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Neural network search for optimal pulse trains for qubit dynamics control

Michael A. Sergeev, M. V. Bastrakova, Vsevolod A. Vozhakov, N. V. Klenov, Igor I. Soloviev, Maxim V Tereshonok

Published Jan 1, 2024• 1 citation

Abstract

Despite its insensitivity to charge noise, the transmon's anharmonicity and control pulse length are limited. Transmon state control traditionally involves a quadrature mixer that mixes microwave signals from a room-temperature oscillator and an arbitrary waveform generator to control the single qubit states. Scaling upquan tum processors faces challenges in hardware, management of qubit operations, and read-out procedure due to the large amount of expensive room-temperature equipment required for each qubit. Operating at millikelvin temperatures, these devices introduce thermal noise, reducing qubit lifetime and distorting control signals. An alternative promising control method is based on superconducting digital electronics. In these digital circuits, a bit of information is represented by a short unipolar voltage pulse generated when a single flux quantum (SFQ) pulse passes through a Josephson junction. The qubit states are controlled by the action of a sequence of SFQ pulses, with the pulse-to-pulse timing adjusted to induce a coherent rotation of the state vector in the computational subspace and to minimize leakage to the outside. The paper discusses a method for controlling the states of a transmon qubit using digital superconducting electronics. In this approach, the sequences of picosecond voltage pulses are used to control the state of a quantum computing system. We have considered a control scheme based on a bipolar pulse generator and proposed an algorithm for finding the optimal implementation of a bipolar short pulse control sequence for performing high-precision single-bit operations (with fidelity equal to 99,99 %) using deep learning algorithms with rein forcement: AlphaGo Zero, AlphaZero and Proximal Policy.

DOI: 10.36724/2072-8735-2024-18-7-56-63

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Nowadays most of superconducting quantum processors use charge qubits of a transmon type. They require implementation of energy efficient qubit state control scheme. A promising approach is the use of superconducting digital circuits operating with single-flux-quantum (SFQ) pulses. The duration of SFQ pulse control sequence is typically larger than that of conventional microwave drive pulses but its length can be optimized for the system with known parameters. Here we introduce a genetic algorithm for unipolar or bipolar SFQ control sequence search that minimize qubit state leakage from the computational subspace. The algorithm is also able to find a solution in the form of a repeating subsequence in order to save memory on the control chip. Its parallel implementation can find the appropriate sequence for arbitrary system parameters from a practical range in a reasonable time. The algorithm is illustrated by the example of the rotation gate around the Y-axis by an angle

\pi/2

with fidelity over 99.99

\%

. In this paper, we present the results for a single-qubit system, but in the future we will apply the developed approach to study a system of two qubits.

Abstract The development of quantum computers based on superconductors requires the improvement of the qubit state control approach aimed at the increase of the hardware energy efficiency. A promising solution to this problem is the use of superconducting digital circuits operating with single-flux-quantum (SFQ) pulses, moving the qubit control system into the cold chamber. However, the qubit gate time under SFQ control is still longer than under conventional microwave driving. Here we introduce the bipolar SFQ pulse control based on ternary pulse sequences. We also develop a robust optimization algorithm for finding a sequence structure that minimizes the leakage of the transmon qubit state from the computational subspace. We show that the appropriate sequence can be found for arbitrary system parameters from the practical range. The proposed bipolar SFQ control reduces a single qubit gate time by halve compared to nowadays unipolar SFQ technique, while maintaining the gate fidelity over 99.99%.

Today, most superconducting quantum processors are based on transmons, the modifications of charge qubits. Traditional transmon control schemes for implementing high-fidelity quantum gates are based on the analog microwave signals. Current problems with this type of control are bulkiness, high cost, and unwanted feedback from the microwave equipment, which increases with the number of qubits involved. A promising breakthrough is the use of superconducting digital circuits operating with picosecond (single flux quantum or SFQ) pulses. In our previous work, we have shown how to use SFQ control sequences to implement the rotation of a qubit at rest on the Bloch sphere around the Y-axis by an angle

\pi/2

with fidelity better than 99.99

\%

. The next important step is to implement two-qubit operations. Here we present the Genetic Algorithm for SFQ Control Sequence Search, which implements the original control protocol using the ZX operation as an example. The algorithm also takes into account the leakage to the higher energy states of the system. Its parallel implementation can find the appropriate sequence for arbitrary system parameters from a practical range in a reasonable time. As a result of numerical experiments, control sequences were found that implement the ZX operation with 0.999 target level population.

Compared to traditional semiconductor control electronics (TSCE) located at room temperature, cryogenic single flux quantum (SFQ) electronics can provide qubit measurement and control alternatives that address critical issues related to scalability of cryogenic quantum processors. Single-qubit control and readout have been demonstrated recently using SFQ circuits coupled to superconducting qubits. Experiments where the SFQ electronics are co-located with the qubit have suffered from excess decoherence and loss due to quasiparticle poisoning of the qubit. A previous experiment by our group showed that moving the control electronics to the 3 K stage of the dilution refrigerator avoided this source of decoherence in a high-coherence 3D transmon geometry. In this paper, we also generate the pulses at the 3 K stage but have optimized the qubit design and control lines for scalable 2D transmon devices. We directly compare the qubit lifetime

T_1

, coherence time

T_2^*

and gate fidelity when the qubit is controlled by the Josephson pulse generator (JPG) circuit versus the TSCE setup. We find agreement to within the daily fluctuations for

T_1

and

T_2^*

, and agreement to within 10% for randomized benchmarking. We also performed interleaved randomized benchmarking on individual JPG gates demonstrating an average error per gate of

0.46

% showing good agreement with what is expected based on the qubit coherence and higher-state leakage. These results are an order of magnitude improvement in gate fidelity over our previous work and demonstrate that a Josephson microwave source operated at 3 K is a promising component for scalable qubit control.

Abstract Reaching high-speed, high-fidelity qubit operations requires precise control over the shape of the underlying pulses. For weakly anharmonic systems, such as superconducting transmon qubits, short gates lead to leakage to states outside of the computational subspace. Control pulses designed with open-loop optimal control may reduce such leakage. However, model inaccuracies can severely limit the usability of such pulses. We implemented a closed-loop optimization that simultaneously adapts all control parameters based on measurements of a cost function built from Clifford gates. We directly optimize the amplitude and phase of each sample point of the digitized control pulse. We thereby fully exploit the capabilities of the pulse generation electronics and create a 4.16 ns single-qubit pulse with 99.76 % fidelity and 0.044 % leakage. This is a sevenfold reduction of the leakage rate and a threefold reduction in standard errors of the best DRAG pulse we have calibrated at such short durations on the same system.

In the traditional approach to controlling superconducting qubits using microwave pulses, the field of pulse shaping has emerged in order to assist in the removal of leakage and increase gate fidelity. However, the challenge of scaling microwave control electronics has created an opportunity to explore alternative methods such as single-flux quantum (SFQ) pulses. For qubits controlled by SFQ pulses, high fidelity gates can be achieved by optimizing the binary control sequence. We extend the notion of the derivative removal by adiabatic gate (DRAG) framework a transmon qubit controlled by SFQ drivers. The proposed implementation of SFQ pulse sequences can be stored in 22 bits or fewer, with gate fidelities exceeding 99.99%. This modest memory requirement could help reduce the footprint of the SFQ coprocessors and power dissipation while preserving their inherent advantages of scalability and cost-effectiveness.