SuperEncoder: Towards Universal Neural Approximate Quantum State Preparation

TL;DR

This work tackles the bottleneck of quantum state preparation for amplitude encoding by leveraging a pre-trained neural network to directly generate PQC parameters from target states. It introduces SuperEncoder, an MLP-based model that learns a deterministic mapping $f: |oldsymbol{ angle} \rightarrow oldsymbol{\theta}$ to enable iteration-free approximate QSP with a hardware-efficient PQC. By adopting a state-oriented loss $\mathcal{L}_3 = 1 - |\\langle \psi|\hat{\psi}\rangle|^2$, the approach achieves substantial runtime speedups over iterative AAE while maintaining competitive fidelity on synthetic data and comparable downstream QML performance, though fidelity can degrade on larger qubit counts or noisy devices. The work lays groundwork for a universal neural design for QSP and identifies directions for noise-aware training and architectural scaling to improve real-world applicability.

Abstract

Numerous quantum algorithms operate under the assumption that classical data has already been converted into quantum states, a process termed Quantum State Preparation (QSP). However, achieving precise QSP requires a circuit depth that scales exponentially with the number of qubits, making it a substantial obstacle in harnessing quantum advantage. Recent research suggests using a Parameterized Quantum Circuit (PQC) to approximate a target state, offering a more scalable solution with reduced circuit depth compared to precise QSP. Despite this, the need for iterative updates of circuit parameters results in a lengthy runtime, limiting its practical application. In this work, we demonstrate that it is possible to leverage a pre-trained neural network to directly generate the QSP circuit for arbitrary quantum state, thereby eliminating the significant overhead of online iterations. Our study makes a steady step towards a universal neural designer for approximate QSP.

Figures (11)

• Figure 1: Breakdown of normalized runtime for QNN inference. Original data are listed in Table \ref{['tab:aae_breakdown']}.
• Figure 2: An example PQC with two blocks, with each block consisting of a rotation layer (filled blue) plus an entangler layer (filled red).
• Figure 3: Comparison between AAE and SuperEncoder.
• Figure 4: Virtualization of states generated by SuperEncoder trained with different loss functions. $\mathcal{L}_2$ is omitted as it produces very similar results to $\mathcal{L}_3$.
• Figure 5: Convergence of different loss functions.