Quantum Computation Over Continuous Variables

Takaya Matsuura

Tom Douce, Damian Markham, Elham Kashefi +5 more

We study the translation of a recently introduced complexity class, Instantaneous Quantum Computing, to the regime of Continuous Variables (CV). Following the existing proof for the case of Discrete Variables (DV), we prove that CV IQP circuits are hard to classically simulate by exploring the properties of post-selected CV IQP circuits.

Christian Weedbrook, Bhaskar Roy Bardhan

Sophie Choe

In this Near Intermediate-Scale Quantum era, there are two types of near-term quantum devices available on cloud: superconducting quantum processing units (QPUs) based on the discrete variable model and linear optics (photonics) QPUs based on the continuous variable (CV) model. Quantum computation in the discrete variable model is performed in a finite dimensional quantum state space and the CV model in an infinite dimensional space. In implementing quantum algorithms, the CV model offers more quantum gates that are not available in the discrete variable model. CV-based photonic quantum computers provide additional flexibility of controlling the length of the output vectors of quantum circuits, using different methods of measurement and the notion of cutoff dimension.

Xi‐Feng Ren, Guang-Can Guo

The article comments on a comprehensive review of integrated continuous-variable quantum light sources, high lighting its structured synthesis of recent advances and its relevance to scalable CV quantum computing.

Daniel Alejandro Lopez, Oscar Montiel, Oscar Castillo +1 more

Continuous-variable (CV) quantum computing offers a promising framework for scalable quantum machine learning, leveraging optical systems with infinite-dimensional Hilbert spaces. While discrete-variable (DV) quantum neural networks have shown remarkable progress in various computer vision tasks, CV quantum models remain comparatively underexplored. In this work, we present a feasibility study of continuous-variable quantum neural networks (CV-QCNNs) applied to biomedical image classification. Utilizing photonic circuit simulation frameworks, we construct CV quantum circuits composed of Gaussian gates, such as displacement, squeezing, rotation, and beamsplitters to emulate convolutional behavior. Our experiments are conducted on the MedMNIST dataset collection, a set of annotated medical image benchmarks for multiple diagnostic tasks. We evaluate CV-QCNN's performance in terms of classification accuracy, model expressiveness, and resilience to Gaussian noise, comparing against classical CNNs and equivalent DV quantum circuits. This study aims to identify trade-offs between DV and CV paradigms for quantum-enhanced medical imaging. Our results highlight the potential of continuous-variable models and their viability for future computer-aided diagnosis systems.