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Review of Scientific Instruments

A co-simulation of superconducting qubit and control electronics for quantum computing

Zhanhong Jin, Shaowei Li, Xinzhe Wang, Futian Liang, Cheng-Zhi Peng

Published Oct 1, 2023• 4 citations
Publisher

Abstract

As the number of qubits in quantum computing increases, the scalability of existing qubit circuit structures and control systems may become insufficient for large-scale expansion and high-fidelity control. To address this challenge, we propose a behavioral-level model of a superconducting qubit and its control electronics, followed by a co-simulation to evaluate their performance. In this paper, we present the modeling process, simulation procedure, and resulting design specifications for the qubit control system. Our co-simulation approach utilizes MATLAB and Simulink, enabling us to derive critical circuit design specifications, such as the required Digital-to-Analog Converter (DAC) resolution, which should be 8 bits or higher, to achieve high-fidelity control. By taking into account factors such as DAC sampling rates, integral and differential nonlinearities, and filter characteristics, we optimize the control system for efficient and accurate qubit manipulation. Our model and simulation approach offer a promising solution to the scalability challenges in quantum computing, providing valuable insights for the design of large-scale superconducting quantum computing systems.

DOI
10.1063/5.0163725

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As the number of qubits in quantum computing increases, the scalability of existing qubit circuit structures and control systems may become insufficient for large-scale expansion and high-fidelity control. To address this challenge, we propose a behavioral-level model of a superconducting qubit and its control electronics, followed by a co-simulation to evaluate their performance. In this paper, we present the modeling process, simulation procedure, and resulting design specifications for the qubit control system. Our co-simulation approach utilizes MATLAB and Simulink, enabling us to derive critical circuit design specifications, such as the required Digital-to-Analog Converter (DAC) resolution, which should be 8 bits or higher, to achieve high-fidelity control. By taking into account factors such as DAC sampling rates, integral and differential nonlinearities, and filter characteristics, we optimize the control system for efficient and accurate qubit manipulation. Our model and simulation approach offer a promising solution to the scalability challenges in quantum computing, providing valuable insights for the design of large-scale superconducting quantum computing systems.
Quantum computers based on superconducting qubits have emerged as a leading candidate for a scalable quantum processor architecture. The core of a quantum processor consists of quantum devices that are manipulated using classical electronic circuits, which need to be co-designed for optimal performance and operation. As the principles governing the behavior of the classical circuits and the quantum devices are different, this presents a unique challenge in terms of the simulation, design and optimization of the joint system. A methodology is presented to transform the behavior of small-scale quantum processors to equivalent circuit models that are usable with classical circuits in a generic electrical simulator, enabling the detailed analysis of the impact of many important non-idealities. The methodology has specifically been employed to derive a circuit model of a superconducting qubit interacting with the quantized electromagnetic field of a superconducting resonator. Based on this technique, a comprehensive analysis of the qubit operation is performed, including the coherent control and readout of the qubit using electrical signals. Furthermore, the effect of several non-idealities in the system such as qubit relaxation, decoherence and leakage out of the computational subspace are captured, in contrast to previous works. As the presented method enables the co-simulation of the control electronics with the quantum system, it facilitates the design and optimization of near-term superconducting quantum processors.
Scaling up to a full-scale multi-qubit processor adds complexity to the control signals input requirements which can be addressed by the use of specially designed cryogenic interface circuits. In this paper, we discuss the use of cryogenic classical electronics for control of a fluxonium artificial atom. In recent years, fluxonium has gained notoriety among the superconducting qubit community for exceptionally long coherence times and large anharmonicity - both highly desirable properties when designing the next generation of qubit systems. The feasibility of controlling a fluxonium based quantum processors with a compact control system ultimately enables a highly scalable system; however, the cryogenic environment poses very strict requirements on electronics. Many trade-offs arise in terms of noise, power consumption, and circuit complexity. Addressing these requires comprehensive simulations that account for the physics of fluxonium qubits and the potential impact of control circuits on their performance. This paper focuses on the models and specification derivation for qubit control and explores constraints in fluxonium-based system design. The models and specifications derived enable the design of optimal control circuits targeted for scalable fluxonium quantum processors.
Control electronics for superconducting quantum processors have strict requirements for accurate command of the sensitive quantum states of their qubits. Hinging on the purity of ultra-phase-stable oscillators to upconvert very-low-noise baseband pulses, conventional control systems can become prohibitively complex and expensive when scaling to larger quantum devices, especially as high sampling rates become desirable for fine-grained pulse shaping. Few-gigahertz radio-frequency (RF) digital-to-analog converters (DACs) present a more economical avenue for high-fidelity control while simultaneously providing greater command over the spectrum of the synthesized signal. Modern RF DACs with extra-wide bandwidths are able to directly synthesize tones above their sampling rates, thereby keeping the system clock rate at a level compatible with modern digital logic systems while still being able to generate high-frequency pulses with arbitrary profiles. We have incorporated custom superconducting qubit control logic into off-the-shelf hardware capable of low-noise pulse synthesis up to 7.5 GHz using an RF DAC clocked at 5 GHz. Our approach enables highly linear and stable microwave synthesis over a wide bandwidth, giving rise to high-resolution control and a reduced number of required signal sources per qubit. We characterize the performance of the hardware using a five-transmon superconducting device and demonstrate consistently reduced two-qubit gate error (as low as 1.8%), which we show results from superior control chain linearity compared to traditional configurations. The exceptional flexibility and stability further establish a foundation for scalable quantum control beyond intermediate-scale devices.
The advancement of scalable quantum information processing relies on the accurate and parallel manipulation of a vast number of qubits, potentially reaching into the millions. Superconducting qubits, traditionally controlled through individual circuitry, currently face a formidable scalability challenge due to the excessive use of wires. This challenge is nearing a critical point where it might soon surpass the capacities of on-chip routing, I/O packaging, testing platforms, and economically feasible solutions. Here we introduce a multiplexed control scheme that efficiently utilizes shared control lines for operating multiple qubits and couplers. By integrating quantum hardware-software co-design, our approach utilizes advanced techniques like frequency multiplexing and individual tuning. This enables simultaneous and independent execution of single- and two-qubit gates with significantly simplified wiring. This scheme has the potential to diminish the number of control lines by one to two orders of magnitude in the near future, thereby substantially enhancing the scalability of superconducting quantum processors.
A quantum computer fundamentally comprises a quantum processor and a classical controller. The classical electronic controller is used to correct and manipulate the qubits, the core components of a quantum processor. To enable quantum computers scalable to millions of qubits, as required in practical applications, the simultaneous optimization of both the classical electronic and quantum systems is needed. In this paper, a co-design methodology is proposed for obtaining an optimized qubit performance while considering practical trade-offs in the control circuits, such as power consumption, complexity, and cost. The SPINE (SPIN Emulator) toolset is introduced for the co-design and co-optimization of electronic/quantum systems. It comprises a circuit simulator enhanced with a Verilog-A model emulating the quantum behavior of single-electron spin qubits. Design examples show the effectiveness of the proposed methodology in the optimization, design and verification of a whole electronic/quantum system.
Cryogenic classical electronics for the control of qubits can be placed near quantum processors for a more compact system, ultimately enabling a highly scalable one. However, cryogenic operation poses very strict power requirements on electronics, in addition to heavy constraints on precision in both amplitude and phase, as well as noise, so as to achieve the necessary fidelity. To test all the trade-offs that arise from these requirements, detailed simulations based on the physics of qubits and on the effects that circuits may have on them are needed. This paper focuses on the models and the simulation framework needed for quantum processors that can be efficiently executed on classical hardware. These models allow circuit design and specification derivation at all levels of the design. The suitability of the approach is demonstrated with superconducting qubit platforms and their control and characterization.