We present a detailed study of the coherence of a tunable capacitively-shunted flux qubit, designed for coherent quantum annealing applications. The measured relaxation at the qubit symmetry point is mainly due to intrinsic flux noise in the main qubit loop for qubit frequencies below $\sim3~\text{GHz}$. At higher frequencies, thermal noise in the bias line makes a significant contribution to the relaxation, arising from the design choice to experimentally explore both fast annealing and high-frequency control. The measured dephasing rate is primarily due to intrinsic low-frequency flux noise in the two qubit loops, with additional contribution from the low-frequency noise of control electronics used for fast annealing. The flux-bias dependence of the dephasing time also reveals apparent noise correlation between the two qubit loops, possibly due to non-local sources of flux noise or junction critical-current noise. Our results are relevant for ongoing efforts toward building superconducting quantum annealers with increased coherence.

We observe blockade of microwave photons in a Tavis-Cummings system comprising a superconducting cavity and up to N=3 transmon qubits. The effect is characterized with photon number-resolving spectroscopy using an additional dispersively coupled transmon "witness" qubit to directly probe the cavity's photon number distribution. We first observe polariton formation with splitting proportional to √(N), confirming the Tavis-Cummings coupling, and subsequently obtain sub-Poissonian cavity photon statistics when the cavity is driven at polariton frequencies.

Landau-Zener tunneling, which describes the transition in a two-level system during a sweep through an anti-crossing, is a model applicable to a wide range of physical phenomena. Realistic quantum systems are affected by dissipation due to coupling to their environments. An important aspect of understanding such open quantum systems is the relative energy scales of the system itself and the system-environment coupling, which distinguishes the weak- and strong-coupling regimes. Using a tunable superconducting flux qubit, we observe the crossover from weak to strong coupling to the environment in Landau-Zener tunneling. Our results confirm previous theoretical studies of dissipative Landau-Zener tunneling in the weak and strong coupling limits. We devise a spin bath model that effectively captures the crossover regime. This work is relevant for understanding the role of dissipation in quantum annealing, where the system is expected to go through a cascade of Landau-Zener transitions before reaching the target state.

We perform readout of a quantum-dot hybrid qubit coupled to a superconducting resonator through a parametric, longitudinal interaction mechanism. Our experiments are performed with the qubit and resonator frequencies detuned by ~10 GHz, demonstrating that longitudinal coupling can facilitate semiconductor qubit operation in the ‘ultra-dispersive’ regime of circuit quantum electrodynamics.

Arrays of coupled superconducting qubits are analog quantum simulators able to emulate a wide range of tight-binding models in parameter regimes that are difficult to access or adjust in natural materials. In this work, we use a superconducting qubit array to emulate a tight-binding model on the rhombic lattice, which features flat bands. Enabled by broad adjustability of the dispersion of the energy bands and of on-site disorder, we examine regimes where flat-band localization and Anderson localization compete. We observe disorder-induced localization for dispersive bands and disorder-induced delocalization for flat bands. Remarkably, we find a sudden transition between the two regimes and, in its vicinity, the semblance of quantum critical scaling.

This paper describes a novel multi-metal layered interconnect-based heterogeneous integration approach for developing a reworkable superconducting qubit package. Various microbump options, including gold, tin, indium, and tin indium, were used to achieve the desired flip-chip configurations. As a case study, we demonstrate a reworkable cryogenic superconducting qubit package capable of interconnecting up to 32 microwave lines. The flip-chip package configurations show low (below 30 dB @ RT) nearest-neighbor crosstalk up to 10 GHz. Initial qubit measurements at low temperatures (~10 mK) show qubit lifetime T 1 > 100 μs (Q > 2M), which is comparable to the planar versions measured in our standard Al wirebonded package. Keywords—qubit, heterogeneous integration, interconnect, flip-chip, crosstalk.

Flux tunability is an important engineering resource for superconducting circuits. Large-scale quantum computers based on flux-tunable superconducting circuits face the problem of flux crosstalk, which needs to be accurately calibrated to realize high-fidelity quantum operations. Typical calibration methods either assume that circuit elements can be effectively decoupled and simple models can be applied, or require a large amount of data. Such methods become ineffective as the system size increases and circuit interactions become stronger. Here we propose a new method for calibrating flux crosstalk, which is independent of the underlying circuit model. Using the fundamental property that superconducting circuits respond periodically to external fluxes, crosstalk calibration of N flux channels can be treated as N independent optimization problems, with the objective functions being the periodicity of a measured signal depending on the compensation parameters. We demonstrate this method on a small-scale quantum annealing circuit based on superconducting flux qubits, achieving comparable accuracy with previous methods. We also show that the objective function usually has a nearly convex landscape, allowing efficient optimization.

Superconducting quantum processors are a compelling platform for analogue quantum simulation due to the precision control, fast operation and site-resolved readout inherent to the hardware. Arrays of coupled superconducting qubits natively emulate the dynamics of interacting particles according to the Bose-Hubbard model. However, many interesting condensed-matter phenomena emerge only in the presence of electromagnetic fields. Here we emulate the dynamics of charged particles in an electromagnetic field using a superconducting quantum simulator. We realize a broadly adjustable synthetic magnetic vector potential by applying continuous modulation tones to all qubits. We verify that the synthetic vector potential obeys the required properties of electromagnetism: a spatially varying vector potential breaks time-reversal symmetry and generates a gauge-invariant synthetic magnetic field, and a temporally varying vector potential produces a synthetic electric field. We demonstrate that the Hall effect-the transverse deflection of a charged particle propagating in an electromagnetic field-exists in the presence of the synthetic electromagnetic field. Arrays of superconducting transmon qubits can be used to study the Bose-Hubbard model. Synthetic electromagnetic fields have now been added to this analogue quantum simulation platform.

Entanglement and its propagation are central to understanding many physical properties of quantum systems1-3. Notably, within closed quantum many-body systems, entanglement is believed to yield emergent thermodynamic behaviour4-7. However, a universal understanding remains challenging owing to the non-integrability and computational intractability of most large-scale quantum systems. Quantum hardware platforms provide a means to study the formation and scaling of entanglement in interacting many-body systems8-14. Here we use a controllable 4 × 4 array of superconducting qubits to emulate a 2D hard-core Bose-Hubbard (HCBH) lattice. We generate superposition states by simultaneously driving all lattice sites and extract correlation lengths and entanglement entropy across its many-body energy spectrum. We observe volume-law entanglement scaling for states at the centre of the spectrum and a crossover to the onset of area-law scaling near its edges.

The large physical size of superconducting qubits and their associated on-chip control structures presents a practical challenge toward building a large-scale quantum computer. In particular, transmons require a high-quality-factor shunting capacitance that is typically achieved by using a large coplanar capacitor. Other components, such as superconducting microwave resonators used for qubit state readout, are typically constructed from coplanar waveguides, which are millimeters in length. Here, we use compact superconducting through-silicon vias to realize lumped-element capacitors in both qubits and readout resonators to significantly reduce the on-chip footprint of both of these circuit elements. We measure two types of devices to show that through-silicon vias are of sufficient quality to be used as capacitive circuit elements and provide a significant reduction in size over existing approaches.

Superconducting integrated circuit (SIC) is a promising "beyond-CMOS" device technology enables speed-of-light, nearly lossless communications to advance cryogenic (4 K or lower) computing. However, the lack of large-area superconducting IC has hindered the development of scalable practical systems. Herein, we describe a novel approach to interconnect 16 high-resolution deep UV (DUV EX4, 248 nm lithography) full reticle circuits to fabricate an extremely large (88mm X 88 mm) area superconducting integrated circuit (ELASIC). The fabrication process starts by interconnecting four high-resolution DUV EX4 (22 mm X 22 mm) full reticles using a single large-field (44 mm X 44 mm) I-line (365 nm lithography) reticle, followed by I-line reticle stitching at the boundaries of 44 mm X 44 mm fields to fabricate the complete ELASIC field (88 mm X 88 mm). The ELASIC demonstrated a 2X-12X reduction in circuit features and maintained high-stitched line superconducting critical currents. We examined quantum flux parametron (QFP) circuits to demonstrate the viability of common active components used for data buffering and transmission. Considering that no stitching requirement for high-resolution EX4 DUV reticles is employed, the present fabrication process has the potential to advance the scaling of superconducting quantum devices.

The slow-down of Moore's-Law-related lithographic scaling in high-density semiconductor integrated circuits has created a major impact on the design of computing hardware architecture. Computer architects are exploring heterogeneous assemblies of specialized chips (called “chiplets”) as an alternative way (i.e., “More-Than-Moore”) to provide the increasing computing capability needed to satisfy our data intensive future. Microelectronics packaging is evolving to meet the computing demands of increasing power and performance in ever smaller packages. To accomplish this, new packaging structures need to be able to integrate more chiplets with smaller technology nodes (5-, 7-, or 10-nanometer), higher I/O counts, and smaller interconnect pitches, while reducing the overall assembly footprint. This paper describes a new extremely large area integrated circuit (ELAIC) solution suitable for combining multiple chiplets of varying type (e.g., memory, ASICs, CPU, GPU, power conditioning) into a single package on a common interconnect platform. The ELAIC approach helps to rearchitect heterogeneous chip tiling for developing highly complex systems having desired circuit density and performance. Recent work on large-area superconducting integrated circuits to join multiple individual die is highlighted, with particular attention paid to the processing of the high-density electrical interconnects formed between the individual die. A variety of ELAIC assemblies were fabricated and characterized using several techniques (i.e., scanning-electron microscopy (SEM), optical microscopy, confocal microscopy, X-ray) to investigate the integration quality, minimum feature size, silicon content, die-to-die spacing, and gap filling. Silicon dioxide, benzocyclobutene (BCB), epoxy, polyimide, and silicone-based dielectrics were used for gap fill, via formation and redistribution layers (RDLs). For the ELAIC approach, the thermal stability is improved by reducing the die-to-die (D2D) gap and increasing the silicon content, allowing assemblers to mitigate the problem of mismatch in coefficient of thermal expansion (CTE) for different substrates/modules integration schemes, which is important for allowing the broad temperature range stability from reflow to operation at room or even cryogenic temperatures. ELAIC technology facilitates more space-efficient designs and can accommodate most heterogeneous die without compromising stability or introducing CTE mismatch or warpage. A variety of heterogeneous chips were used to fabricate ELAIC modules. The present process allows fabrication of ELAIC buildup layers having thickness in the range of 1–10 microns, which allows packaging structures having both finer pitch and higher density. The processes and materials used to achieve smaller feature dimensions, satisfy stringent registration requirements, and achieve robust electrical interconnections are discussed.

Superconducting quantum processors comprising flux-tunable data and coupler qubits are a promising platform for quantum computation. However, magnetic flux crosstalk between the flux-control lines and the constituent qubits impedes precision control of qubit frequencies, presenting a challenge to scaling this platform. In order to implement high-fidelity digital and analog quantum operations, one must characterize the flux crosstalk and compensate for it. In this work, we introduce a learning-based calibration protocol and demonstrate its experimental performance by calibrating an array of 16 flux-tunable transmon qubits. To demonstrate the extensibility of our protocol, we simulate the crosstalk matrix learning procedure for larger arrays of transmon qubits. We observe an empirically linear scaling with system size, while maintaining a median qubit frequency error below $300$ kHz.

Superconducting cavities have emerged as a key tool for measuring the spin states of quantum dots. So far, however, few experiments have explored longitudinal couplings between quantum dots and cavities, and no solid-state qubit experiments have explicitly probed the "adiabatic" regime, where the Purcell decay is strongly suppressed. Here we report measurements of a double-quantum-dot charge qubit coupled to a high-impedance resonator via a "flip-chip" design geometry. By applying an adiabatic ac drive to the qubit through two different channels, and studying the effects of qubit energy detuning, interdot tunneling, and driving strength, we are able to unequivocally confirm the presence of a longitudinal coupling between the qubit and the cavity, while the qubit remains in its ground state. Since this coupling is proportional to the driving amplitude, and is therefore switchable, it has the potential to become a powerful tool in qubit experiments.

Entanglement and its propagation are central to understanding a multitude of physical properties of quantum systems. Notably, within closed quantum many-body systems, entanglement is believed to yield emergent thermodynamic behavior. However, a universal understanding remains challenging due to the non-integrability and computational intractability of most large-scale quantum systems. Quantum hardware platforms provide a means to study the formation and scaling of entanglement in interacting many-body systems. Here, we use a controllable $4 \times 4$ array of superconducting qubits to emulate a two-dimensional hard-core Bose-Hubbard lattice. We generate superposition states by simultaneously driving all lattice sites and extract correlation lengths and entanglement entropy across its many-body energy spectrum. We observe volume-law entanglement scaling for states at the center of the spectrum and a crossover to the onset of area-law scaling near its edges.

Spin chains have long been considered an effective medium for long-range interactions, entanglement generation, and quantum state transfer. In this work, we explore the properties of a spin chain implemented with superconducting flux circuits, designed to act as a connectivity medium between two superconducting qubits. The susceptibility of the chain is probed and shown to support long-range, cross-chain correlations. In addition, interactions between the two end qubits, mediated by the coupler chain, are demonstrated. This work has direct applicability in near term quantum annealing processors as a means of generating long-range, coherent coupling between qubits.

Arrays of Geiger-mode avalanche photodiodes (GmAPDs) are fabricated on a new type of engineered substrates with an epitaxial layer grown on silicon-on-insulator (SOI) wafers. The SOI-based structure facilitates rapid die-level bump bonding of the GmAPD array to a CMOS readout integrated circuit (ROIC) followed by substrate removal to make a backilluminated image sensor. To fabricate the engineered substrate, a commercial substrate with a 70-nm-thick SOI layer is implanted with BF2 ions to create a p+-doped passivation layer on the light illumination surface. Subsequently, a lightly p-doped silicon layer on which the GmAPD will be fabricated is grown using a homoepitaxy process. This approach allows for the use of chip-level hybridization to CMOS, avoiding the high cost and demanding wafer flatness and smoothness requirements of wafer-scale 3D integration processes. The new process yields cleaner wafers and allows for tighter control of detector layer thickness compared to the previous process. GmAPDs fabricated on 5-μm-thick epitaxial silicon have over 70% photon detection efficiency (PDE) when 532 nm light is focused into the center 3 μm of the device with an oxide layer that remains after substrate removal. With an anti-reflective coating, the PDE can be improved.

Superconducting cavities have emerged as a key tool for measuring the spin states of quantum dots. So far however, few experiments have explored longitudinal couplings between dots and cavities, and no solid-state qubit experiments have explicitly probed the"adiabatic"regime, where the Purcell decay is strongly suppressed. Here, we report measurements of a double-quantum-dot charge qubit coupled to a high-impedance resonator via a"flip-chip"design geometry. By applying an adiabatic ac drive to the qubit through two different channels, and studying the effects of qubit energy detuning, interdot tunneling, and driving strength, we are able to unequivocally confirm the presence of a longitudinal coupling between the qubit and cavity, while the qubit remains in its ground state. Since this coupling is proportional to the driving amplitude, and is therefore switchable, it has the potential to become a powerful new tool in qubit experiments.

Superconducting cavities have emerged as a key tool for measuring the spin states of quantum dots. So far however, few experiments have explored longitudinal couplings between dots and cavities, and no solid-state qubit experiments have explicitly probed the "adiabatic" regime, where the Purcell decay is strongly suppressed. Here, we report measurements of a double-quantum-dot charge qubit coupled to a high-impedance resonator via a "flip-chip" design geometry. By applying an adiabatic ac drive to the qubit through two different channels, and studying the effects of qubit energy detuning, interdot tunneling, and driving strength, we are able to unequivocally confirm the presence of a longitudinal coupling between the qubit and cavity, while the qubit remains in its ground state. Since this coupling is proportional to the driving amplitude, and is therefore switchable, it has the potential to become a powerful new tool in qubit experiments.