Entropic Measures Detect Superradiance and Dynamics of Magic in Hybrid Quantum Systems

Hybrid systems combining the properties of spins and bosons represent a promising frontier in quantum technology, and researchers are now developing new ways to quantify the unique resources these systems offer. Samuel Crew, Ying-Lin Li, and Heng-Hsi Li, all from National Tsing Hua University, along with Po-Yao Chang from both National Tsing Hua University and Kyoto University, introduce entropic measures to characterise the non-classical behaviour within these hybrid systems. Their work defines a new ‘magic entropy’ that reveals how quantum advantages are distributed between the spin and bosonic components, offering a powerful tool to detect key phenomena like superradiance and track the evolution of quantum properties following rapid changes. This development provides a practical computational scheme for analysing complex many-body systems, potentially accelerating the design and optimisation of future quantum devices.

Entanglement is a well-recognised feature distinguishing quantum and classical correlations, but it is not the sole resource defining quantum complexity. Non-stabilizerness, often referred to as “magic”, represents the resources beyond those available in stabiliser quantum computation. Researchers now introduce analogous hybrid magic entropy and a mutual magic entropy to capture how quantum magic is distributed across spin and bosonic subsystems. Using these entropic measures, they demonstrate the detection of the superradiant phase transition in the Dicke model and track the dynamics of magic in the Jaynes-Cummings model following a sudden change in conditions. To facilitate computation in complex systems, the team developed a Monte Carlo numerical scheme.

Characterising and Simulating Non-Stabilizer Quantum States

This research focuses on quantum states that cannot be easily expressed as combinations of simpler, “stabiliser” states. These non-stabiliser states are believed to be essential for achieving quantum advantage, where quantum computers outperform their classical counterparts. The work investigates how to characterise, detect, and simulate these more complex states, building on the “resource theory of magic”, which quantifies the non-stabilizerness of a quantum state. A significant portion of the research involves developing and refining Monte Carlo methods for simulating these states, as directly simulating them can be computationally demanding.

The authors employ techniques like Pauli basis sampling and autocorrelation estimation to improve the efficiency and accuracy of these simulations. They also utilise the Weyl operator and Weyl function to represent and analyse quantum states in a different way, potentially leading to new simulation algorithms. The research draws connections to quantum optics and the phenomenon of superradiance, and relies heavily on the Qutip Python framework for numerical simulations. Researchers demonstrate that their refined Monte Carlo algorithms can efficiently simulate non-stabiliser states with high accuracy, even for relatively large systems. The research reveals a connection between non-stabilizerness and critical phenomena in quantum spin chains, finding that these states tend to emerge near critical points where long-range correlations exist. This work contributes to the development of more efficient and accurate methods for simulating quantum systems, crucial for designing and testing quantum algorithms, and strengthens the foundation of the resource theory of quantum computation.

Entropic Measures Quantify Quantum Computational Magic

Researchers have developed new methods to quantify a crucial quantum resource known as “magic”, essential for achieving advantages in quantum computation beyond what classical computers can achieve. This magic refers to the non-Clifford nature of quantum states, qualities that go beyond the capabilities of operations efficiently simulated on classical machines. The team’s work introduces “entropic measures”, specifically, a stabilizer Rényi entropy, to precisely measure the amount of this magic within complex quantum systems. This new approach builds upon the principles of geometric quantisation, offering a direct way to assess the non-Clifford content of a quantum state without relying on complex optimisation procedures.

The researchers demonstrate the applicability of this entropy to both discrete qubit systems and continuous-variable systems, revealing formal analogies between these seemingly different quantum platforms. They extended their analysis to “hybrid spin-boson systems”, combining the properties of both spin and bosonic particles, and developed a practical numerical scheme to calculate the entropy in these complex many-body systems. A key application of these new measures is the ability to detect “superradiance” in the Dicke model, a phenomenon where collective emission of photons dramatically enhances light output. The researchers also investigated the dynamics of magic following a sudden change in the Jaynes-Cummings model. This work provides a powerful new toolkit for quantifying and understanding the essential quantum resources needed to unlock the full potential of quantum technologies.

Hybrid Quantum Systems, Magic Entropy Characterisation

This work introduces new methods for quantifying non-classical resources in complex hybrid quantum systems, combining spin and bosonic components. Researchers developed entropic measures, including hybrid magic entropy and mutual magic entropy, to characterise the distribution of these resources across different parts of the system. These tools were then successfully applied to the Dicke model, where they detected superradiance, and the Jaynes-Cummings model, where they tracked the evolution of quantum magic following a sudden change in conditions. The development of a Monte Carlo numerical scheme is a key contribution, enabling practical calculations for many-body systems where analytical solutions are difficult to obtain. Results from this scheme align well with analytical predictions, validating the approach and demonstrating its potential for wider application. This research provides valuable tools for understanding and characterising quantum behaviour in increasingly complex systems, potentially aiding the development of future quantum technologies.