Non-native Quantum Generative Optimization with Adversarial Autoencoders

TL;DR

The paper tackles the challenge of solving large-scale, non-native optimization problems on near-term quantum hardware by introducing the Adversarial Quantum Autoencoder Model (AQAM), a hybrid quantum-classical framework that maps non-native designs to a native latent space and performs Boltzmann sampling via a quantum-adversarial channel. It combines a classical autoencoder with a quantum MCMC-like updater that respects detailed balance to generate Boltzmann-consistent samples, guided by an energy-matching discriminator that ties native and non-native energy landscapes together. In numerical studies on a 12-qubit neutral-atom metasurface design, AQAM achieves lower Renyi divergence and larger spectral gaps than classical samplers, demonstrating stronger convergence to Boltzmann distributions and improved energy matching. The approach provides a practical route to leverage existing quantum samplers for non-native engineering inverse design and broadens the scope of quantum-enhanced generative modeling in near-term applications.

Abstract

Large-scale optimization problems are prevalent in several fields, including engineering, finance, and logistics. However, most optimization problems cannot be efficiently encoded onto a physical system because the existing quantum samplers have too few qubits. Another typical limiting factor is that the optimization constraints are not compatible with the native cost Hamiltonian. This work presents a new approach to address these challenges. We introduce the adversarial quantum autoencoder model (AQAM) that can be used to map large-scale optimization problems onto existing quantum samplers while simultaneously optimizing the problem through latent quantum-enhanced Boltzmann sampling. We demonstrate the AQAM on a neutral atom sampler, and showcase the model by optimizing 64px by 64px unit cells that represent a broad-angle filter metasurface applicable to improving the coherence of neutral atom devices. Using 12-atom simulations, we demonstrate that the AQAM achieves a lower Renyi divergence and a larger spectral gap when compared to classical Markov Chain Monte Carlo samplers. Our work paves the way to more efficient mapping of conventional optimization problems into existing quantum samplers.

Figures (7)

• Figure 1: Adversarial Quantum Autoencoder Model (AQAM): a generative quantum machine learning method Kao2023ExploringChemistryLopez-Piqueres2023SymmetricOptimization for MCMC sampling of non-native design spaces, shown here generating novel photonic metasurface unit cells. (A) By matching the native energy for each native sample ${z}_t$ (Purple line) with the objective function of the non-native design space (blue line), a native MCMC algorithm can explore a Boltzmann distribution in the non-native space (displayed images) by decoding samples from the native space. (B). A non-native unit cell design $\mathbf{\chi}$ (left) is encoded into a native bitstring ${z}_0$ using a classical encoder $\tilde{q}_\phi({z}_0|\mathbf{\chi})$. Each native bitstring sample ${z}_t$ is updated to the next sample ${z}_{t+1}$ using a quantum sampler ${z}_{t+1} \sim \Gamma_3({z}_{t+1} \vert {z}_{t})$.
• Figure 2: Spectral properties of classical and quantum MCMC samplers (A) A phase plot shows the spectral gap of a neutral atom quantum sampler with fixed inverse temperature $\tau = 10^{-1}$ for varying detuning strengths $\Delta \in [0, 7.8)$ (MHz) and evolution times $t_q \in [0, 3.8) \mu$s. The selected parameters for the quantum channel sampler are enclosed in the purple square. (B) Temperature $\tau \in [10^{-1}, 10^5]$ compares the spectral gap $\delta$ of the quantum $r_q$, single bit-flip $r_l$, and uniform $r_u$ proposal samplers.
• Figure 3: Broad Angle Filter: a periodic dielectric metasurface with a $\text{SiO}_2$ substrate and $\text{SiN}$ nanopillars. The filter reflects $840$nm light at an angle of incidence $\theta > 0.14$. The substrate and nanopillars thicknesses are 200nm and 420nm, respectively, with a unit cell width / lattice spacing of 1000nm. Transmissivity is plotted for the unit cell $T_u(\theta)$ (red line) and the ideal filter $T_i(\theta)$ (black line). The non-native objective function is the difference between the two lines as shaded in grey.
• Figure 4: AQAM Performance for Boltzmann Sampling of Broad Angle Filters: each point in plots (A) and (B) is averaged over the final 200 training epochs of 10 models with randomly initialized parameters $\mathbf{\theta}$ and $\mathbf{\phi}$ (Figure \ref{['fig:encoder_decoder']}), a constant training temperature $\tau \in [10^{-3}, 10^{3}]$, and a constant channel depth of $3$, i.e., $\Gamma_3$. (A) The binary cross-entropy reconstruction loss (\ref{['eq:aae']}) is measured for increasing training temperatures. The bit-flip sampler's lower reconstruction loss indicates the designs and bitstrings have more mutual information. Above each sampler's plot is an example design representative of the reconstruction quality for that sampler. (B) The discriminator loss $D({z}, \mathbf{\chi})$ is plotted for the same models as in (A). The quantum sampler has lower energy loss, indicating better energy matching between the design space cost function $C_\mathbf{\chi}$ and native energy function $C_{z}$. (C) The Renyi divergences (\ref{['eq:renyi']}) for varying channel depths $\Gamma_1, ..., \Gamma_9$ (color gradient) are plotted against the validation temperatures $\tau$ for both the single bit-flip (dash-dot line) and quantum (solid line) proposal samplers. The smaller Renyi divergence for the quantum proposal sampler and increasing channel depth indicates stronger convergence to a Boltzmann distribution over the validation samples.
• Figure 5: CNN Predictor Model: is a convolutional neural network (CNN) model trained to compute $C_\mathbf{\chi}$. The model utilizes 2D convolutions (gray), 2D batch normalization layers (dark green), Gaussian Error Linear Unit (GELU) activations, and maxpool layers (light green). All layer parameters are the same in each layer, where applicable, with the parameter labels being $k$-kernel size, $s$-stride, and $p$-padding.