Source-linked AI summary
Training of Quantum Circuits on a Hybrid Quantum Computer
D. Zhu, N. M. Linke, M. Benedetti, K. A. Landsman, N. H. Nguyen, C. H. Alderete, A. Perdomo-Ortiz, N. Korda, A. Garfoot, C. Brecque, L. Egan, O. Perdomo, C. Monroe
TL;DR
The paper addresses the limited evidence for successful generative quantum circuits on near-term quantum computers. It trains a high-dimensional universal circuit on Bars-and-Stripes using trapped-ion hardware and classical optimization, finding that Bayesian optimization outperforms Particle Swarm while hardware and sampling constraints remain important.
Problem
The paper targets the lack of a successful demonstration of generative quantum circuits on near-term quantum computers.
Method
The study trains reconfigurable parameterized quantum circuits with Particle Swarm and Bayesian optimization using a trapped-ion quantum computer.
Results
Bayesian optimization shows significant advantages over Particle Swarm for this task, while some target distributions require more circuit layers.
Takeaways & Limitations
Training generative quantum circuits with up to 26 parameters demonstrates a powerful hybrid quantum application and highlights both promise and challenges for hybrid learning.
Takeaways & Limitations
Quantum-computer sampling rate is limited by technical constraints.
Abstract
from arXiv · showhide
Generative modeling is a flavor of machine learning with applications ranging from computer vision to chemical design. It is expected to be one of the techniques most suited to take advantage of the additional resources provided by near-term quantum computers. We implement a data-driven quantum circuit training algorithm on the canonical Bars-and-Stripes data set using a quantum-classical hybrid machine. The training proceeds by running parameterized circuits on a trapped ion quantum computer, and feeding the results to a classical optimizer. We apply two separate strategies, Particle Swarm and Bayesian optimization to this task. We show that the convergence of the quantum circuit to the target distribution depends critically on both the quantum hardware and classical optimization strategy. Our study represents the first successful training of a high-dimensional universal quantum circuit, and highlights the promise and challenges associated with hybrid learning schemes.
One Sentence Summary
The study trains generative modeling circuits on a quantum-classical hybrid computer, highlighting optimization strategy and resource trade-offs.
- The study trains generative modeling circuits on a quantum-classical hybrid computer.
- It emphasizes the trade-off between classical optimization strategy and computational resources.
Introduction
The paper develops and evaluates data-driven quantum circuit learning for generative modeling on trapped-ion hardware, using BAS data and classical optimization. It compares circuit connectivity and optimization strategies while identifying hardware and sampling constraints on training quality.
- Motivation: Hybrid quantum algorithms combine classical and quantum resources to solve potentially difficult problems.
- Motivation: Generative modeling is motivated by applications including computer vision, speech synthesis, missing-text inference, image denoising, and chemical design.
- Data-driven quantum circuit learning: DDQCL trains a parameterized quantum circuit by sampling quantum outputs and updating parameters with a classical optimizer.
- Data-driven quantum circuit learning: After convergence, the circuit produces a quantum state capturing training-data correlations and serves as a generative model.
- Bars-and-Stripes task: The 2-by-2 Bars-and-Stripes data set provides a proof-of-principle generative-modeling task, with each pixel represented by a qubit.
- Experimental contribution: The experiment demonstrates generative quantum circuits trained on multi-qubit quantum hardware, following an earlier single-qubit experiment.
- Optimization strategies: Bayesian optimization shows significant advantages over Particle Swarm Optimization for this task.
- Training pipeline: The training loop executes parameterized circuits on trapped-ion hardware, compares measured and target distributions classically, and iteratively updates parameters.
Results
Training outcomes depended on circuit connectivity, hardware, and optimizer choice. PSO struggled on the deepest experimental circuit, whereas BO converged across the tested circuits while trading lower sample requirements for greater classical computation time.
- PSO was sensitive to initialization seeds, requiring experimentally testing different seeds and potentially multiple independent training rounds.
- The all-to-all circuit with one rotation and one entangling layer produced the desired BAS distribution under PSO.
- The four-layer star-connected simulation modeled BAS, but the trapped-ion experiment failed to converge despite sufficient sampling and a pre-screened seed.The authors attribute the failure to insufficient throughput in the presence of gate imperfections.
- BO experimentally converged for all tested circuits, including the four-layer star-connected circuit, in agreement with simulations.
- BO converged faster and required fewer samples without seed pre-selection, but its classical optimization consumed more time per iteration than PSO.Each BO circuit instance took 2-5 minutes, compared with about 1 minute for PSO circuit instances.
- The study evaluated trained hardware states using KL divergence, qBAS score, and entanglement entropy.Successfully trained circuits generated states consistent with a high level of entanglement.
Discussion
The demonstration trained reconfigurable generative quantum circuits with up to 26 parameters and supports scaling the approach to larger datasets. The discussion emphasizes that classical optimization costs and difficult circuit landscapes constrain hybrid quantum algorithms.
- The demonstration used reconfigurable generative quantum circuits with up to 26 parameters.The authors characterize this as one of the most powerful hybrid quantum applications to date.
- The approach can scale to larger datasets by increasing qubit number and adapting the cost function for sparser sampling.
- The training procedure can be adapted for other types of hybrid quantum algorithms.
- Classical optimization techniques for intermediate-scale quantum computers do not always succeed, and typical variational-circuit cost landscapes may resemble barren plateaus.
- As quantum computers scale to larger problems, the cost of classical optimization such as BO must be weighed against quantum algorithmic advantage.
Materials and Methods
The study trains parameterized circuits on a seven-ion trapped-ion quantum computer using Particle Swarm Optimization and Bayesian Optimization. Circuit performance is evaluated with distribution-based cost functions, while hardware fidelity, sampling rate, and optimizer behavior constrain convergence.
- Trapped Ion Quantum Computer: The trapped-ion platform uses seven 171Yb+ ions with optical pumping initialization, fluorescence readout, and Raman-beam control.Single-qubit gates use resonant Rabi rotations, while two-qubit gates use motional sideband interactions with amplitude modulation to disentangle motion.
- Trapped Ion Quantum Computer: Single-qubit gate fidelities are 99.5(2)%, while two-qubit gate fidelities are 98–99%.Two-qubit fidelity is mainly limited by residual qubit-motion entanglement, coherent crosstalk, and driving-intensity noise.
- Trapped Ion Quantum Computer: Gate errors produce an offset in the converged cost function, whereas ideal-system convergence is not significantly faster because classical optimization limits convergence behavior.Improving gate fidelity is expected to reduce the offset, but not necessarily accelerate convergence substantially.
- Trapped Ion Quantum Computer: The experiment is additionally limited by the quantum computer’s sampling rate, although control-system upload speed can improve it.At larger scale, full connectivity is expected to be sacrificed beyond about 20–30 qubits, with high-fidelity gates restricted to nearest neighbors.
- Classical Optimizers: PSO and BO: The two optimizers are Particle Swarm Optimization, which updates particle positions and velocities, and Bayesian Optimization, which uses a Gaussian-process surrogate and an acquisition function.The Bayesian method incorporates angular periodicity by modeling the parameter space as a hyper-torus rather than a hyper-cube.
- Classical Optimizers: PSO and BO: Bayesian Optimization outperforms PSO because acquisition functions reduce exploration of distant trajectories and surrogate models use historical evaluations more effectively.Its acquisition function trades off exploration against exploitation and accounts for expected improvement or uncertainty.
- Cost Functions: Training uses variants of Kullback-Leibler divergence to compare the target and measured distributions, with clipped negative log-likelihood used for PSO.KL divergence can diverge when the target supports an outcome absent from the model distribution.
Authors’ contributions
The authors divided responsibilities across research design, data collection and analysis, software development, and manuscript preparation. The contribution statement also reports a founding-scientist relationship with IonQ and identifies data availability in the paper and supplementary materials.
- D. Z, N. M. L, M. B, K. A. L, A. P, and C. M designed the research.
- A. L, N. H. N, C. H. A, A. P, L. E, and O. P collected and analyzed data.D. Z, M. B, A. P, and N. are also listed in the contribution statement fragment.
- K, A. G, and C. B contributed to the software used in the study, and all authors contributed to the manuscript.
- C. M. is a founding scientist of IonQ, Inc., while the other authors declare no competing interests.The paper states that all data needed to evaluate its conclusions are present in the paper or supplementary materials, with additional data available upon request.