Superconducting Circuit Research Articles

Mitigating coherent loss in superconducting circuits using molecular self-assembled monolayers

In planar superconducting circuits, decoherence due to materials imperfections, especially two-level-system (TLS) defects at different interfaces, is a primary hurdle for advancing quantum computing and sensing applications. Traditional methods for mitigating TLS loss, such as etching oxide layers at metal and substrate interfaces, have proven to be inadequate due to the persistent challenge of oxide regrowth. In this work, we introduce a novel approach that employs molecular self-assembled monolayers (SAMs) to chemically bind at different interfaces of superconducting circuits. This technique is specifically tested here on coplanar waveguide (CPW) resonators, in which this method not only impedes oxide regrowth after surface etching but can also tailors the dielectric properties at different resonators interfaces. The deployment of SAMs results in a consistent improvement in the measured quality factors across multiple resonators, surpassing those with only oxide-etched resonators. The efficiency of our approach i3s supported by microwave measurements of multiple devices conducted at millikelvin temperatures and correlated with detailed X-ray photoelectron spectroscopy (XPS) and transmission electron microscopy (TEM) characterizations of SAM-passivated resonators. The compatibility of SAMs materials with the established fabrication techniques offers a promising route to improve the performance of superconducting quantum devices.

Stochastic matrix multiplier using superconductor single-flux-quantum circuit

Abstract A superconducting single-flux-quantum (SFQ) circuit is suitable for stochastic computation that represents information in terms of the probability of “1”s in a finite-bit-length number train, due to its high-speed operation. In this paper, we demonstrate a matrix multiplier based on the SFQ logic circuits and superconductive random number generators (SRNGs). The stochastic multiplier required for the matrix product calculation is implemented using an AND gate. The stochastic adder is implemented by a multiplexer where the random number train generated by the SRNG is utilized as a control signal. We implemented 2 × 2 matrix multiplier targeting a frequency of 50 GHz, using the 10 kA/cm^2 Nb 4-layer superconductor circuit fabrication process.

Large-area superconducting nanowire arrays fabricated by nano laser direct writing

We report on the fabrication, structural, and electrical transport characterizations of superconducting nanowire arrays based on nano-laser direct writing (NLDW). The thermal excitation-induced micro/nano fabrication based on the interactions between NLDW and superconducting Nb films was experimentally analyzed and simulated. Experimentally, the arrays of superconducting nanowires have an area of 190 × 190 μm2 with a critical transition temperature Tc of 7.8 K and a critical current density Jc of 20.8 MA cm−2 at 4.0 K. The width and arrangement of the nanowires are precisely controlled, exhibiting a minimal loss of 0.6 K in Tc and excellent Jc after LDW. The width of superconducting nanowires could be further optimized by adjusting parameters such as laser power, irradiation gap, and delay of points. Compared with electron beam lithography and focused ion beam, to some extent, the nanowires fabrication process based on NLDW provides a more efficient and cost-effective path for fabricating large-area superconducting circuits and devices.

Boundary measurement tomography of the Bose Hubbard model on general graphs

Correlated quantum many-body phenomena in lattice models have been identified as a set of physically interesting problems that cannot be solved classically. Analog quantum simulators, in photonics and microwave superconducting circuits, have emerged as near-term platforms to address these problems. An important ingredient in practical quantum simulation experiments is the tomography of the implemented Hamiltonians—while this can easily be performed if we have individual measurement access to each qubit in the simulator, this could be challenging to implement in many hardware platforms. In this paper, we present a scheme for tomography of quantum simulators which can be described by a Bose-Hubbard Hamiltonian while having measurement access to only some sites on the boundary of the lattice. We present an algorithm that uses the experimentally routine transmission and two-photon correlation functions, measured at the boundary, to extract the Hamiltonian parameters at the standard quantum limit. Furthermore, by building on quantum enhanced spectroscopy protocols that, we show that with the additional ability to switch on and off the on-site repulsion in the simulator, we can sense the Hamiltonian parameters beyond the standard quantum limit. Published by the American Physical Society 2024

Ginzburg–Landau simulations of three-terminal operation of a superconducting nanowire cryotron

Abstract Superconducting nanowire cryotrons (nTrons) are expected to be used as interfaces for super-high-performance hybrid devices in which superconductor and semiconductor circuits are combined. However, nTrons are still under development, and diverse analyses of these devices are needed. Accordingly, we have developed a numerical technique to simulate the three-terminal operation of an nTron by using the finite element method to solve the time-dependent Ginzburg–Landau (TDGL) equation and the heat-diffusion equation. Simulations using this technique offer understanding of the dynamics of the order parameter, the thermal behavior, and the characteristics of three-terminal operation, and the TDGL model reproduces qualitatively the results of nTron experiments conducted at the Massachusetts Institute of Technology. In addition, we investigated how some geometric and physical parameters (the design elements) affect the operation characteristics. The TDGL model has far fewer free parameters compared with the lumped-element electrothermal model commonly used for simulating superconducting devices. Furthermore, the TDGL model provides time-dependent visual information about the superconducting state and the normal state, thereby offering insights into the relationship between nTron geometry and three-terminal operation. These simulation results offer a route to nTron optimization and the development of nTron applications.

On-Demand Driven Dissipation for Cavity Reset and Cooling

We present a superconducting circuit device that provides active, on-demand, tunable dissipation on a target mode of the electromagnetic field. Our device is based on a tunable “dissipator” that can be made lossy when tuned into resonance with a broadband filter mode. When driven parametrically, this dissipator induces loss on any mode coupled to it with energy detuning equal to the drive frequency. We demonstrate the use of this device to reset a superconducting qubit’s readout cavity after a measurement, removing photons with a characteristic rate greater than 50μs−1. We also demonstrate that the dissipation can be driven constantly to simultaneously damp and cool the cavity, effectively eliminating thermal photon fluctuations as a relevant decoherence channel. Our results demonstrate the utility of our device as a modular tool for environmental engineering and entropy removal in circuit quantum electrodynamics. Published by the American Physical Society 2024

Gottesman-Kitaev-Preskill State Preparation Using Periodic Driving.

The Gottesman-Kitaev-Preskill (GKP) code may be used to overcome noise in continuous variable quantum systems. However, preparing GKP states remains experimentally challenging. We propose a method for preparing GKP states by engineering a time-periodic Hamiltonian whose Floquet states are GKP states. This Hamiltonian may be realized in a superconducting circuit comprising a SQUID shunted by a superinductor and a capacitor, with a characteristic impedance twice the resistance quantum. The GKP Floquet states can be prepared by adiabatically tuning the frequency of the external magnetic flux drive. Wepredict that highly squeezed >11.9 dB (10.8dB) GKP magic states can be prepared on a microsecond timescale, given a quality factor of 10^{6} (10^{5}) and flux noise at typical rates.

Quantum interference in a high-transition-temperature superconductor based on nanoslits on SrTiO3 substrate

The Josephson junction, a key component of superconducting quantum circuits, is much less mature, especially for the high-transition (high-Tc) temperature cuprate superconductors. Herein, we report on the realization of high-Tc Josephson junction based on nanoslits on a SrTiO3 substrate. We demonstrate the ability to manipulate the current–voltage characteristics of YBa2Cu3O7−x bridges continuously from superconducting current-dominated to Josephson junction behavior by changing the irradiation parameters of the focused Ga+ ion beam on a single-crystal SrTiO3 substrate. The periodic critical current that depends on the magnetic flux coupled into the superconducting quantum interference devices was observed, which exactly reflects the effects of quantum tunneling and flux quantization. To some extent, this weak link within the framework of the semiconductor manufacturing process shows the potential to provide a cost-effective, highly efficient, and reliable pathway for scaling up quantum mechanical superconducting circuits, which is promising for the fabrication process.

High-density superconductive logic circuits utilizing 0 and π josephson junctions

Superconductor Electronics (SCE) is a fast and power-efficient technology with great potential for overcoming conventional CMOS electronics’ scaling limits. Nevertheless, the primary challenge confronting SCE today is its integration level, which lags several orders of magnitude behind CMOS circuits. In this study, we have innovated and simulated a novel logic family grounded in the principles of phase shifts occurring in 0 and π Josephson junctions. The fast phase logic (FPL) eliminates the need for large inductor loops and shunt resistances by combining the half-flux and phase logic. Therefore, the Josephson junction (JJ) area only limits the integration density. The cells designed with this paradigm are fast, and the clock-to-Q delay for logic cells is about 4ps. While maintaining over 50% parameter margins for wiring cells. This logic is power efficient and can increase the integration by at least 100×in the SCE chips.

Hardware-efficient autonomous error correction with linear couplers in superconducting circuits

Large-scale quantum computers will inevitably need quantum error correction (QEC) to protect information against decoherence. Given that the overhead of such error correction is often formidable, autonomous quantum error correction (AQEC) proposals offer a promising near-term alternative. AQEC schemes work by transforming error states into excitations that can be efficiently removed through engineered dissipation. The recently proposed AQEC scheme by Li , called the Star code, can autonomously correct or suppress all single qubit error channels using two transmons as encoders with a tunable coupler and two lossy resonators as a cooling source. The Star code requires only two-photon interactions and can be realized with linear coupling elements, avoiding experimentally challenging higher-order terms needed in many other AQEC proposals, but needs carefully selected parameters to achieve quadratic improvements in logical states' lifetimes. Here, we theoretically and numerically demonstrate the optimal parameter choices in the Star code. We further discuss adapting the Star code to other planar superconducting circuits, which offers a scalable alternative to single qubits for incorporation in larger quantum computers or error correction codes. Published by the American Physical Society 2024

Strong Photon-Magnon Coupling Using a Lithographically Defined Organic Ferrimagnet.

A cavity-magnonic system composed of a superconducting microwave resonator coupled to a magnon mode hosted by the organic-based ferrimagnet vanadium tetracyanoethylene (V[TCNE]x) is demonstrated. This work is motivated by the challenge of scalably integrating a low-damping magnetic system with planar superconducting circuits. V[TCNE]x has ultra-low intrinsic damping, can be grown at low processing temperatures on arbitrary substrates, and can be patterned via electron beam lithography. The devices operate in the strong coupling regime, with a cooperativity exceeding 1000 for coupling between the Kittel mode and the resonator mode at T≈0.4 K, suitable for scalable quantum circuit integration. Higher-order magnon modes are also observed with much narrower linewidths than the Kittel mode. This work paves the way for high-cooperativity hybrid quantum devices in which magnonic circuits can be designed and fabricated as easily as electricalwires.

Geometric Phase of a Transmon in a Dissipative Quantum Circuit.

Superconducting circuits reveal themselves as promising physical devices with multiple uses. Within those uses, the fundamental concept of the geometric phase accumulated by the state of a system shows up recurrently, as, for example, in the construction of geometric gates. Given this framework, we study the geometric phases acquired by a paradigmatic setup: a transmon coupled to a superconductor resonating cavity. We do so both for the case in which the evolution is unitary and when it is subjected to dissipative effects. These models offer a comprehensive quantum description of an anharmonic system interacting with a single mode of the electromagnetic field within a perfect or dissipative cavity, respectively. In the dissipative model, the non-unitary effects arise from dephasing, relaxation, and decay of the transmon coupled to its environment. Our approach enables a comparison of the geometric phases obtained in these models, leading to a thorough understanding of the corrections introduced by the presence of the environment.

Experimental study of modified Tavis-Cummings model with directly-coupled superconducting artificial atoms.

The Tavis-Cummings model is intensively investigated in quantum optics and has important applications in generation of multi-atom entanglement. Here, we employ a superconducting circuit quantum electrodynamic system to study a modified Tavis-Cummings model with directly-coupled atoms. In our device, three superconducting artificial atoms are arranged in a chain with direct coupling through fixed capacitors and strongly coupled to a transmission line resonator. By performing transmission spectrum measurements, we observe different anticrossing structures when one or two qubits are resonantly coupled to the resonator. In the case of the two-qubit Tavis-Cummings model without qubit-qubit interaction, we observe two dips at the resonance point of the anticrossing. The splitting of these dips is determined by Δ λ=2g12+g32, where g1 and g3 are the coupling strengths between Qubit 1 and the resonator, and Qubit 3 and the resonator, respectively. The direct coupling J12 between the two qubits results in three dressed states in the two-qubit Tavis-Cummings model at the frequency resonance point, leading to three dips in the transmission spectrum. In this case, the distance between the two farthest and asymmetrical dips, arising from the energy level splitting, is larger than in the previous case. The frequency interval between these two dips is determined by the difference in eigenvalues (Δ λ=ε 1+-ε 1-), obtained through numerical calculations. What we believe as novel and intriguing experimental results may potentially advance quantum optics experiments, providing valuable insights for future research.

Inductive and Capacitive Coupling Noise in Superconductive VLSI Circuits

Inductive and Capacitive Coupling Noise in Superconductive VLSI Circuits

Quasiperiodic circuit quantum electrodynamics

Superconducting circuits are an extremely versatile platform to realize quantum information hardware and to emulate topological materials. We here show how a simple arrangement of capacitors and conventional superconductor-insulator-superconductor junctions can realize an even broader class of systems, in the form of a nonlinear capacitive element which is quasiperiodic with respect to the quantized Cooper-pair charge. Our setup allows to create protected Dirac points defined in the transport degrees of freedom, whose presence leads to a suppression of the classical finite-frequency current noise. Furthermore, the quasiperiodicity can emulate Anderson localization in charge space, measurable via vanishing charge quantum fluctuations. The realization by means of the macroscopic transport degrees of freedom allows for a straightforward generalization to arbitrary dimensions and implements truly non-interacting versions of the considered models. As an outlook, we discuss potential ideas to simulate a transport version of the magic-angle effect known from twisted bilayer graphene.

Compact superconducting transmon qubit circuits made of ultrathin NbN

We design and fabricate a compact superconducting qubit circuit made of nano-thick NbN film on a high-resistivity silicon substrate, carrying seven transmon qubits. By comparing with the conventional superconducting qubit circuits made of superconducting films with hundred-nanometer thickness, our superconducting qubit circuit has much smaller size in the readout circuit, whose resonator length is only about 1/20 of that in a conventional superconducting circuit. Transmons are measured and characterized in the frequency and time domains with different flux bias. The transition frequency f01 can be adjusted in the range of several GHz. The qubit circuits made of such nano-thick material with high kinetic inductance are promising in the integration of quantum circuits.

GHz operation of a quantum point contact using stub-impedance matching circuit

Quantum point contacts (QPC) are the building blocks of quantum dot qubits and semiconducting quantum electrical metrology circuits. QPCs also make highly sensitive electrical amplifiers with the potential to operate in the quantum-limited regime. Though the inherent operational bandwidth of QPCs can eclipse the THz regime, the impedance mismatch with the external circuitry limits the operational frequency to a few kHz. Lumped-element impedance-matching circuits are successful only up to a few hundreds of MHz in frequency. QPCs are characterised by a complex impedance consisting of quantized resistance, capacitance, and inductance elements. Characterising the complex admittance at higher frequencies and understanding the coupling of QPC to other circuit elements and electromagnetic environments will provide valuable insight into its sensing and backaction properties. In this work, we couple a QPC galvanically to a superconducting stub tuner impedance matching circuit realised in a coplanar waveguide architecture to enhance the operation frequency into the GHz regime and investigate the electrical amplification and complex admittance characteristics. The device, operating at ∼ 1.96GHz, exhibits a conductance sensitivity of 2.92×10−5(e2/h)/Hz with a bandwidth of 13MHz. Besides, the RF reflected power unambiguously reveals the complex admittance characteristics of the QPC, shining more light on the behaviour of quantum tunnel junctions at higher operational frequencies.

Determination of the Bit Error Rate Due to Thermal Noise Using JoSIM Superconducting Circuit Simulator and the Monte Carlo Method

Thermal noise requires careful consideration during the design process of RSFQ circuits since it reduces circuit operating margins and can cause switching errors. Bit error rate (BER) provides a useful means of analysing the effect of this noise on a circuit. With tools developed under the IARPA SuperTools project, we present an implementation of the Monte-Carlo technique for determining BER via simulation. The Monte-Carlo method has been considered previously but not widely implemented due to slow simulation times preventing the determination of small BER values. We use JoSIM – an efficient simulator with SPICE syntax that allows for the simulation of superconducting components and noise sources with improved speed over older superconductor simulators. This speed improvement makes the Monte-Carlo method viable. The simulated BER is plotted against bias current with values in the low-BER region interpolated from the simulated values using MATLAB. We show how the results need to be used as a further qualifier of circuit performance for the characterization of a logic cell library.

An IEEE-Compatible JTAG Test-Access-Port Controller for RSFQ Logic and Systems

JTAG, an IEEE-standard test protocol, is widely used for testing commercial and experimental CMOS chips but appears unused for testing superconducting chips. The test-access-port (TAP) controller described here facilitates the use of JTAG to reduce the cost – in time and effort – of testing superconductive circuits. Our RSFQ-based TAP controller shifts data serially through a scan chain that transfers data in parallel to and from a circuit under test. Suitably designed scan chains can provide initial values to superconducting circuits and retrieve results to explore circuit behavior. A control computer or an internet connection can operate our TAP controller through a simple five-wire interface. Our TAP controller implements the TAP part of IEEE standard 1149.8.1-2012 in an area of only 580 x 280 micrometers, less area than two bonding pads. Our TAP Controller design information and MIT SFQ5ee layout will be freely available.

Stripline Topology for Flux Mitigation

The increasing complexity of modern single flux quantum (SFQ) circuits has increased the importance of flux trapping and trapped magnetic fields within SFQ systems. This trapped flux reduces margins while damaging the operability of superconductive circuits. In this paper, an area efficient stripline topology is introduced to prevent flux from being trapped within striplines. The topology is composed of coupled narrow lines rather than wide striplines. The proposed topology uses a fingered narrow line configuration. The fingered narrow line topology enhances the scalability of SFQ systems while not requiring additional area. The proposed topology decreases the length of the striplines by exploiting the mutual inductance between narrow parallel lines. The topology requires less area while preventing flux from being trapped within wide superconductive striplines. Due to the configuration of the proposed stripline, residual current is eliminated in VLSI complexity SFQ circuits. The fingered narrow line topology also reduces coupling capacitance between striplines. The proposed topology is compatible with automated routing of large scale SFQ integrated circuits.