Low-T_c direct current superconducting quantum interference device magnetometer-based 36-channel magnetocardiography system in a magnetically shielded room

We constructed a 36-channel magnetocardiography（MCG） system based on low-Tc direct current（DC） superconducting quantum interference device（SQUID） magnetometers operated inside a magnetically shielded room（MSR）. Weakly damped SQUID magnetometers with large Steward–Mc Cumber parameter βc（βc≈ 5）, which could directly connect to the operational amplifier without any additional feedback circuit, were used to simplify the readout electronics. With a flux-to-voltage transfer coefficient V / Φ larger than 420 μV/Φ0, the SQUID magnetometers had a white noise level of about 5.5 f T·Hz-1/2when operated in MSR. 36 sensing magnetometers and 15 reference magnetometers were employed to realize software gradiometer configurations. The coverage area of the 36 sensing magnetometers is 210×210 mm2. MCG measurements with a high signal-to-noise ratio of 40 d B were done successfully using the developed system.

Implementation of quantum partial search with superconducting quantum interference device qudits in cavity QED

We present a method to implement the quantum partial search of the database separated into any number of blocks with qudits, D-level quantum systems. Compared with the partial search using qubits, our method needs fewer iteration steps and uses the carriers of the information more economically. To illustrate how to realize the idea with concrete physical systems, we propose a scheme to carry out a twelve-dimensional partial search of the database partitioned into three blocks with superconducting quantum interference devices （SQUIDs） in cavity QED. Through the appropriate modulation of the amplitudes of the microwave pulses, the scheme can overcome the non-identity of the cavity-SQUID coupling strengths due to the parameter variations resulting from the fabrication processes. Numerical simulation under the influence of the cavity and SQUID decays shows that the scheme could be achieved efficiently within current state-of-the-art technology.

Superconducting quantum bits

Superconducting quantum bits （qubits） and circuits are the leading candidate for the implementation of solid-state quantum computation. They have also been widely used in a variety of studies of quantum physics, atomic physics, quantum optics, and quantum simulation. In this article, we will present an overview of the basic principles of the superconducting qubits, including the phase, flux, charge, and transmon （Xmon） qubits, and the progress achieved so far concerning the improvements of the device design and quantum coherence property. Experimental studies in various research fields using the superconducting qubits and circuits will be briefly reviewed.

Demonstration of quantum permutation parity determine algorithm in a superconducting qutrit

A quantum algorithm provides a new way in solving certain computing problems and usually faster than classical algorithms. Here we report an implementation of a quantum algorithm to determine the parity of permutation in a single three-dimensional（3D） superconducting transmon qutrit system. The experiment shows the capacity to speed up in a qutrit,which can also be extended to a multi-level system for solving high-dimensional permutation parity determination problem.

Jnconventional Geometric Phase Gate with Superconducting Quantum Interference Device Qubits in Cavity QED

In the system with superconducting quantum interference devices （SQUID） in cavity, a scheme for constructing two-qubit quantum phase gate via a conventional geometric phase-shift is proposed by using a quantized cavity field and classical microwave pulses. In this scheme, the gate operation is realized in the subspace spanned by the two lower flux states of the SQUID system mud the population operator of the excited state has no effect on it. Thus the effect of decoherence caused from the levels of the SQUID system is possible to minimize. Under cavity decay, our strictly numerical simulation shows that it is also possible to realize the unconventional geometric phase gate. The experimental feasibility is discussed in detail.

Phase-controlled coherent population trapping in superconducting quantum circuits

We investigate the influences of the-applied-field phases and amplitudes on the coherent population trapping behavior in superconducting quantum circuits. Based on the interactions of the microwave fields with a single A-type three-level fluxonium qubit, the coherent population trapping could be obtainable and it is very sensitive to the relative phase and amplitudes of the applied fields. When the relative phase is tuned to 0 or π, the maximal atomic coherence is present and coherent population trapping occurs. While for the choice of π/2, the atomic coherence becomes weak. Meanwhile, for the fixed relative phase π/2, the value of coherence would decrease with the increase of Rabi frequency of the external field coupled with two lower levels. The responsible physical mechanism is quantum interference induced by the control fields, which is indicated in the dressed-state representation. The microwave coherent phenomenon is present in our scheme, which will have potential applications in optical communication and nonlinear optics in solid-state devices.

Unconventional Geometric Phase-Shift Gates Based on Superconducting Quantum Interference Devices Coupled to a Single-Mode Cavity

We present a scheme to realize geometric phase-shift gate for two superconducting quantum interference device （SQUID） qubits coupled to a single-mode microwave field. The geometric phase-shift gate operation is performed in two lower flux states, and the excited state [2〉 would not participate in the procedure. The SQUIDs undergo no transitions during the gate operation. Thus, the docoherence due to energy spontaneous emission based on the levels of SQUIDs are suppressed. The gate is insensitive to the cavity decay throughout the operation since the cavity mode is displaced along a circle in the phase space, acquiring a phase conditional upon the two lower flux states of the SQUID qubits, and the cavity mode is still in the original vacuum state. Based on the SQUID qubits interacting with the cavity mode, our proposed approach may open promising prospects for quantum iogic in SQUID-system.

Modulation of energy spectrum and control of coherent microwave transmission at single-photon level by longitudinal field in a superconducting quantum circuit

We study the effect of longitudinally applied field modulation on a two-level system using superconducting quantum circuits. The presence of the modulation results in additional transitions and changes the magnitude of the resonance peak in the energy spectrum of the qubit. In particular, when the amplitude ,λz and the frequency COl of the modulation field meet certain conditions, the resonance peak of the qubit disappears. Using this effect, we further demonstrate that the longitudinal field modulation of the Xmon qubit coupled to a one-dimensional transmission line could be used to dynamically control the transmission of single-photon level coherent resonance microwave.

Quantum search via superconducting quantum interference devices in a cavity

We propose a scheme for implementing the Grover search algorithm with two superconducting quantum interference devices （SQUIDs） in a cavity. Our scheme only requires single resonant interaction of the SQUID-cavity system and the required interaction time is very short. The simplicity of the process and the reduction of the interaction time are important for restraining decoherence.

True Random Number Generator Realized by Extracting Entropy from a Negative-Inductance Superconducting Quantum Interference Device

A new type of superconductive true random number generator (TRNG) based on a negative-inductance superconducting quantum interference device (nSQUID) is proposed. The entropy harnessed to generate random numbers comes from the phenomenon of symmetry breaking in the nSQUID. The experimental circuit is fabricated by the Nb-based lift-off process. Low-temperature tests of the circuit verify the basic function of the proposed TRNG. The frequency characteristics of the TRNG have been analyzed by simulation. The generation rate of random numbers is expected to achieve hundreds of megahertz to tens of gigahertz.

Design and implementation of control system for superconducting RSFQ circuit

The superconducting rapid single flux quantum(RSFQ)integrated circuit is a promising solu-tion for overcoming speed and power bottlenecks in high-performance computing systems in the post-Moore era.This paper presents an architecture designed to improve the speed and power limitations of high-performance computing systems using superconducting technology.Since superconducting microprocessors,which operate at cryogenic temperatures,require support from semiconductor cir-cuits,the proposed design utilizes the von Neumann architecture with a superconducting RSFQ mi-croprocessor,cryogenic semiconductor memory,a room temperature field programmable gate array(FPGA)controller,and a host computer for input/output.Additionally,the paper introduces two key circuit designs:a start/stop controllable superconducting clock generator and an asynchronous communication interface between the RSFQ and semiconductor chips used to implement the control system.Experimental results demonstrate that the proposed design is feasible and effective,provi-ding valuable insights for future superconducting computer systems.

Fabrication and characterization of superconducting multiqubit device with niobium base layer

Superconducting transmon qubits are the leading platform in solid-state quantum computing and quantum simulation applications.In this work,we develop a fabrication process for the transmon multiqubit device with a niobium base layer,shadow-evaporated Josephson junctions,and airbridges across the qubit control lines to suppress crosstalk.Our results show that these multiqubit devices have well-characterized readout resonators,and that the energy relaxation and Ramsey(spin-echo)dephasing times are up to∼40µs and 14(47)µs,respectively.We perform single-qubit gate operations that demonstrate a maximum gate fidelity of 99.97%.In addition,two-qubit vacuum Rabi oscillations are measured to evaluate the coupling strength between qubits,and the crosstalk among qubits is found to be less than 1%with the fabricated airbridges.Further improvements in qubit coherence performance using this fabrication process are also discussed.

Structure formation of entanglement entropy in a system of two superconducting qubits coupled with an LC-resonator

This paper investigates theoretically the evolutions of the entanglement entropy of a system of two coupled-charge- qubits interacting with an LC-resonator. It is found that when the initial states of the two qubits are prepared in a given superposition excited state, the evolution of the von Neumann entropy of the system depends significantly on the coupling strength between the two Josephson charge qubits. With the variation of the coupling strength, the evolution of the entanglement entropy of the system forms some structures, especially the periodically bistable properties, which are the first discovered for such a system to our knowledge. It is found that the relative entropy entanglement of the system is also sensitive to the variation of the coupling strength between the two charge qubits, some novel ＇collective oscillations＇ of the relative entropy are found for the system.

Quantum Entanglement of Two Flux Qubits Induced by an Auxiliary SQUID

We revisit a theoretical scheme to create quantum entanglement of two three-level superconducting quantuminterference devices (SQUIDs) with the help of an auxiliary SQUID.In this scenario,two three-level systems are coupledto a quantized cavity field and a classical external field and thus form dark states.The quantum entanglement can beproduced by a quantum measurement on the auxiliary SQUID.Our investigation emphasizes the quantum effect of theauxiliary SQUID.For the experimental feasibility and accessibility of the scheme,we calculate the time evolution of thewhole system including the auxiliary SQUID.To ensure the efficiency of generating quantum entanglement,relationsbetween the measurement time and dominate parameters of the system are analyzed according to detailed calculations.

Controlling group velocity in a superconductive quantum circuit

We investigate the controllable group velocity of a microwave probe field in a superconductive quantum circuit（SQC） pumped by microwave fields,and the use of such a SQC function as an artificial Λ-type three-level atom.The exchange between the subluminal and the superluminal states of the probe field can be realized simply by sweeping the pumping intensity,and the superluminal state is usually realized with a lower absorption.This work is one of the efforts to extend the study of electromagnetically induced transparency and its related properties from the lightwave band to the microwave band.

Interaction induced non-reciprocal three-level quantum transport

Besides its fundamental importance, non-reciprocity has also found many potential applications in quantum technology. Recently, many quantum systems have been proposed to realize non-reciprocity, but stable non-reciprocal process is still experimentally difficult in general, due to the needed cyclical interactions in artificial systems or operational difficulties in solid state materials. Here, we propose a new kind of interaction induced non-reciprocal operation, based on the conventional stimulated-Raman-adiabatic-passage (STIRAP) setup, which removes the experimental difficulty of requiring cyclical interaction, and thus it is directly implementable in various quantum systems. Furthermore, we also illustrate our proposal on a chain of three coupled superconducting transmons, which can lead to a non-reciprocal circulator with high fidelity without a ring coupling configuration as in the previous schemes or implementations. Therefore, our protocol provides a promising way to explore fundamental non-reciprocal quantum physics as well as realize non-reciprocal quantum device.

Implementation of a Controlled-Phase Gate and Deutsch-Jozsa Algorithm with Superconducting Charge Qubits in a Cavity

Based on superconducting quantum interference devices （SQUIDs） coupled to a cavity, we propose a scheme for implementing a quantum controlled-phase gate （QPG） and Deutsch-Jozsa （D J） algorithm by a controllable interaction. In the present scheme, the SQUID works in the charge regime, and the cavity field is ultilized as quantum data-bus, which is sequentially coupled to only one qubit at a time. The interaction between the selected qubit and the data bus, such as resonant and dispersive interaction, can be realized by turning the gate capacitance of each SQUID. Especially, the bus is not excited and thus the cavity decay is suppressed during the implementation of DJ algorithm. For the QPG operation, the mode of the bus is unchanged in the end of the operation, although its mode is really excited during the operations. Finally, for typical experiment data, we analyze simply the experimental feasibility of the proposed scheme. Based on the simple operation, our scheme may be realized in this solid-state system, and our idea may be realized in other systems.

Multiplexing technology based on SQUID for readout of superconducting transition-edge sensor arrays

Multiplexing technologies based on superconducting quantum interference devices(SQUIDs) are crucial to cryogenic readout of superconducting transition-edge sensor(TES) arrays. Demands for large-scale TES arrays promote the development of multiplexing technologies towards large multiplexing factors and low readout noise. The development of multiplexing technologies also facilitates new applications of TES arrays in a wide range of frequencies. Here we summarize different types of SQUID-based multiplexing technologies including time-division multiplexing, code-division multiplexing, frequency-division multiplexing and microwave SQUID multiplexing. The advances and parameter constraints of each multiplexing technology are also discussed.

Switching from positive to negative absorption with electromagnetically induced transparency in circuit quantum electrodynamics

We present a theoretical study of electromagnetically induced transparency （EIT） in a superconducting quantum circuit with a tunable V-shaped energy spectrum derived from two superconducting Josephson charge qubits coupled with each other through a superconducting quantum interference device. Using the density matrix formalism and the steady-state approximation, we obtain the analytical expressions of the first-order matrix element associated with the absorption and dispersion of the probe field for two different V-type schemes. Our results show that, for this superconducting quantum system, it is possible to realize a remarkable phenomenon that dynamic conversion between EIT and EIT with amplification without population inversion. Such a unique optical feature has potential applications in quantum optical devices and quantum information processing.

Increasing linear flux range of SQUID amplifier using self-feedback effect

Superconducting quantum interference devices(SQUIDs) are low-noise amplifiers that are essential for the readouts of translation edge sensors(TESs). The linear flux range is an important parameter for SQUID amplifiers, especially those controlled by high-bandwidth digital flux-locked-loop circuits. A large linear flux range conduces to accurately measuring the input signal and also increasing the multiplexing factor in the time-division multiplexed(TDM) readout scheme of the TES array. In this work, we report that the linear flux range of an SQUID can be improved by using self-feedback effect. When the SQUID loop is designed to be asymmetric, a voltage-biased SQUID shows an asymmetric current–flux(I–Φ) response curve. The linear flux range is improved along the I–Φ curve with a shallow slope. The experimental results accord well with the numerical simulations. The asymmetric SQUID will be able to serve as a building block in the development of the TDM readout systems for large TES arrays.