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Routing quantum information between non-local computational nodes is a foundation for extensible networks of quantum processors. Quantum information transfer between arbitrary nodes is generally mediated either by photons that propagate between them, or by resonantly coupling nearby nodes. The utility is determined by the type of emitter, propagation channel, and receiver. Conventional approaches involving propagating microwave photons have limited fidelity due to photon loss and are often unidirectional, whereas architectures that use direct resonant coupling are bidirectional in principle, but can generally accommodate only a few local nodes. Here we demonstrate high-fidelity, on-demand, directional, microwave photon emission. We do this using an artificial molecule comprising two superconducting qubits strongly coupled to a bidirectional waveguide, effectively creating a chiral microwave waveguide. Quantum interference between the photon emission pathways from the molecule generates single photons that selectively propagate in a chosen direction. This circuit will also be capable of photon absorption, making it suitable for building interconnects within extensible quantum networks.

System noise identification is crucial to the engineering of robust quantum systems. Although existing quantum noise spectroscopy (QNS) protocols measure an aggregate amount of noise affecting a quantum system, they generally cannot distinguish between the underlying processes that contribute to it. Here, we propose and experimentally validate a spin-locking-based QNS protocol that exploits the multi-level energy structure of a superconducting qubit to achieve two notable advances. First, our protocol extends the spectral range of weakly anharmonic qubit spectrometers beyond the present limitations set by their lack of strong anharmonicity. Second, the additional information gained from probing the higher-excited levels enables us to identify and distinguish contributions from different underlying noise mechanisms., Comment: 23 pages, 9 figures

We consider mediated interactions in an array of floating transmons, where each qubit capacitor consists of two superconducting pads galvanically isolated from ground. Each such pair contributes two quantum degrees of freedom, one of which is used as a qubit, while the other remains fixed. However, these extraneous modes can generate coupling between the qubit modes that extends beyond the nearest neighbor. We present a general formalism describing the formation of this coupling and calculate it for a one-dimensional chain of transmons. We show that the strength of coupling and its range (that is, the exponential falloff) can be tuned independently via circuit design to realize a continuum from nearest-neighbor-only interactions to interactions that extend across the length of the chain. We present designs with capacitance and microwave simulations showing that various interaction configurations can be achieved in realistic circuits. Such coupling could be used in analog simulation of different quantum regimes or to increase connectivity in digital quantum systems. Thus mechanism must also be taken into account in other types of qubits with extraneous modes., 10 pages, 5 figures

The practical viability of any qubit technology stands on long coherence times and high-fidelity operations, with the superconducting qubit modality being a leading example. However, superconducting qubit coherence is impacted by broken Cooper pairs, referred to as quasiparticles, with a density that is empirically observed to be orders of magnitude greater than the value predicted for thermal equilibrium by the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity. Previous work has shown that infrared photons significantly increase the quasiparticle density, yet even in the best isolated systems, it still remains higher than expected, suggesting that another generation mechanism exists. In this Letter, we provide evidence that ionizing radiation from environmental radioactive materials and cosmic rays contributes to this observed difference, leading to an elevated quasiparticle density that would ultimately limit superconducting qubits of the type measured here to coherence times in the millisecond regime. We further demonstrate that introducing radiation shielding reduces the flux of ionizing radiation and positively correlates with increased coherence time. Albeit a small effect for today's qubits, reducing or otherwise mitigating the impact of ionizing radiation will be critical for realizing fault-tolerant superconducting quantum computers., Comment: 16 pages, 12 figures

Models of light–matter interactions in quantum electrodynamics typically invoke the dipole approximation1,2, in which atoms are treated as point-like objects when compared to the wavelength of the electromagnetic modes with which they interact. However, when the ratio between the size of the atom and the mode wavelength is increased, the dipole approximation no longer holds and the atom is referred to as a ‘giant atom’2,3. So far, experimental studies with solid-state devices in the giant-atom regime have been limited to superconducting qubits that couple to short-wavelength surface acoustic waves4–10, probing the properties of the atom at only a single frequency. Here we use an alternative architecture that realizes a giant atom by coupling small atoms to a waveguide at multiple, but well separated, discrete locations. This system enables tunable atom–waveguide couplings with large on–off ratios3 and a coupling spectrum that can be engineered by the design of the device. We also demonstrate decoherence-free interactions between multiple giant atoms that are mediated by the quasi-continuous spectrum of modes in the waveguide—an effect that is not achievable using small atoms11. These features allow qubits in this architecture to switch between protected and emissive configurations in situ while retaining qubit–qubit interactions, opening up possibilities for high-fidelity quantum simulations and non-classical itinerant photon generation12,13. Superconducting giant atoms are realized in a waveguide by coupling small atoms to the waveguide at multiple discrete locations, producing tunable atom–waveguide coupling and enabling decoherence-free interactions.

The pursuit of superconducting-based quantum computers has advanced the fabrication of and experimentation with custom lattices of qubits and resonators. Here, we describe a roadmap to use present experimental capabilities to simulate an interacting many-body system of bosons and measure quantities that are exponentially difficult to calculate numerically. We focus on the two-dimensional hard-core Bose–Hubbard model implemented as an array of floating transmon qubits. We describe a control scheme for such a lattice that can perform individual qubit readout and show how the scheme enables the preparation of a highly excited many-body state, in contrast with atomic implementations restricted to the ground state or thermal equilibrium. We discuss what observables could be accessed and how they could be used to better understand the properties of many-body systems, including the observation of the transition of eigenstate entanglement entropy scaling from area-law behavior to volume-law behavior.

Since the first observation of coherent quantum behaviour in a superconducting qubit, now more than 20 years ago, there have been substantial developments in the field of superconducting quantum circuits. One such advance is the introduction of the concepts of cavity quantum electrodynamics (QED) to superconducting circuits, to yield what is now known as circuit QED. This approach realizes in a single architecture the essential requirements for quantum computation, and has already been used to run simple quantum algorithms and to operate tens of superconducting qubits simultaneously. For these reasons, circuit QED is one of the leading architectures for quantum computation. In parallel to these advances towards quantum information processing, circuit QED offers new opportunities for the exploration of the rich physics of quantum optics in novel parameter regimes in which strongly nonlinear effects are readily visible at the level of individual microwave photons. We review circuit QED in the context of quantum information processing and quantum optics, and discuss some of the challenges on the road towards scalable quantum computation. The introduction of concepts from cavity quantum electrodynamics to superconducting circuits yielded circuit quantum electrodynamics, a platform eminently suitable to quantum information processing and for the exploration of novel regimes in quantum optics.

Squeezing of the electromagnetic vacuum is an essential metrological technique used to reduce quantum noise in applications spanning gravitational wave detection, biological microscopy, and quantum information science. In superconducting circuits, the resonator-based Josephson-junction parametric amplifiers conventionally used to generate squeezed microwaves are constrained by a narrow bandwidth and low dynamic range. In this work, we develop a dual-pump, broadband Josephson traveling-wave parametric amplifier that combines a phase-sensitive extinction ratio of 56 dB with single-mode squeezing on par with the best resonator-based squeezers. We also demonstrate two-mode squeezing at microwave frequencies with bandwidth in the gigahertz range that is almost two orders of magnitude wider than that of contemporary resonator-based squeezers. Our amplifier is capable of simultaneously creating entangled microwave photon pairs with large frequency separation, with potential applications including high-fidelity qubit readout, quantum illumination and teleportation.

One major challenge to scaling quantum dot qubits is the dense wiring requirements, making it difficult to envision fabricating large 2D arrays of nearest-neighbor-coupled qubits necessary for error correction. We describe a method to ameliorate this issue by spacing out the qubits using superconducting resonators facilitated by 3D integration. To prove the viability of this approach, we use integration to couple an off-chip high-impedance TiN resonator to a double quantum dot in a Si/SiGe heterostructure. Using the resonator as a dispersive gate sensor, we tune the device down to the single electron regime with an SNR = 5.36. Characterizing the individual systems shows 3D integration can be done while maintaining low-charge noise for the quantum dots and high-quality factors for the superconducting resonator (single photon QL = 2.14 × 104 with Qi ≈ 3 × 105), necessary for readout and high-fidelity two-qubit gates.

High-fidelity two-qubit gates at scale are a key requirement to realize the full promise of quantum computation and simulation. The advent and use of coupler elements to tunably control two-qubit interactions has improved operational fidelity in many-qubit systems by reducing parasitic coupling and frequency crowding issues. Nonetheless, two-qubit gate errors still limit the capability of near-term quantum applications. The reason, in part, is the existing framework for tunable couplers based on the dispersive approximation does not fully incorporate three-body multi-level dynamics, which is essential for addressing coherent leakage to the coupler and parasitic longitudinal ($ZZ$) interactions during two-qubit gates. Here, we present a systematic approach that goes beyond the dispersive approximation to exploit the engineered level structure of the coupler and optimize its control. Using this approach, we experimentally demonstrate CZ and $ZZ$-free iSWAP gates with two-qubit interaction fidelities of $99.76 \pm 0.07$% and $99.87 \pm 0.23$%, respectively, which are close to their $T_1$ limits., Comment: 34 pages, 39 figures

We introduce CircuitQ, an open-source toolbox for the analysis of superconducting circuits implemented in Python. It features the automated construction of a symbolic Hamiltonian of the input circuit and a dynamic numerical representation of the Hamiltonian with a variable basis choice. The software implementation is capable of choosing the basis in a fully automated fashion based on the potential energy landscape. Additional features include the estimation of the T 1 lifetimes of the circuit states under various noise mechanisms. We review previously established circuit quantization methods and formulate them in a way that facilitates the software implementation. The toolbox is then showcased by applying it to practically relevant qubit circuits and comparing it to specialized circuit solvers. Our circuit quantization is applicable to circuit inputs from a large design space, and the software is open-sourced. We thereby add an important resource for the design of new quantum circuits for quantum information processing applications.

Accurate characterization of the noise influencing a quantum system of interest has far-reaching implications across quantum science, ranging from microscopic modeling of decoherence dynamics to noise-optimized quantum control. While the assumption that noise obeys Gaussian statistics is commonly employed, noise is generically non-Gaussian in nature. In particular, the Gaussian approximation breaks down whenever a qubit is strongly coupled to discrete noise sources or has a non-linear response to the environmental degrees of freedom. Thus, in order to both scrutinize the applicability of the Gaussian assumption and capture distinctive non-Gaussian signatures, a tool for characterizing non-Gaussian noise is essential. Here, we experimentally validate a quantum control protocol which, in addition to the spectrum, reconstructs the leading higher-order spectrum of engineered non-Gaussian dephasing noise using a superconducting qubit as a sensor. This first experimental demonstration of non-Gaussian noise spectroscopy represents a major step toward demonstrating a complete spectral estimation toolbox for quantum devices., 21 pages, 12 figures

Superconducting circuits have emerged as a promising platform to build quantum processors. The challenge of designing a circuit is to compromise between realizing a set of performance metrics and reducing circuit complexity and noise sensitivity. At the same time, one needs to explore a large design space, and computational approaches often yield long simulation times. Here, we automate the circuit design task using SCILLA. The software SCILLA performs a parallelized, closed-loop optimization to design superconducting circuit diagrams that match predefined properties, such as spectral features and noise sensitivities. We employ it to design 4-local couplers for superconducting flux qubits and identify a circuit that outperforms an existing proposal with a similar circuit structure in terms of coupling strength and noise resilience for experimentally accessible parameters. This work demonstrates how automated design can facilitate the development of complex circuit architectures for quantum information processing.

Superconducting qubits are a promising platform for building a larger-scale quantum processor capable of solving otherwise intractable problems. In order for the processor to reach practical viability, the gate errors need to be further suppressed and remain stable for extended periods of time. With recent advances in qubit control, both single- and two-qubit gate fidelities are now in many cases limited by the coherence times of the qubits. Here we experimentally employ closed-loop feedback to stabilize the frequency fluctuations of a superconducting transmon qubit, thereby increasing its coherence time by 26\% and reducing the single-qubit error rate from $(8.5 \pm 2.1)\times 10^{-4}$ to $(5.9 \pm 0.7)\times 10^{-4}$. Importantly, the resulting high-fidelity operation remains effective even away from the qubit flux-noise insensitive point, significantly increasing the frequency bandwidth over which the qubit can be operated with high fidelity. This approach is helpful in large qubit grids, where frequency crowding and parasitic interactions between the qubits limit their performance., Comment: 15 pages, 7 figures

For the past three decades, nanoscience has widely affected many areas in physics, chemistry, and engineering, and has led to numerous fundamental discoveries as well as applications and products. Concurrently, quantum science and technology has developed into a cross-disciplinary research endeavour connecting these same areas and holds a burgeoning commercial promise. Although quantum physics dictates the behaviour of nanoscale objects, quantum coherence, which is central to quantum information, communication and sensing has not played an explicit role in much of nanoscience. This Review describes fundamental principles and practical applications of quantum coherence in nanoscale systems, a research area we call quantum-coherent nanoscience. We structure this manuscript according to specific degrees of freedom that can be quantum-coherently controlled in a given nanoscale system such as charge, spin, mechanical motion, and photons. We review the current state of the art and focus on outstanding challenges and opportunities unlocked by the merging of nanoscience and coherent quantum operations., Comment: 34 pages, 6 figures, 2 boxes

Dielectrics with low loss at microwave frequencies are imperative for high-coherence solid-state quantum computing platforms. We study the dielectric loss of hexagonal boron nitride (hBN) thin films in the microwave regime by measuring the quality factor of parallel-plate capacitors (PPCs) made of NbSe$_{2}$-hBN-NbSe$_{2}$ heterostructures integrated into superconducting circuits. The extracted microwave loss tangent of hBN is bounded to be at most in the mid-10$^{-6}$ range in the low temperature, single-photon regime. We integrate hBN PPCs with aluminum Josephson junctions to realize transmon qubits with coherence times reaching 25 $\mu$s, consistent with the hBN loss tangent inferred from resonator measurements. The hBN PPC reduces the qubit feature size by approximately two-orders of magnitude compared to conventional all-aluminum coplanar transmons. Our results establish hBN as a promising dielectric for building high-coherence quantum circuits with substantially reduced footprint and, with a high energy participation that helps to reduce unwanted qubit cross-talk.

As progress is made towards the first generation of error-corrected quantum computers, robust characterization and validation protocols are required to assess the noise environments of physical quantum processors. While standard coherence metrics and characterization protocols such as T1 and T2, process tomography, and randomized benchmarking are now ubiquitous, these techniques provide only partial information about the dynamic multiqubit loss channels responsible for processor errors, which can be described more fully by a Lindblad operator in the master equation formalism. Here, we introduce and experimentally demonstrate Lindblad tomography, a hardware-agnostic characterization protocol for tomographically reconstructing the Hamiltonian and Lindblad operators of a quantum noise environment from an ensemble of time-domain measurements. Performing Lindblad tomography on a small superconducting quantum processor, we show that this technique naturally builds on standard process tomography and T1/T2 measurement protocols, characterizes and accounts for state-preparation and measurement errors, and allows one to place bounds on the fit to a Markovian model. Comparing the results of single- and two-qubit measurements on a superconducting quantum processor, we demonstrate that Lindblad tomography can also be used to identify and quantify sources of crosstalk on quantum processors, such as the presence of always-on qubit-qubit interactions.

Interacting many-body quantum systems show a rich array of physical phenomena and dynamical properties, but are notoriously difficult to study: they are challenging analytically and exponentially difficult to simulate on classical computers. Small-scale quantum information processors hold the promise to efficiently emulate these systems, but characterizing their dynamics is experimentally challenging, requiring probes beyond simple correlation functions and multi-body tomographic methods. Here, we demonstrate the measurement of out-of-time-ordered correlators (OTOCs), one of the most effective tools for studying quantum system evolution and processes like quantum thermalization. We implement a 3x3 two-dimensional hard-core Bose-Hubbard lattice with a superconducting circuit, study its time-reversibility by performing a Loschmidt echo, and measure OTOCs that enable us to observe the propagation of quantum information. A central requirement for our experiments is the ability to coherently reverse time evolution, which we achieve with a digital-analog simulation scheme. In the presence of frequency disorder, we observe that localization can partially be overcome with more particles present, a possible signature of many-body localization in two dimensions.

We experimentally demonstrate a new method of generating entangled itinerant photons using waveguide quantum electrodynamics., Realizing a fully connected network of quantum processors requires the ability to distribute quantum entanglement. For distant processing nodes, this can be achieved by generating, routing, and capturing spatially entangled itinerant photons. In this work, we demonstrate the deterministic generation of such photons using superconducting transmon qubits that are directly coupled to a waveguide. In particular, we generate two-photon N00N states and show that the state and spatial entanglement of the emitted photons are tunable via the qubit frequencies. Using quadrature amplitude detection, we reconstruct the moments and correlations of the photonic modes and demonstrate state preparation fidelities of 84%. Our results provide a path toward realizing quantum communication and teleportation protocols using itinerant photons generated by quantum interference within a waveguide quantum electrodynamics architecture.

Noise that exhibits significant temporal and spatial correlations across multiple qubits can be especially harmful to both fault-tolerant quantum computation and quantum-enhanced metrology. However, a complete spectral characterization of the noise environment of even a two-qubit system has not been reported thus far. We propose and experimentally demonstrate a protocol for two-qubit dephasing noise spectroscopy based on continuous-control modulation. By combining ideas from spin-locking relaxometry with a statistically motivated robust estimation approach, our protocol allows for the simultaneous reconstruction of all the single-qubit and two-qubit cross-correlation spectra, including access to their distinctive nonclassical features. Only single-qubit control manipulations and state-tomography measurements are employed, with no need for entangled-state preparation or readout of two-qubit observables. While our experimental demonstration uses two superconducting qubits coupled to a shared, colored engineered noise source, our methodology is portable to a variety of dephasing-dominated qubit architectures. By pushing quantum noise spectroscopy beyond the single-qubit setting, our work heralds the characterization of spatiotemporal correlations in both engineered and naturally occurring noise environments., PRX Quantum, 1 (1), ISSN:2691-3399

© 2000-2012 IEEE. Quantum processing has the potential to transform the computing landscape by enabling efficient solutions to problems that are intractable using classical processors. The field was sparked by a suggestion from physicist Richard Feynman in 1981 that a controllable quantum system can be used to simulate other quantum systems, such as the energy band structure of complex materials or the chemical reaction rates of intricate molecules. In the 1990s, interest in quantum computing grew rapidly with the introduction of the first quantum "killer app"-the potential of a large-scale quantum processor to break certain types of public encryption schemes [1]. Recently, there has been growing consensus that myriad other fields besides data security could be impacted by the development of a quantum processor, including machine learning [2], many optimization problems [3], and Feynman's original idea of the simulation of materials properties [4]. In recent years, the field has progressed rapidly, but many technical challenges must be overcome before a large-scale quantum processor can be built. This article focuses on the development of packaging for solid-state qubits and the use of 3D integration to address this challenge.

Lossy dielectrics are a significant source of decoherence in superconducting quantum circuits. In this report, we model and compare the dielectric loss in bulk and interfacial dielectrics in titanium nitride (TiN) and aluminum (Al) superconducting coplanar waveguide (CPW) resonators. We fabricate isotropically trenched resonators to produce a series of device geometries that accentuate a specific dielectric region's contribution to resonator quality factor. While each dielectric region contributes significantly to loss in TiN devices, the metal-air interface dominates the loss in the Al devices. Furthermore, we evaluate the quality factor of each TiN resonator geometry with and without a post-process hydrofluoric (HF) etch, and find that it reduced losses from the substrate-air interface, thereby improving the quality factor.

Resonant transverse driving of a two-level system as viewed in the rotating frame couples two degenerate states at the Rabi frequency, an amazing equivalence that emerges in quantum mechanics. While spectacularly successful at controlling natural and artificial quantum systems, certain limitations may arise (e.g., the achievable gate speed) due to non-idealities like the counter-rotating term. Here, we explore a complementary approach to quantum control based on non-resonant, non-adiabatic driving of a longitudinal parameter in the presence of a fixed transverse coupling. We introduce a superconducting composite qubit (CQB), formed from two capacitively coupled transmon qubits, which features a small avoided crossing -- smaller than the environmental temperature -- between two energy levels. We control this low-frequency CQB using solely baseband pulses, non-adiabatic transitions, and coherent Landau-Zener interference to achieve fast, high-fidelity, single-qubit operations with Clifford fidelities exceeding $99.7\%$. We also perform coupled qubit operations between two low-frequency CQBs. This work demonstrates that universal non-adiabatic control of low-frequency qubits is feasible using solely baseband pulses.

The dominant source of decoherence in contemporary frequency-tunable superconducting qubits is 1/$f$ flux noise. To understand its origin and find ways to minimize its impact, we systematically study flux noise amplitudes in more than 50 flux qubits with varied SQUID geometry parameters and compare our results to a microscopic model of magnetic spin defects located at the interfaces surrounding the SQUID loops. Our data are in agreement with an extension of the previously proposed model, based on numerical simulations of the current distribution in the investigated SQUIDs. Our results and detailed model provide a guide for minimizing the flux noise susceptibility in future circuits., 14 pages, 6 figures

Solid-state qubits with transition frequencies in the microwave regime, such as superconducting qubits, are at the forefront of quantum information processing. However, high-fidelity, simultaneous control of superconducting qubits at even a moderate scale remains a challenge, partly due to the complexities of packaging these devices. Here, we present an approach to microwave package design focusing on material choices, signal line engineering, and spurious mode suppression. We describe design guidelines validated using simulations and measurements used to develop a 24-port microwave package. Analyzing the qubit environment reveals no spurious modes up to 11GHz. The material and geometric design choices enable the package to support qubits with lifetimes exceeding 350 {\mu}s. The microwave package design guidelines presented here address many issues relevant for near-term quantum processors., Comment: 15 pages, 9 figures

With the increasing size of quantum processors, sub-modules that constitute the processor hardware will become too large to accurately simulate on a classical computer. Therefore, one would soon have to fabricate and test each new design primitive and parameter choice in time-consuming coordination between design, fabrication, and experimental validation. Here we show how one can design and test the performance of next-generation quantum hardware -- by using existing quantum computers. Focusing on superconducting transmon processors as a prominent hardware platform, we compute the static and dynamic properties of individual and coupled transmons. We show how the energy spectra of transmons can be obtained by variational hybrid quantum-classical algorithms that are well-suited for near-term noisy quantum computers. In addition, single- and two-qubit gate simulations are demonstrated via Suzuki-Trotter decomposition. Our methods pave a promising way towards designing candidate quantum processors when the demands of calculating sub-module properties exceed the capabilities of classical computing resources., Comment: 17 pages, 8 figures. accepted version to appear in Phys. Rev. Appl

In condensed matter systems, coherent backscattering and quantum interference in the presence of time-reversal symmetry lead to well-known phenomena such as weak localization (WL) and universal conductance fluctuations (UCF). Here we use multi-pass Landau-Zener transitions at the avoided crossing of a highly-coherent superconducting qubit to emulate these phenomena. The average and standard deviation of the qubit transition rate exhibit a dip and peak when the driving waveform is time-reversal symmetric, analogous to WL and UCF, respectively. The higher coherence of this qubit enabled the realization of both effects, in contrast to earlier work arXiv:1204.6428, which successfully emulated UCF, but did not observe WL. This demonstration illustrates the use of non-adiabatic control to implement quantum emulation with superconducting qubits., 14 pages, 7 figures; two reference added; figure 4 changed; 2 more figures added in Suppl. Info

Models of light-matter interactions in quantum electrodynamics typically invoke the dipole approximation

© 2019 IEEE. As designs for superconducting qubits become more complex, 3D integration of two or more vertically bonded chips will become necessary to enable increased density and connectivity. Precise control of the spacing between these chips is required for accurate prediction of circuit performance. In this paper, we demonstrate an improvement in the planarity of bonded superconducting qubit chips while retaining device performance by utilizing hard-stop silicon spacer posts. These silicon spacers are defined by etching several microns into a silicon substrate and are compatible with 3D-integrated qubit fabrication. This includes fabrication of Josephson junctions, superconducting air-bridge crossovers, underbump metallization and indium bumps. To qualify the integrated process, we demonstrate high-quality factor resonators on the etched surface and measure qubit coherence (T1, T2,echo > 40 μs) in the presence of silicon posts as near as 350 μm to the qubit.