26th Australian Institute of Physics Congress and the Australian and New Zealand Conference on Optics and Photonics

Quantum Circuit Fragments and Link Products in Continuous Variables

Not scheduled

20m

Belinda Hutchinson Building (The University of Sydney )

Contributed Oral ANZOS | Quantum Computing and Quantum Information (ANZCOP QCQI)

Speaker

Amalina Lai (Nanyang Technological University)

Description

Many quantum-information tasks do not neatly fit the picture of a single quantum process acting on an input state to produce an output to be measured. For example, a probe of a system need not be a one-shot measurement, but a series of interventions adapted based on a previous time-step. The dynamics being probed may also be non-Markovian, where the presence of memory may imply that the dynamics of a future time-step may be affected by the past. The natural objects describing these settings are therefore not closed quantum channels, but open circuit fragments.

In finite dimensions, quantum circuit fragments and their link products provide a systematic means to characterize such dynamics. Like Lego blocks, modular circuit fragments can be connected to each other with composition rules outlined by the link product, allowing us to create larger quantum processes and interact them.

While studies on this framework and its application have so far focused on finite-dimensional quantum systems, continuous variable (CV) systems are also natural settings for such a perspective: multi-time measurements are gaining interest in sensing and communication, while CV non-Markovianity has been experimentally observed using opto-mechanical systems.

Here, we develop the corresponding framework for CV systems. We introduce CV circuit fragments and their associated link products. We then show that these objects admit a particularly efficient simplification in the Gaussian regime. There, Gaussian circuit fragments are represented by covariance matrices, and their link products can be evaluated directly by a covariance-matrix algorithm which we outline, avoiding explicit manipulation of infinite-dimensional density operators. We illustrate the framework through state-channel and channel-channel composition, and then use it to characterize Gaussian non-Markovian processes and complex agent-environmental interactions. This extends the circuit fragment toolkit to continuous variables, providing systematic methods for adaptive sensing, non-Markovian noise mitigation, and higher-order quantum circuit design.