RhoDARTS: Differentiable Quantum Architecture Search with Density Matrix Simulations

TL;DR

ρDARTS reframes quantum architecture search as a differentiable, density-matrix–based optimization problem, enabling end-to-end training of both circuit architecture and gate parameters without circuit sampling. By representing the search space as a mixed quantum state and incorporating generic noise channels (e.g., depolarizing), it overcomes fundamental limitations of state-vector–based methods. The method supports macro and micro search settings, uses entropy and angle regularization to balance exploration and parameter stability, and demonstrates improved fidelity and reduced simulation budgets across state initialization, VQE, and max-cut tasks. This approach yields robustness to noise and offers a scalable framework for designing PQCs tailored to VQAs and quantum machine learning applications.

Abstract

Variational Quantum Algorithms (VQAs) are a promising approach to leverage Noisy Intermediate-Scale Quantum (NISQ) computers. However, choosing optimal quantum circuits that efficiently solve a given VQA problem is a non-trivial task. Quantum Architecture Search (QAS) algorithms enable automatic generation of quantum circuits tailored to the provided problem. Existing QAS approaches typically adapt classical neural architecture search techniques, training machine learning models to sample relevant circuits, but often overlook the inherent quantum nature of the circuits they produce. By reformulating QAS from a quantum perspective, we propose a sampling-free differentiable QAS algorithm that models the search process as the evolution of a quantum mixed state, which emerges from the search space of quantum circuits. The mixed state formulation also enables our method to incorporate generic noise models, for example the depolarizing channel, which cannot be modeled by state vector simulation. We validate our method by finding circuits for state initialization and Hamiltonian optimization tasks, namely the variational quantum eigensolver and the unweighted max-cut problems. We show our approach to be comparable to, if not outperform, existing QAS techniques while requiring significantly fewer quantum simulations during training, and also show improved robustness levels to noise.

Figures (18)

• Figure 1: A schematic overview of $\rho$DARTS showing the optimization loop. $\rho$DARTS provides for macro and micro searches which generate global circuits and local subcircuits, respectively.
• Figure 2: A matrix encoding of a 4-qubit circuit comprising all of the gates in our chosen gate set, and the associated quantum circuit.
• Figure 3: Results of state initialization experiments. a) The fidelities of the states found by $\rho$DARTS and qDARTS, using 1 and 10 quantum simulations per epoch, when initializing the GHZ and W states, averaged over three runs. b) Comparing the normalized mean entropies of the gate distributions after every search for the entangled state experiments. c) The average fidelities of the states found when initializing the image states. d) The best image states found for the digit 5. The error bars indicate one standard deviation from the mean, clipped between 0 and 1.
• Figure 4: An example of the super circuit structure used in micro search for the max cut problem. The vertices map to the qubits, and edges map to subcircuits acting only on the qubits they connect.
• Figure 5: Comparing the max-cut experiments in noisy simulations. The plots show the mean of the metrics $E_m$ and $P_m$, with error bars denoting standard deviation, over macro search experiments with hidden units present. The dashed line and shaded regions denote the mean and standard deviation of the metric values for the maximally mixed state averaged over every graph in the dataset.