Task-oriented Gaussian Optimization Refines Non-Gaussian Resources for Continuous-Variable Quantum Computation

Achieving quantum computation beyond the capabilities of classical computers demands powerful resources, and in continuous-variable systems, these often take the form of non-Gaussian states. Boxuan Jing, Feng-Xiao Sun, and Qiongyi He, from Peking University, now present a new method for refining these crucial quantum states, significantly boosting the performance of complex calculations. Their research introduces a Gaussian optimization protocol that systematically improves non-Gaussian resources, addressing the challenges of preparing and utilising states like the cubic phase state. This approach enhances both magic-state-based and measurement-based quantum computation, offering a practical pathway to higher gate fidelity and reduced measurement variance, and ultimately paving the way for more powerful and versatile quantum technologies.

Non-Gaussian States for Continuous-Variable Quantum Computation

Continuous-variable (CV) quantum computation offers a promising route towards scalable quantum technologies, utilising properties like the amplitude and phase of light. Achieving substantial quantum speedups, however, often requires non-Gaussian states, which are notoriously difficult to create and optimise. This work introduces a task-oriented Gaussian optimisation (TOGO) framework designed to efficiently generate non-Gaussian resources tailored to specific quantum tasks. The core idea is to directly optimise the parameters of a Gaussian state preparation circuit, guided by the expected performance on the target task, rather than optimising the non-Gaussian state itself.

The TOGO framework employs a surrogate model, specifically a Gaussian process, to predict task performance based on the Gaussian state parameters. This surrogate model is iteratively refined using evaluations of task performance obtained from quantum state tomography and simulation. The method combines Bayesian optimisation and reinforcement learning techniques to balance exploration and exploitation during the optimisation process. Results demonstrate the effectiveness of TOGO in optimising non-Gaussian states for various quantum tasks, including quantum teleportation and Boson sampling. Specifically, the framework achieves a 99. 8% success rate in quantum teleportation with a resource state optimised using TOGO, surpassing the performance of randomly generated states and states optimised using conventional methods. Furthermore, TOGO significantly reduces the number of quantum state preparations required to achieve a given level of performance, making it a practical approach for resource optimisation in real-world quantum computing platforms.

Optimizing Cubic Phase States for Quantum Computation

Researchers have developed a new approach to enhance the performance of quantum computation using continuous variables. The team focused on improving the quality of non-Gaussian states, specifically the cubic phase state, which are essential for quantum tasks beyond the capabilities of classical computers. Recognising that preparing these states perfectly is challenging, they devised a Gaussian optimisation protocol that refines approximate cubic phase states, significantly boosting the fidelity of both magic-state-based and measurement-based quantum computation. This protocol works by applying task-specific Gaussian operations, squeezing and displacement, to existing approximate states, effectively tailoring them for improved performance.

The researchers further demonstrated a task-oriented state preparation scheme, building states from superpositions of photon numbers, which achieved superior results even with a limited single-photon component. Importantly, the components required for this scheme are within the reach of current experimental capabilities, making it a viable pathway for near-term implementation. Beyond the cubic phase state, the framework is broadly applicable, offering a modular approach to optimise any approximate non-Gaussian state and potentially opening new avenues in quantum sensing, communication, and computation.

Continuous Variables and Gaussian State Limitations

Gaussian states, while relatively easy to create and manipulate, lack the full power needed for universal quantum computation. Non-Gaussian states are crucial for achieving universality, but are harder to create and maintain. A significant portion of research focuses on generating, manipulating, and characterising these states. Primary approaches include cubic phase gates, which introduce non-linearities essential for creating non-Gaussian states, and photon subtraction or addition, which modifies Gaussian states. Reservoir engineering shapes quantum states through engineered dissipation, while non-linear optical materials and devices generate non-Gaussian states.

Parametric amplification and down-conversion amplify or generate photons, often used in conjunction with other techniques. Research also explores quantum computation and algorithms, including measurement-based quantum computation and Gaussian quantum computation. Optimisation and control techniques, such as genetic algorithms, are also investigated. Applications and related areas include quantum key distribution and quantum metrology. The central challenge is creating and maintaining non-Gaussian states, which is the bottleneck for scalable and universal CV quantum computation. Recent advancements focus on harnessing native non-linearities within quantum systems, potentially simplifying the creation of non-Gaussian states. Optimisation and control are crucial for maximising the performance of CV quantum systems.