Minimizing classical resources in variational measurement-based quantum computation for generative modeling
Arunava Majumder, Hendrik Poulsen Nautrup, Hans J. Briegel
TLDR
A new VMBQC model for generative modeling drastically reduces classical resources by adding only one trainable parameter.
Key contributions
- VMBQC leverages measurement randomness for generative modeling tasks.
- Traditional VMBQC models have high parameter counts (N x D), hindering optimization.
- Introduces a restricted VMBQC model requiring only one additional trainable parameter.
- Demonstrates this minimal extension outperforms unitary models in generating distributions.
Why it matters
VMBQC offers advantages in generative modeling by exploiting quantum randomness, but its high parameter count has been a barrier. This paper makes VMBQC more practical and efficient by drastically cutting down classical resource requirements. It shows that even with minimal overhead, VMBQC can achieve capabilities beyond traditional unitary models.
Original Abstract
Measurement-based quantum computation (MBQC) is a framework for quantum information processing in which a computational task is carried out through one-qubit measurements on a highly entangled resource state. Due to the indeterminacy of the outcomes of a quantum measurement, the random outcomes of these operations, if not corrected, yield a variational quantum channel family. Traditionally, this randomness is corrected through classical processing in order to ensure deterministic unitary computations. Recently, variational measurement-based quantum computation (VMBQC) has been introduced to exploit this measurement-induced randomness to gain an advantage in generative modeling. A limitation of this approach is that the corresponding channel model has twice as many parameters compared to the unitary model, scaling as $N \times D$, where $N$ is the number of logical qubits (width) and $D$ is the depth of the VMBQC model. This can often make optimization more difficult and may lead to poorly trainable models. In this paper, we present a restricted VMBQC model that extends the unitary setting to a channel-based one using only a single additional trainable parameter. We show, both numerically and algebraically, that this minimal extension is sufficient to generate probability distributions that cannot be learned by the corresponding unitary model.
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