Python Library Simulates Continuous-Variable Quantum Circuits with Gaussian and Number-Resolving Detectors

Simulating complex quantum circuits presents a significant challenge for researchers developing future quantum technologies, and accurately modelling continuous-variable circuits is particularly demanding. Olga Solodovnikova, Ulrik L. Andersen, and Jonas S. Neergaard-Nielsen, all from the Center for Macroscopic Quantum States at the Technical University of Denmark, have developed a new open-source Python library that dramatically speeds up these simulations. Their framework, which combines established techniques with a novel approach to representing quantum states, allows researchers to efficiently model the behaviour of multi-mode circuits, even those with imperfect components. This advance promises to accelerate the development of practical quantum technologies, including fault-tolerant quantum computing, by enabling faster optimisation and analysis of complex quantum circuits.

Detector capabilities underpin a new framework that merges the linear combination of Gaussians methodology with the coherent state decomposition of arbitrary non-Gaussian states. This integration establishes a connection between Gaussian and Fock basis representations, allowing for comprehensive analysis of quantum states. By tracking the Wigner function, the framework simulates the action of Gaussian channels and measurements on multi-mode systems with both speed and accuracy. The formalism facilitates convenient calculation of quantum state quality measures, and the researchers derive analytical gradients of these measures with respect to parameterized circuit elements, enabling efficient optimisation. They demonstrate the utility of this methodology by optimising the heralded preparation of states.

Gaussian State Tomography and Optimization Methods

This document details the mathematical foundations of Gaussian state tomography and optimization within a quantum computing context. The core goal is to reconstruct an unknown quantum state and optimize a quantum circuit to achieve a desired outcome, utilizing Gaussian states as a starting point due to their ease of preparation and manipulation. The document provides the mathematical tools to estimate state parameters, optimize circuit parameters, and efficiently calculate gradients. The appendices detail derivatives of Gaussian operations and measurements, crucial for updating state estimates and calculating how state parameters change after applying operations like squeezing, two-mode squeezing, beamsplitters, and displacement.

These derivatives, used with the chain rule of calculus, calculate the gradient of a cost function with respect to circuit parameters, guiding adjustments to maximize performance. The document utilizes symplectic matrices to represent quantum operations and quadrature operators to represent the position and momentum of a quantum harmonic oscillator. Consider preparing a specific Gaussian state using a beamsplitter and a squeezing operation. The process involves starting with an initial state, applying the operations, measuring the output, calculating a cost function, and then using the derivatives to calculate the gradient. This gradient guides adjustments to the beamsplitter angle and squeezing parameter using a gradient-based optimization algorithm, iteratively minimizing the cost function. This approach bridges a gap between different ways of representing quantum states, allowing for more efficient and accurate modeling of quantum systems. The framework leverages the strengths of both Gaussian and non-Gaussian representations, offering a versatile tool for exploring quantum computation and information processing. The core of lcg_plus lies in its ability to track the Wigner function, a mathematical tool that describes the quantum state of a system, accurately simulating the behavior of multi-mode systems with improved speed and precision.

This is particularly important for circuits incorporating imperfect components, where traditional simulation methods often struggle. The framework’s design allows for the efficient calculation of key metrics that assess the quality of quantum states, and importantly, it provides a way to calculate how changes to the circuit’s parameters affect these metrics. A key demonstration of lcg_plus’s capabilities involved optimizing the creation of a “qunaught” state, a crucial building block for fault-tolerant quantum computers, even when the circuit included components with inefficiencies. This optimization process was made possible by the framework’s ability to calculate gradients.

The framework’s performance represents a significant advancement in simulating quantum systems. By combining different mathematical representations and providing efficient gradient calculations, lcg_plus enables researchers to explore more complex quantum circuits and optimize their performance, with implications for the development of more robust and scalable quantum technologies. The ability to accurately model imperfect components is especially valuable, as it allows for the design of circuits that are more resilient to real-world noise and limitations.

Optimizing Heralded Qubit Preparation with LCG+

The research team developed lcg_plus, a new open-source Python library for simulating continuous-variable quantum circuits. This framework combines the linear combination of Gaussians methodology with a coherent state decomposition technique, allowing for efficient and accurate modeling of quantum systems utilizing both generaldyne and single-photon detectors. By tracking the Wigner function, the library effectively simulates how Gaussian channels and measurements affect multi-mode systems, and facilitates the calculation of quantum state quality measures with analytical gradients for circuit optimization. The utility of lcg_plus was demonstrated through the optimization of heralded qunaught state preparation, a crucial step in building fault-tolerant quantum computers, even when components within the Gaussian Boson sampling circuit experience inefficiencies.

The library’s ability to simulate mixed states and seamlessly integrate different detector types represents a valuable addition to the growing toolkit for simulating continuous-variable quantum optical circuits. The authors acknowledge certain limitations, notably the absence of phase noise modeling, which would require computationally intensive simulations. They also note that while the library currently focuses on operations decomposable within the linear combination of Gaussians framework, other non-Gaussian operations could potentially be incorporated in future iterations. Future work may focus on expanding the library’s capabilities and refining its performance for increasingly complex quantum simulations. The code and associated tutorials are publicly available to facilitate wider adoption and further development by the research community.