Speaker
Description
Instantaneous Quantum Polynomial Quantum Circuit Born Machines (IQP-QCBM) are emerging quantum generative models that have attracted increasing attention. IQP-QCBMs represent probability distributions over bitstrings through Born-rule measurements of parameterized IQP circuits. IQP-QCBMs are distinguished from many other quantum machine learning (QML) models in two ways: First, the models are conjectured to inherit the classical sampling hardness from IQP circuits under standard complexity-theoretic assumptions. Second, as showed, by exploiting the special circuit architectures of IQP circuits, the models can be trained on a classical computer using the maximum mean discrepancy (MMD) loss, while deployment on a quantum computer is required for sample generation.
In this work, we show that whether an IQP-QCBM exhibits a barren plateau (BP) depends on two practical design choices: the IQP circuit architecture and the kernel used in the MMD. We derived the closed-form expression of variance of the MMD loss gradient, and we identified the "critical rank" of the IQP-QCBM model, the dimension of the space spanned by the anti-commuting generators w.r.t. the observable, as the deciding factor for the presence or absence of BP.
Our analytical work provides guidance for avoiding architectures that are provably susceptible to BPs and narrows the design space of trainable IQP-QCBMs.
Specifically, we show that IQP-QCBMs whose architecture connectivity is generated by a sparse ER graph with $\mathcal{O}(n\log n)$ edges are trainable, while their output distribution family remains hard to approximate classically.
The full presentation will also include the characterization of IQP-QCBM’s expressivity and experiment results for material science applications.
| Topic | Quantum variational circuits and their applications |
|---|