Quantum Control Unifies Classical & Quantum Systems

Scientists at Zhejiang University, led by Zhu-yao Jin, have unveiled a unified theoretical framework demonstrating a fundamental connection between classical and quantum control systems. Their research reveals that seemingly disparate control approaches for both classical and quantum continuous-variable systems are interconnected via differential manifolds of ancillary representations. The team demonstrates that utilising the Liouville equation and a second quantisation process enables nonadiabatic passages to target states in both standard and non-Hermitian systems, offering a novel pathway for manipulating quantum states. This theoretical framework successfully predicts the generation of highly squeezed states, achieving a squeezing level of 29.3 dB for single-mode states and 20.5 dB for double-mode states, representing a key advance in quantum state preparation and control.

Simplifying complex dynamics via symplectic transformations and dynamical invariants

The core of this advance lies in the application of ‘ancillary representations’, a sophisticated mathematical technique designed to simplify the often-intractable dynamics of both classical and quantum systems. These representations can be conceptualised as a coordinate transformation, analogous to using a detailed map to navigate complex terrain. The process begins with a symplectic transformation applied to the original canonical variables of the system, variables describing position and momentum, or their quantum equivalents. This transformation mathematically rearranges these variables, creating the ancillary variables while crucially preserving their fundamental relationships, dictated by the symplectic structure. The symplectic structure ensures that the transformed variables maintain the same commutation relations as the original, a vital property for preserving the underlying physics. These newly created ancillary variables then function as dynamical invariants, meaning they remain constant or change predictably during the system’s evolution. This property allows for the guidance of the system through changes without relying on typical, gradual adiabatic processes, proving particularly useful for achieving rapid, nonadiabatic transitions between states. The mathematical foundation rests on the Hamilton-Jacobi equation, which, when satisfied by the ancillary variables, guarantees their invariant behaviour. This unified framework successfully generated single-mode squeezed states reaching 29.3 dB and double-mode squeezed states achieving 20.5 dB, representing important advancements in quantum state preparation. Based on the second quantization of the Liouville equation, a classical equation describing the time evolution of a probability density, the method demonstrates a fundamental connection between classical and quantum system control, and enables nonadiabatic passages to target states in both standard and non-Hermitian systems. Non-Hermitian systems are particularly relevant as they model open quantum systems where interactions with the environment lead to dissipation and decoherence.

Record squeezed state generation enables advances in quantum precision and control

A record squeezing level of 29.3 dB has now been generated for single-mode systems, a substantial improvement over previous achievements of approximately 15 dB. Squeezing refers to the reduction of quantum noise in one quadrature of a quantum field, at the expense of increased noise in the other. This allows for enhanced precision in measurements that are sensitive to the squeezed quadrature. Previously unattainable low noise levels, which severely limited the sensitivity of quantum sensors and the security of quantum communication protocols, are now surpassed by this breakthrough, opening doors for applications requiring high precision measurements, such as gravitational wave detection and atomic clocks. Furthermore, the framework successfully generated double-mode squeezed states reaching 20.5 dB, expanding the possibilities for manipulating quantum information and enabling more complex quantum algorithms. The team meticulously mapped the dynamics of a dissipative single-mode system, effectively mimicking the behaviour of circuit-QED systems where energy loss can be converted into gain through a process known as parametric amplification. Numerical simulations, truncating the Hilbert space, the space of all possible quantum states, at 1400 dimensions, were performed to validate the approach. These simulations revealed a strong correlation between squeezing level and the strength of the driving field; an ideal squeezed state exhibited a predictable relationship between these parameters, confirming the theoretical predictions. However, these results are obtained under ideal conditions and do not yet demonstrate durability against the imperfections inherent in real-world quantum devices, representing a significant hurdle to practical implementation. Factors such as imperfect control pulses, detector inefficiencies, and environmental noise can all degrade the squeezing level and limit the performance of quantum devices.

High-fidelity quantum squeezing bridges classical and quantum noise reduction techniques

Quantum control is being pushed to new limits, achieving unprecedented levels of squeezing, a technique for reducing noise in quantum systems, with potential benefits for sensitive instruments and secure communication networks. The ability to generate such high levels of squeezing represents a significant step towards realising the full potential of quantum technologies. While this unified theoretical framework elegantly connects classical and quantum approaches, offering a deeper understanding of the underlying principles governing both, it offers limited insight into the practical challenges of scaling up this technology beyond the demonstrated double-mode system. Building larger, more complex quantum systems while maintaining high fidelity control and coherence remains a formidable task. It remains important to acknowledge the challenges in building stable quantum devices, including the need for cryogenic cooling, precise electromagnetic shielding, and robust control electronics, but this offers a valuable theoretical advance. Reducing noise to an extraordinarily low level, achieving 29.3 dB of squeezing demonstrates the potential of this unified approach to control both classical and quantum systems. The reliance on a non-Hermitian Hamiltonian, derived using the Lindblad master equation, a mathematical framework for describing the evolution of open quantum systems, introduces complexity, and maintaining coherence in real-world devices, susceptible to unavoidable imperfections, could prove difficult. This establishes a unified theoretical framework demonstrating a fundamental link between classical and quantum control systems. By employing a symplectic transformation, variables were created that act as dynamical invariants, enabling nonadiabatic transitions, rapid shifts between states, in both standard and non-Hermitian systems, accounting for energy loss. This approach successfully predicted the generation of highly squeezed states, achieving levels of 29.3 dB for single-mode systems and 20.5 dB for double-mode systems, surpassing previous benchmarks.

The research demonstrated a unified theoretical framework connecting classical and quantum control systems through the use of dynamical invariants derived from symplectic transformations. This reveals a fundamental link between how these seemingly different systems are managed, offering a deeper understanding of their underlying principles. The theory accurately predicted the generation of single-mode squeezed states reaching 29.3 dB and double-mode squeezed states at 20.5 dB, representing a significant advance in squeezing levels. The authors suggest this work provides a foundation for further investigation into the control of more complex quantum systems.