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arXiv:2008.02873 · IEEE Transactions on Quantum Engineering

High-Fidelity Control of Superconducting Qubits Using Direct Microwave Synthesis in Higher Nyquist Zones

William D. Kalfus, Diana F. Lee, Guilhem J. Ribeill, Spencer D. Fallek, Andrew Wagner, Brian Donovan, Diego Ristè, Thomas A. Ohki

Published Jan 1, 2020• 27 citations

Abstract

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.

DOI: 10.1109/tqe.2020.3042895

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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.

Current state of the art quantum computing experiments in the microwave regime use control pulses generated by modulating microwave tones with baseband signals generated by an arbitrary waveform generator (AWG). Recent advances in digital analog conversion technology have made it possible to directly synthesize arbitrary microwave pulses with sampling rates up to 92 gigasamples per second (GS/s). These new high bandwidth AWG's could dramatically simplify the classical control chain for quantum computing experiments, enabling more advanced pulse shaping and reducing the number of components that need to be carefully calibrated. Here we use a high speed AWG to study the viability of such a simplified scheme. We characterize the AWG and perform randomized benchmarking of a superconducting qubit, achieving average single qubit gate error rates below

5\times10^{-4}

.

Superconducting qubits are the promising candidate to realize large-scale quantum computing systems. Well-known quantum algorithms, such as Shor's algorithm, require at least

10^{5}

to

10^{6}

qubits to execute. Accordingly, classical systems for controlling superconducting qubits must also be scalable. One critical scalability challenge lies in the circuit cost of an RF pulse generator used to implement quantum gate operations. This poster proposes a cost-effective architecture for an RF pulse generator tailored to superconducting qubits. Most existing works use arbitrary waveform generators (AWGs) that require both a high-bandwidth memory (HBM) and a high-performance digital-analog converter (DAC) to achieve the highest gate fidelity with an optimized RF pulse waveform. The proposed pulse generator architecture significantly simplifies both the generator circuit and the waveform of the RF pulse to cost-aware square pulses. This architecture eliminates the requirement for power- and cost-intensive AWG, which is a major obstacle in realizing scalable quantum computers. Additionally, this poster demonstrates that our architecture can mitigate the error source associated with simplified RF pulses. Quantum dynamics simulation of transmon qubits, wherein the state of the system evolves with time, demonstrates that our pulse generator can achieve practically the same fidelity of gate operations for single and multiple qubits as ideal RF pulses while substantially reducing the sampling rate of DACs and the bandwidth of memories.

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.

We investigate the XY control and manipulation of the superconducting qubit state using direct digital synthesis (DDS) for the microwave pulse signal generation. The decoherence time, gate fidelity, and other qubit properties are measured and carefully characterized, and compared with the results obtained by using the traditional mixing technique for the microwave pulse generation. In particular, the qubit performance in the state manipulation with respect to the sampling rate of DDS is studied. Our results demonstrate that the present technique provides a simple and effective method for the XY control and manipulation of the superconducting qubit state. Realistic applications of the technique for the possible future scalable superconducting quantum computation are discussed.

Control electronics synchronization is of vital importance in scaling up modular quantum computer implementations. It is a critical performance parameter in distributed quantum computing. We present a White Rabbit-based control electronics synchronization architecture using multiple AMD Ultrascale+ architecture-based Radio Frequency System on Chips (RFSoC). White Rabbit ensures precise synchronization across all Radio Frequency Digital-to-Analog Converters (RF-DACs) and Analog-to-Digital Converters (RF-ADCs) in a multi-board architecture and also establishes a classical network between the boards. This synchronization is crucial for generating multiple control signals required for scaling up the number of qubits in quantum computing architectures. By minimizing phase jitter and timing inconsistencies across boards, this approach can significantly improve qubit gate operations, error correction efficiency, and overall system performance.

Building a large-scale quantum computer requires the co-optimization of both the quantum bits (qubits) and their control electronics. By operating the CMOS control circuits at cryogenic temperatures (cryo-CMOS), and hence in close proximity to the cryogenic solid-state qubits, a compact quantum-computing system can be achieved, thus promising scalability to the large number of qubits required in a practical application. This work presents a cryo-CMOS microwave signal generator for frequency-multiplexed control of 4 × 32 qubits (32 qubits per RF output). A digitally intensive architecture offering full programmability of phase, amplitude, and frequency of the output microwave pulses and a wideband RF front end operating from 2 to 20 GHz allow targeting both spin qubits and transmons. The controller comprises a qubit-phase-tracking direct digital synthesis (DDS) back end for coherent qubit control and a single-sideband (SSB) RF front end optimized for minimum leakage between the qubit channels. Fabricated in Intel 22-nm FinFET technology, it achieves a 48-dB SNR and 45-dB spurious-free dynamic range (SFDR) in a 1-GHz data bandwidth when operating at 3 K, thus enabling high-fidelity qubit control. By exploiting the on-chip 4096-instruction memory, the capability to translate quantum algorithms to microwave signals has been demonstrated by coherently controlling a spin qubit at both 14 and 18 GHz.