Robust Implementation of Generative Modeling with Parametrized Quantum Circuits

I. INTRODUCTION

• DDQCL was proposed to probe NISQ-device capabilities in generative modeling and to compare hybrid-algorithm choices such as circuit connectivity, gate type, and optimizer.The paper situates this role alongside hybrid algorithms including VQE and QAOA [7].Source: §I · p. 1
• Earlier on-hardware DDQCL studies explored circuit ansätze on superconducting qubits and quantum-processing proposals plus optimizer choice on ion-trap hardware.The introduction identifies these as prior implementations [2] and [3].Source: §I · pp. 1–2
• Solver variability across random initializations makes a single training curve an unreliable indicator of typical performance, while each curve typically requires thousands of hardware circuits.The paper argues that several runs per setting are needed to compare optimizers and entangling connectivities robustly.Source: §I · p. 2
• The study presents an experimentally robust comparison of hybrid quantum-classical algorithm components using DDQCL as its performance framework.Rigetti’s Quantum Cloud Services supports the study with pre-compilation, active reset, and low-latency co-location of quantum and classical hosts.Source: §I · p. 2

II. DDQCL EXECUTION ON RIGETTI’S QPU

• The (2, 2) Bars and Stripes task uses six bitstrings, each with target probability 1/6, and zero probability for other bitstrings.Dark pixels map to 1 and white pixels to 0; the six encodings are {0000, 1010, 0101, 0011, 1100, 1111}.Source: §II · p. 2, Figure 2 · p. 2
• The four-qubit circuit uses star or line entangling topology, with native CZ gates and Ry rotations that keep amplitudes real while reducing parameter count.The authors state that real amplitudes suffice for the generative model’s target.Source: §II · p. 2
• Training evaluates the output distribution against the target distribution using Jensen-Shannon divergence, then updates circuit parameters with a classical optimizer.Optimization seeks to minimize the divergence score.Source: §II · p. 2

III. RESULTS

• DKL was 0.14 for the best star-topology model and 0.44 for the best line-topology model, both obtained with ZOOPT.The Rigetti result at DKL = 0.14 was better than the reported IBM Tokyo result of 0.36 and comparable to the trapped-ion result of 0.09.Source: §III · p. 3
• The benchmark compares ZOOPT, SVHC, and ADAM using five independent random initializations per setting.Each run evaluated 2,000 circuit realizations with 3,000 measurement shots each.Source: §III · p. 3
• A second entangling round significantly improved star-topology performance, while line topology showed significantly less improvement or slower convergence.Noiseless simulations did not establish a clear advantage for star over line connectivity.Source: §III · p. 3
• The paper reports qBAS scores for the main experimental features in Table I, calculated using the procedure in Ref. [1].The supplied passage does not state the table’s individual score values.Source: §III · p. 3, Table I · p. 3

IV. SUMMARY AND OUTLOOK

• The on-hardware comparison tests entangling layout and depth, classical optimizer selection, and post-processing strategies such as readout correction.Source: §IV · p. 3
• The study is not exhaustive; optimizing the classical solvers themselves remains difficult, and automatic hyperparameter setting is left to future work.Source: §IV · p. 3
• The authors identify gradient-based training and adding ancillary qubits as directions for experimental extensions of DDQCL.Source: §IV · p. 3
• The qBAS score is presented as a way to measure NISQ-device power beyond single- and two-qubit gate fidelity; robust benchmarking infrastructure is described as a step toward comparing algorithmic and hardware proposals.Source: §IV · pp. 3, 5
• Figure 3 compares ADAM, SVHC, and ZOOPT across line and star topologies on the (2, 2) BAS and Stripes dataset, including the lowest-cost distribution and its KL divergence from the target.Source: Figure 3 · p. 4
• Circuit depth is compared across line and star layouts; the figure describes a relative improvement for star topology while one- and two-layer learning-curve variances overlap.A four-qubit entangling layer uses 6 Ry rotations and 3 CZ gates in either topology.Source: Figure 4 · p. 4

Appendix A: DDQCL pipeline

• DDQCL represents binary dataset examples as computational-basis states and aims for a quantum state whose measurement probabilities mimic the dataset distribution.Source: Appendix A · pp. 5–6
• A parametrized circuit of single-qubit rotations and entangling gates prepares the model state; its parameters are tuned to minimize the loss from its distribution to the dataset distribution.Source: Appendix A · p. 6
• The pipeline uses Jensen–Shannon divergence as its loss, a symmetrized and smoothed version of Kullback–Leibler divergence defined using the average of two distributions.Source: Appendix A · p. 6
• After evaluating the divergence between the model and target distributions, a classical optimizer updates the circuit parameters to reduce the loss, repeating until a convergence criterion is met.Source: Appendix A · p. 6

• The two-qubit U2 gate maps three parameters one-to-one to real-amplitude two-qubit states, which are paired by topology to build four-qubit circuits.The study uses line and star topologies, with circuits up to 16 local rotations and 6 CZ gates.Source: §1 · p. 6
• Noiseless in-silico simulations show the layout can learn a quantum model that reproduces the (2, 2)BAS target probability.Source: §1 · p. 6
• The layout reduces parameters relative to arbitrary single-qubit rotations, but the trade-off between model flexibility and optimization difficulty is beyond this work’s scope.Additional parameters could open more paths in Hilbert space and increase the number of states that could yield a perfect PX.Source: §1 · p. 6

• The three benchmarked solvers are ZOOPT, SVHC, and ADAM.Source: §2 · pp. 6–7
• ZOOPT and SVHC handle the stochastic cost function with “value suppression” and start from a search point selected by evaluating 3L random initial circuits.Source: §2 · p. 7
• ADAM uses learning rate α = 0.2 and decay rates β1 = 0.9 and β2 = 0.999, following the setup in Ref. [2].Source: §2 · p. 7

• Because the procedure characterizes all 2^N projectors, it uses an exponential number of experiments, a choice made for the study’s small qubit count.Source: §3 · p. 7
• The procedure measures output distributions for each computational-basis input, forms a transition matrix, and applies its inverse to the observed readout distribution.The matrix is recalculated before each batch of five learning curves.Source: §3 · p. 7
• KL divergence reaches ∼0.13 with readout correction, compared with ∼1.0 for bare readouts.The comparison is shown in the full learning curves and histograms.Source: Figure 5 · p. 7, §3 · p. 7

• The simulations assume noiseless qubits but retain finite-readout stochasticity, using 3,000 shots per circuit.Source: Figure 6 · p. 8
• Table II reports performance figures of merit from in-silico simulations of the different HQC features explored.Source: Table II · p. 8