Approximate Quantum State Preparation with Tree-Based Bayesian Optimization Surrogates

TL;DR

This work addresses approximate quantum state preparation on near-term devices by minimizing the distributional discrepancy between a parameterized circuit and a target state, formalized as $f(\boldsymbol{\theta}) = \text{TVD}(p_{\boldsymbol{\theta}}, p^\star)$. It introduces CircuitTree, a surrogate-guided Bayesian Optimization framework that uses Gradient Boosted Regression Trees to model the non-smooth, stochastic loss and employs a layerwise distributed optimization to exploit circuit structure. Theoretical analysis provides convergence guarantees under mild noise assumptions, with a rate of $\mathcal{O}(t^{-1/d})$, and empirical results show faster convergence, reduced circuit depth, and robustness on synthetic benchmarks and real IBM hardware. This approach enables practical approximate state preparation for near-term quantum algorithms like QSP and VQE, and the authors provide open-source code for replication.

Abstract

We study the problem of approximate state preparation on near-term quantum computers, where the goal is to construct a parameterized circuit that reproduces the output distribution of a target quantum state while minimizing resource overhead. This task is especially relevant for near-term algorithms where distributional matching suffices, but it is challenging due to stochastic outputs, limited circuit depth, and a high-dimensional, non-smooth parameter space. We propose CircuitTree, a surrogate-guided optimization framework based on Bayesian Optimization with tree-based models, which avoids the scalability and smoothness assumptions of Gaussian Process surrogates. Our framework introduces a structured layerwise decomposition strategy that partitions parameters into blocks aligned with variational circuit architecture, enabling distributed and sample-efficient optimization with theoretical convergence guarantees. Empirical evaluations on synthetic benchmarks and variational tasks validate our theoretical insights, showing that CircuitTree achieves low total variation distance and high fidelity while requiring significantly shallower circuits than existing approaches.

Figures (7)

• Figure 1: In this work, we use Bayesian Optimization (BO) with tree-based surrogates to update layered circuit parameters during approximate state preparation.
• Figure 2: TVD during optimization of 3 different RQCs, using GBRT, QRF, and GBQR. GBRT significantly outperforms both QRF and GBQR in terms of TVD and runtime. CircuitTree's results with the final layered optimization design are shown for comparison.
• Figure 3: TVD during optimization of 3 different RQCs, using GBRT. Convergence is compared across full-space optimization, random subspace splitting, and layered splitting. CircuitTree adopts layered splitting with distributed surrogate optimization to maximize stability and fidelity.
• Figure 4: Analyzing the impact of (a) the number of ansätze layers and (b) the number of measurement shots on the performance of CircuitTree using VQE tasks.
• Figure 5: Comparison of CircuitTree and BQSKit on QSP and VQE workloads executed on IBM ibm_nazca. CircuitTree achieves higher fidelity with fewer gates and shallower depth, at the cost of increased but consistent classical runtime.

Theorems & Definitions (17)

• Definition 2.1: Approximate State Preparation Objective
• Remark 2.2
• Definition 2.3: Surrogate-Guided Optimization
• Remark 2.4
• Definition 3.1: Surrogate Model
• Remark 3.2
• Definition 3.3: Layerwise Decomposition
• Remark 3.4
• Remark 4.4
• Lemma 4.5: Predictive Variance at Unexplored Points