implement an optimizer that searches for a logical subspace and control parameters to better preserve quantum information. We demonstrate our method on a system of a harmonic oscillator coupled to a lossy qubit, and find that varying the Hamiltonian distance in Fock space -- a proxy for the control hardware complexity -- leads to discovery of different and new error correcting schemes. We discover what we call the $\sqrt{3}$ code, realizable with a Hamiltonian distance $d=2$, and propose a hardware-efficient implementation based on superconducting circuits., Comment: 14 pages, 7 figures. (includes appendices)

Intensity modulators are an essential component in optics for controlling free-space beams. Many applications require the intensity of a free-space beam to be modulated at a single frequency, including wide-field lock-in detection for sensitive measurements, mode-locking in lasers, and phase-shift time-of-flight imaging (LiDAR). Here, we report a new type of single frequency intensity modulator that we refer to as a longitudinal piezoelectric resonant photoelastic modulator. The modulator consists of a thin lithium niobate wafer coated with transparent surface electrodes. One of the fundamental acoustic modes of the modulator is excited through the surface electrodes, confining an acoustic standing wave to the electrode region. The modulator is placed between optical polarizers; light propagating through the modulator and polarizers is intensity modulated with a wide acceptance angle and record breaking modulation efficiency in the megahertz frequency regime. As an illustration of the potential of our approach, we show that the proposed modulator can be integrated with a standard image sensor to effectively convert it into a time-of-flight imaging system., Comment: 23 pages, 11 figures

It has been demonstrated that dynamic refractive index modulation, which breaks time-reversal symmetry, can be used to create on-chip non-reciprocal photonic devices. In order to achieve amplitude non-reciprocity, all such devices moreover require modulations that break spatial symmetries, which adds complexity in implementations. Here we introduce a modal circulator, which achieves amplitude non-reciprocity through a circulation motion among three modes. We show that such a circulator can be achieved in a dynamically-modulated structure that preserves mirror symmetry, and as a result can be implemented using only a single standing-wave modulator, which significantly simplifies the implementation of dynamically-modulated non-reciprocal device. We also prove that in terms of the number of modes involved in the transport process, the modal circulator represents the minimum configuration in which complete amplitude non-reciprocity can be achieved while preserving spatial symmetry.

Periodically poled thin-film lithium niobate (TFLN) waveguides have emerged as a leading platform for highly efficient frequency conversion in the near-infrared. However, the commonly used silica bottom-cladding results in high absorption loss at wavelengths beyond 2.5 $\mu$m. In this work, we demonstrate efficient frequency conversion in a TFLN-on-sapphire platform, which features high transparency up to 4.5 $\mu$m. In particular, we report generating mid-infrared light up to 3.66 $\mu$m via difference-frequency generation of a fixed 1-$\mu$m source and a tunable telecom source, with normalized efficiencies up to 200%/W-cm$^2$. These results show TFLN-on-sapphire to be a promising platform for integrated nonlinear nanophotonics in the mid-infrared., Comment: The first four authors contributed equally to this work. 5 pages, 3 figures

Second-order nonlinear optical processes are used to convert light from one wavelength to another and to generate quantum entanglement. Creating chip-scale devices to more efficiently realize and control these interactions greatly increases the reach of photonics. Optical crystals and guided wave devices made from lithium niobate and potassium titanyl phosphate are typically used to realize second-order processes but face significant drawbacks in scalability, power, and tailorability when compared to emerging integrated photonic systems. Silicon or silicon nitride integrated photonic circuits enhance and control the third-order optical nonlinearity by confining light in dispersion-engineered waveguides and resonators. An analogous platform for second-order nonlinear optics remains an outstanding challenge in photonics. It would enable stronger interactions at lower power and reduce the number of competing nonlinear processes that emerge. Here we demonstrate efficient frequency doubling and parametric oscillation in a thin-film lithium niobate photonic circuit. Our device combines recent progress on periodically poled thin-film lithium niobate waveguidesand low-loss microresonators. Here we realize efficient >10% second-harmonic generation and parametric oscillation with microwatts of optical power using a periodically-poled thin-film lithium niobate microresonator. The operating regimes of this system are controlled using the relative detuning of the intracavity resonances. During nondegenerate oscillation, the emission wavelength is tuned over terahertz by varying the pump frequency by 100's of megahertz. We observe highly-enhanced effective third-order nonlinearities caused by cascaded second-order processes resulting in parametric oscillation. These resonant second-order nonlinear circuits will form a crucial part of the emerging nonlinear and quantum photonics platforms., Comment: 14 pages, 8 figures. Equal contribution by the first two authors

A room-temperature mechanical oscillator undergoes thermal Brownian motion with an amplitude much larger than the amplitude associated with a single phonon of excitation. This motion can be read out and manipulated using laser light using a cavity-optomechanical approach. By performing a strong quantum measurement, i.e., counting single photons in the sidebands imparted on a laser, we herald the addition and subtraction of single phonons on the 300K thermal motional state of a 4GHz mechanical oscillator. To understand the resulting mechanical state, we implement a tomography scheme and observe highly non-Gaussian phase-space distributions. Using a maximum likelihood method, we infer the density matrix of the oscillator and confirm the counter-intuitive doubling of the mean phonon number resulting from phonon addition and subtraction., Comment: 13 pages, 9 figures

Integrated photonics is at the heart of many classical technologies, from optical communications to biosensors, LIDAR, and data center fiber interconnects. There is strong evidence that these integrated technologies will play a key role in quantum systems as they grow from few-qubit prototypes to tens of thousands of qubits. The underlying laser and optical quantum technologies, with the required functionality and performance, can only be realized through the integration of these components onto quantum photonic integrated circuits (QPICs) with accompanying electronics. In the last decade, remarkable advances in quantum photonic integration and a dramatic reduction in optical losses have enabled benchtop experiments to be scaled down to prototype chips with improvements in efficiency, robustness, and key performance metrics. The reduction in size, weight, power, and improvement in stability that will be enabled by QPICs will play a key role in increasing the degree of complexity and scale in quantum demonstrations. In the next decade, with sustained research, development, and investment in the quantum photonic ecosystem (i.e. PIC-based platforms, devices and circuits, fabrication and integration processes, packaging, and testing and benchmarking), we will witness the transition from single- and few-function prototypes to the large-scale integration of multi-functional and reconfigurable QPICs that will define how information is processed, stored, transmitted, and utilized for quantum computing, communications, metrology, and sensing. This roadmap highlights the current progress in the field of integrated quantum photonics, future challenges, and advances in science and technology needed to meet these challenges., Comment: Submitted to the Journal of Physics: Photonics

We present a comprehensive architectural analysis for a proposed fault-tolerant quantum computer based on cat codes concatenated with outer quantum error-correcting codes. For the physical hardware, we propose a system of acoustic resonators coupled to superconducting circuits with a two-dimensional layout. Using estimated physical parameters for the hardware, we perform a detailed error analysis of measurements and gates, including CNOT and Toffoli gates. Having built a realistic noise model, we numerically simulate quantum error correction when the outer code is either a repetition code or a thin rectangular surface code. Our next step toward universal fault-tolerant quantum computation is a protocol for fault-tolerant Toffoli magic state preparation that significantly improves upon the fidelity of physical Toffoli gates at very low qubit cost. To achieve even lower overheads, we devise a new magic-state distillation protocol for Toffoli states. Combining these results together, we obtain realistic full-resource estimates of the physical error rates and overheads needed to run useful fault-tolerant quantum algorithms. We find that with around 1,000 superconducting circuit components, one could construct a fault-tolerant quantum computer that can run circuits which are currently intractable for classical computers. Hardware with 18,000 superconducting circuit components, in turn, could simulate the Hubbard model in a regime beyond the reach of classical computing., Comment: 117 pages (main text 32 pages), 62 figures, 15 tables. Comments welcome! V2 adds additional appendices and conforms to journal specifications

A transducer of single photons between microwave and optical frequencies can be used to realize quantum communication over optical fiber links between distant superconducting quantum computers. A promising scalable approach to constructing such a transducer is to use ensembles of quantum emitters interacting simultaneously with electromagnetic fields at optical and microwave frequencies. However, inhomogeneous broadening in the transition frequencies of the emitters can be detrimental to this collective action. In this article, we utilise a gradient-based optimization strategy to design the temporal shape of the laser field driving the transduction system to mitigate the effects of inhomogeneous broadening. We study the improvement of transduction efficiencies as a function of inhomogeneous broadening in different single-emitter cooperativity regimes and correlate it with a restoration of superradiance effects in the emitter ensembles. Furthermore, to assess the optimality of our pulse designs, we provide certifiable bounds on the design problem and compare them to the achieved performance., Comment: 8 pages, 5 figures; added calculation of upper bounds; added new appendices; expanded the introduction

We demonstrate a collinear acousto-optic modulator in a suspended film of lithium niobate employing a high-confinement, wavelength-scale waveguide. By strongly confining the optical and mechanical waves, this modulator improves by orders of magnitude a figure-of-merit that accounts for both acousto-optic and electro-mechanical efficiency. Our device demonstration marks a significant technological advance in acousto-optics that promises a novel class of compact and low-power frequency shifters, tunable filters, non-magnetic isolators, and beam deflectors., Comment: 14 pages, 10 figures

We investigate the performance of microwave-frequency phononic crystal resonators fabricated on thin-film lithium niobate for integration with superconducting quantum circuits. For different design geometries at millikelvin temperatures, we achieve mechanical internal quality factors $Q_i$ above $10^5 - 10^6$ at high microwave drive power, corresponding to $5\times10^6$ phonons inside the resonator. By sweeping the defect size of resonators with identical mirror cell designs, we are able to indirectly observe signatures of the complete phononic bandgap via the resonators' internal quality factors. Examination of quality factors' temperature dependence shows how superconducting and two-level system (TLS) loss channels impact device performance. Finally, we observe an anomalous low-temperature frequency shift consistent with resonant TLS decay and find that material choice can help to mitigate these losses., Comment: 15 pages, 12 figures

Acoustic devices play an important role in classical information processing. The slower speed and lower losses of mechanical waves enable compact and efficient elements for delaying, filtering, and storing of electric signals at radio and microwave frequencies. Discovering ways of better controlling the propagation of phonons on a chip is an important step towards enabling larger scale phononic circuits and systems. We present a platform, inspired by decades of advances in integrated photonics, that utilizes the strong piezoelectric effect in a thin film of lithium niobate on sapphire to excite guided acoustic waves immune from leakage into the bulk due to the phononic analogue of index-guiding. We demonstrate an efficient transducer matched to 50 ohm and guiding within a 1-micron wide mechanical waveguide as key building blocks of this platform. Putting these components together, we realize acoustic delay lines, racetrack resonators, and meander line waveguides for sensing applications. To evaluate the promise of this platform for emerging quantum technologies, we characterize losses at low temperature and measure quality factors on the order of 50,000 at 4 kelvin. Finally, we demonstrate phononic four-wave mixing in these circuits and measure the nonlinear coefficients to provide estimates of the power needed for relevant parametric processes., Comment: 15 pages,12 figures, the first two authors contributed equally

We demonstrate acousto-optic phase modulators in X-cut lithium niobate films on sapphire, detailing the dependence of the piezoelectric and optomechanical coupling coefficients on the crystal orientation. This new platform supports highly confined, strongly piezoelectric mechanical waves without suspensions, making it a promising candidate for broadband and efficient integrated acousto-optic devices, circuits, and systems., Comment: 8 pages, 5 figures

Quantum networks are likely to have a profound impact on the way we compute and communicate in the future. In order to wire together superconducting quantum processors over kilometer-scale distances, we need transducers that can generate entanglement between the microwave and optical domains with high fidelity. We present an integrated electro-optic transducer that combines low-loss lithium niobate photonics with superconducting microwave resonators on a sapphire substrate. Our triply-resonant device operates in a dilution refrigerator and converts microwave photons to optical photons with an on-chip efficiency of $6.6\times 10^{-6}$ and a conversion bandwidth of 20 MHz. We discuss design trade-offs in this device, including strategies to manage acoustic loss, and outline ways to increase the conversion efficiency in the future., Comment: 15 pages, 10 figures. First two authors contributed equally to this work

Low-loss fiber optic links have the potential to connect superconducting quantum processors together over long distances to form large scale quantum networks. A key component of these future networks is a quantum transducer that coherently and bidirectionally converts photons from microwave frequencies to optical frequencies. We present a platform for electro-optic photon conversion based on silicon-organic hybrid photonics. Our device combines high quality factor microwave and optical resonators with an electro-optic polymer cladding to perform microwave-to-optical photon conversion from 6.7 GHz to 193 THz (1558 nm). The device achieves an electro-optic coupling rate of 330 Hz in a millikelvin dilution refrigerator environment. We use an optical heterodyne measurement technique to demonstrate the single-sideband nature of the conversion with a selectivity of approximately 10 dB. We analyze the effects of stray light in our device and suggest ways in which this can be mitigated. Finally, we present initial results on high-impedance spiral resonators designed to increase the electro-optic coupling., Comment: 31 pages, 13 figures

Just as classical information technology rests on a foundation built of interconnected information-processing systems, quantum information technology (QIT) must do the same. A critical component of such systems is the interconnect, a device or process that allows transfer of information between disparate physical media, for example, semiconductor electronics, individual atoms, light pulses in optical fiber, or microwave fields. While interconnects have been well engineered for decades in the realm of classical information technology, quantum interconnects (QuICs) present special challenges, as they must allow the transfer of fragile quantum states between different physical parts or degrees of freedom of the system. The diversity of QIT platforms (superconducting, atomic, solid-state color center, optical, etc.) that will form a quantum internet poses additional challenges. As quantum systems scale to larger size, the quantum interconnect bottleneck is imminent, and is emerging as a grand challenge for QIT. For these reasons, it is the position of the community represented by participants of the NSF workshop on Quantum Interconnects that accelerating QuIC research is crucial for sustained development of a national quantum science and technology program. Given the diversity of QIT platforms, materials used, applications, and infrastructure required, a convergent research program including partnership between academia, industry and national laboratories is required. This document is a summary from a U.S. National Science Foundation supported workshop held on 31 October - 1 November 2019 in Alexandria, VA. Attendees were charged to identify the scientific and community needs, opportunities, and significant challenges for quantum interconnects over the next 2-5 years., Comment: This is an updated version V2, including expanded text and listing of all co-authors. To whom correspondence should be addressed: Marko Lon\v{c}ar: loncar@seas.harvard.edu; Michael G. Raymer: raymer@uoregon.edu

Tuning and reconfiguring nanophotonic components is needed to realize systems incorporating many components. The electrostatic force can deform a structure and tune its optical response. Despite the success of electrostatic actuators, they suffer from trade-offs between tuning voltage, tuning range, and on-chip area. Piezoelectric actuation could resolve all these challenges. Standard materials possess piezoelectric coefficients on the order of ${0.01}~\text{nm/V}$, suggesting extremely small on-chip actuation using potentials on the order of one volt. Here we propose and demonstrate compact piezoelectric actuators, called nanobenders, that transduce tens of nanometers per volt. By leveraging the non-uniform electric field from submicron electrodes, we generate bending of a piezoelectric nanobeam. Combined with a sliced photonic crystal cavity to sense displacement, we show tuning of an optical resonance by $\sim 5~\text{nm/V}~({0.6}~\text{THz/V})$ and between $1520$ and $1560~\text{nm}$ ($\sim 400$ linewidths) with only $ {4}~\text{V}$. Finally, we consider other tunable nanophotonic components enabled by nanobenders., Comment: 24 pages, 5 + 12 figures

Efficient interconversion of both classical and quantum information between microwave and optical frequency is an important engineering challenge. The optomechanical approach with gigahertz-frequency mechanical devices has the potential to be extremely efficient due to the large optomechanical response of common materials, and the ability to localize mechanical energy into a micron-scale volume. However, existing demonstrations suffer from some combination of low optical quality factor, low electrical-to-mechanical transduction efficiency, and low optomechanical interaction rate. Here we demonstrate an on-chip piezo-optomechanical transducer that systematically addresses all these challenges to achieve nearly three orders of magnitude improvement in conversion efficiency over previous work. Our modulator demonstrates acousto-optic modulation with $V_{\pi} = {0.02}$ V. We show bidirectional conversion efficiency of $10^{-5}$ with ${3.3}$ microwatts red-detuned optical pump, and $5.5\%$ with $323$ microwatts blue-detuned pump. Further study of quantum transduction at millikelvin temperatures is required to understand how the efficiency and added noise are affected by reduced mechanical dissipation, thermal conductivity, and thermal capacity., Comment: 20 pages, 14 figures

The evenly-spaced modes of an electromagnetic resonator are coupled to each other by appropriate time-modulation, leading to dynamics analogous to those of particles hopping between different sites of a lattice. This substitution of a real spatial dimension of a lattice with a "synthetic'" dimension in frequency space greatly reduces the hardware complexity of an analog quantum simulator. Complex control and read-out of a highly multi-moded structure can thus be accomplished with very few physical control lines. We demonstrate this concept with microwave photons in a superconducting transmission line resonator by modulating the system parameters at frequencies near the resonator's free spectral range and observing propagation of photon wavepackets in time domain. The linear propagation dynamics are equivalent to a tight-binding model, which we probe by measuring scattering parameters between frequency sites. We extract an approximate tight-binding dispersion relation for the synthetic lattice and initialize photon wavepackets with well-defined quasimomenta and group velocities. As an example application of this platform in simulating a physical system, we demonstrate Bloch oscillations associated with a particle in a periodic potential and subject to a constant external field. The simulated field strongly affects the photon dynamics despite photons having zero charge. Our observation of photon dynamics along a synthetic frequency dimension generalizes immediately to topological photonics and single-photon power levels, and expands the range of physical systems addressable by quantum simulation., Comment: 23 pages, 11 figures

We present a piezoelectric transducer in thin-film lithium niobate that converts a 1.7 GHz microwave signal to a mechanical wave in a single mode of a 1 micron-wide waveguide. We measure a -12 dB conversion efficiency that is limited by material loss. The design method we employ is widely applicable to the transduction of wavelength-scale structures used in emerging phononic circuits like those at the heart of many optomechanical microwave-to-optical quantum converters., Comment: 9 pages, 7 figures. First two authors contributed equally to this work