Source-linked AI summary
Quantum Circuit Design Search
Mohammad Pirhooshyaran, Tamas Terlaky
TL;DR
Finding trainable parameterized quantum circuits remains an open design challenge, with vanishing gradients reported for broad classes of circuits. The paper searches discrete designs using random search, reinforcement learning, and Bayesian optimization, and reports better-performing designs on Iris and an unseen Glass dataset.
Problem
Finding more trainable PQC designs remains underexplored, while random designs and global-observable cost functions can produce exponentially vanishing gradients.
Source: §1 · p. 1Method
The paper searches discrete PQC designs using random search with survival of the fittest, reinforcement learning, and black-box Bayesian optimization, with data reuploading as an option.
Source: §1 · p. 2, §3.2 · p. 5, §4 · p. 8Results
Some discovered designs perform considerably better than the benchmark in train and test losses on Iris, and selected designs perform meaningfully better on unseen Glass.
Source: §4 · p. 7, §4.1 · p. 11Takeaways & Limitations
The authors conclude that optimization strategies can have a strong impact on PQC design and yield nontrivial automated architectures that are hard to design by hand.
Source: §5 · p. 13
Abstract
from arXiv · showhide
This article explores search strategies for the design of parameterized quantum circuits. We propose several optimization approaches including random search plus survival of the fittest, reinforcement learning both with classical and hybrid quantum classical controllers and Bayesian optimization as decision makers to design a quantum circuit in an automated way for a specific task such as multi-labeled classification over a dataset. We introduce nontrivial circuit architectures that are arduous to be hand-designed and efficient in terms of trainability. In addition, we introduce reuploading of initial data into quantum circuits as an option to find more general designs. We numerically show that some of the suggested architectures for the Iris dataset accomplish better results compared to the established parameterized quantum circuit designs in the literature. In addition, we investigate the trainability of these structures on the unseen dataset Glass. We report meaningful advantages over the benchmarks for the classification of the Glass dataset which supports the fact that the suggested designs are inherently more trainable.
1 Introduction
Although PQCs are widely used and gradient methods can tune their parameters, finding designs that remain trainable has not been fully explored. This study searches discrete circuit designs for supervised learning, including multi-label classification, using several optimization strategies.
1 Introduction
- Vanishing gradients in broad classes of PQCs motivate the search for more trainable designs, a problem the authors say remains underexplored.Random designs and global-observable cost functions can yield exponentially vanishing partial gradients.Source: §1 · p. 1
- Prior circuit-search approaches include rotation selection, Gibbs-objective ansatz search, evolutionary optimization, and reinforcement learning for QAOA circuits.The cited approaches are Rotoselect [20], AAS [21], evolutionary methods [23], and QAOA circuit optimization.Source: §1 · p. 1
- The study focuses on discrete design search for trainability and extends benchmark PQC modeling by making data reuploading an option.The authors distinguish this focus from Zhang et al. [25], which uses a continuous differentiable search space.Source: §1 · p. 2
- Random search with survival of the fittest, reinforcement learning, and black-box Bayesian optimization are used to search for designs.The reinforcement-learning approach includes classical and hybrid quantum-classical policy-gradient controllers.Source: §1 · p. 2
- The study seeks better test accuracy or loss while keeping parameter counts fixed, evaluating multi-label classification on small-to-moderate Iris and Glass datasets.The authors prioritize trainability over device efficiency and do not require designs to use only operations already applied on real quantum devices.Source: §1 · p. 2
2 Theory and Background
Parameterized quantum circuits (PQCs) combine quantum operations with classical optimization and can be used for supervised learning. This section describes their objective and circuit structure, including optional data reuploading and an observable suited to classification.
2 Theory and Background
- PQC training minimizes the expected loss between circuit output f(x; θ) and labels y, with expectations reflecting stochastic data sampling, noise, and measurement.The circuit output is the expectation of observable H after U(x; θ) acts on the initial state.Source: §2 · p. 2
- A general PQC chains unitary transformations over N qubits and L layers, with an option to reupload initial input features at later layers.Feature reuploading can be rejected for a layer; nonparametric gates may include Pauli, Hadamard, CNOT, CSwap, and Toffoli operations.Source: §2 · pp. 2–3
- For classification, the introduced observable produces outputs that can pass through a classical softmax; the number of measured output qubits need not equal the input-qubit count.The observable is described as trainable and classification-suitable, though lacking the operational interpretation of trace-distance cost functions.Source: §2 · p. 3
- Parameterized gates generated by Hermitian operators with two unique eigenvalues, including Pauli matrices, permit partial derivatives to be calculated with the parameter-shift rule [12].Source: §2 · p. 3
- PQCs may be components of larger classical or quantum architectures, and their measured outputs can feed another model; when used last, measured-qubit count is set to the number of classes.The final PQC output is then evaluated with negative log-likelihood loss.Source: §2 · p. 3
- A controller can propose a circuit design, receive its training accuracy or loss, and update its parameters using policy-gradient reinforcement learning.The update also considers suggested-design entropy and the policy distribution.Source: Figure 1 · p. 4
3 Design Search
QCDS searches a discrete space of circuit designs using reinforcement learning, random search, or Bayesian optimization, with validation accuracy or loss as the performance metric.
3 Design Search
- Each qubit can accept or reject data reuploading, choose an Rx, Ry, or Rz rotation, and select a nonparametric gate from eight options.For a four-qubit layer, this search space contains more than five million designs.Source: §3 · p. 4
3.1 Reinforcement learning for QCDS
- The reinforcement-learning controller samples a circuit design from a policy, receives validation accuracy or loss after circuit training, and updates its policy using policy gradients.Controllers may propose a complete design or a layer repeated throughout the circuit; hybrid controllers use small PQCs to make design decisions.Source: §3.1 · pp. 4–5, Figure 2 · p. 5, Figure 3 · p. 5
3.2 Random Search
- Random search samples distinct designs, trains them briefly, retains better-performing candidates, and repeats until remaining designs can be fully trained or rankings stabilize.In the reported numerical cases, initial training uses two epochs and retains the better half of designs.Source: §3.2 · pp. 5–6
3.3 Black-Box Bayesian Optimization
- Bayesian optimization treats each circuit as a black-box objective, maps discrete choices to integer outcomes in bounded intervals, and selects designs using logarithmic expected improvement on validation loss.The acquisition function seeks the design with the greatest expected validation-loss reduction.Source: §3.3 · p. 6
4 Results
Across Iris and Glass, searched circuit designs sometimes outperform the Ry rotation + CNOT benchmark, while unoptimized data reuploading can perform worse. On Glass, Iris-selected designs also show higher test accuracy than the benchmark.
4 Results
- On Iris, some of the best 1000 random designs reached 100% test accuracy quicker than the benchmark and largely maintained it, while the benchmark’s accuracy dropped slightly.Many random designs were not competitive; only 30,000 designs were sampled, a tiny fraction of the search space.Source: §4 · p. 7, Figure 6 · p. 8
- Reuploading the initial data at every layer made the benchmark design perform worse, so the paper treats reuploading as an option to optimize rather than a fixed choice.The authors caution that adding gates without careful design or optimization can yield less-trainable circuits.Source: §4 · pp. 7–8
- The four policy-gradient R-QCDS schemes converged to a unique design in fewer than 50 feedback loops, with stable train and test accuracy but marginally worse test loss than the benchmark.Each suggested circuit was trained from scratch for 50 epochs per feedback loop.Source: §4 · p. 8, Figure 7 · p. 9
- After about 70 function evaluations, Bayesian optimization suggested a design that performed better than the Ry rotation + CNOT benchmark.The PQCs were trained for 100 epochs at each evaluation, and validation loss was the comparison metric.Source: Figure 4 · p. 6, §4 · p. 8
4.1 Generalization
- On Glass, the best test accuracy was 64.1% versus the benchmark’s 54.7%, and six designs improved test accuracy.The best result came from a randomly discovered design; the second-best was found by R-QCDS.Source: §4.1 · p. 11, Figure 11 · p. 11
5 Conclusion
The paper applies random search, reinforcement learning, and Bayesian optimization to quantum circuit design search, with the goal of finding trainable designs. It reports nontrivial automated circuits and compares their performance with benchmark designs, including on an unseen dataset.
5 Conclusion
- The paper presents quantum circuit design search focused on the trainability of parameterized quantum circuits.It describes the work as one of the first studies focused on this framework.Source: §5 · p. 13
- Three strategies search for efficient circuit designs: random search with survival of the fittest, reinforcement learning, and Bayesian optimization.The resulting nontrivial automated designs are described as hard to design by hand.Source: §5 · p. 13
- The authors evaluate the designs against benchmark parameterized circuits, including on an unseen dataset, and report a strong impact of optimization strategies on circuit design.Source: §5 · p. 13