AI methods for approximate compiling of unitaries

TL;DR

The paper tackles approximate unitary synthesis for superconducting hardware by proposing a three-stage AI-based transpiler: (i) template selection via a deep classifier, (ii) initial parameter prediction via an encoder-based model, and (iii) gradient-descent refinement to maximize fidelity. It demonstrates that 2-qubit template prediction can reach near-perfect accuracy ($ ext{approx. }0.96$) and that 2-qubit parameter starting fidelities can be very high ($ ext{approx. }0.95$), while 3-qubit results are more challenging (top-1 about $0.77$, top-5 about $0.98$, starting fidelity around $0.5$) but improve with optimization. The work shows meaningful speedups over exhaustive template search and random starts, with Toffoli-like circuits converging efficiently, and suggests that compact models and on-the-fly data generation can make AI-augmented transpilation practical on current and near-future quantum hardware. Overall, the approach offers a scalable pathway to more efficient circuit synthesis within realistic hardware constraints.

Abstract

This paper explores artificial intelligence (AI) methods for the approximate compiling of unitaries, focusing on the use of fixed two-qubit gates and arbitrary single-qubit rotations typical in superconducting hardware. Our approach involves three main stages: identifying an initial template that approximates the target unitary, predicting initial parameters for this template, and refining these parameters to maximize the fidelity of the circuit. We propose AI-driven approaches for the first two stages, with a deep learning model that suggests initial templates and an autoencoder-like model that suggests parameter values, which are refined through gradient descent to achieve the desired fidelity. We demonstrate the method on 2 and 3-qubit unitaries, showcasing promising improvements over exhaustive search and random parameter initialization. The results highlight the potential of AI to enhance the transpiling process, supporting more efficient quantum computations on current and future quantum hardware.

Figures (7)

• Figure 1: Examples of two templates for 3 qubits.
• Figure 2: Encoder and decoder networks for template parameter suggestion
• Figure 3: Probability assigned to each template and predicted template as a function of $n/pi$, where $n$ is the angle used in gate CZ for the circuit described in the text.
• Figure 4: Confusion matrix for the 3 qubits template prediction model, for 1000 unitaries sampled uniformly from each template.
• Figure 5: Template used for the 3 qubit, 10 layer parameter suggestion model. Each single qubit unitary gate is decomposed as three RZ gates separated by SX gates, following the instruction set of ibm_torino ibmQuantum_ibm_torino.