Dissipative Qubit Demonstrates Canonical Quantum Mpemba Effect, Exhibiting Exponentially Faster Relaxation Dynamics

The counterintuitive Mpemba effect, where a hotter system can sometimes cool faster than a colder one, has long fascinated physicists, and now researchers have demonstrated a quantum version of this phenomenon. Xingli Li, Yan Li, and Yangqian Yan from The Chinese University of Hong Kong, lead a team that observes this ‘canonical quantum Mpemba effect’ in a carefully controlled quantum system. The team demonstrates that a quantum system starting at a higher temperature relaxes to equilibrium exponentially faster than one beginning at a lower temperature, and crucially, this acceleration depends only on the initial temperature. This discovery not only provides a quantum analogue to a well-known classical puzzle, but also reveals fundamental insights into the dynamics of open quantum systems and opens new avenues for exploring and controlling quantum thermalisation.

A colder initial state typically relaxes more slowly than a warmer one, a phenomenon extensively studied in classical systems. This work presents the quantum analogue of the Mpemba effect, termed the canonical quantum Mpemba effect, using a dissipative qubit. The team demonstrates that, under identical conditions, the relaxation dynamics of a qubit initialised in a thermal state with a higher temperature can be exponentially faster than that of a colder thermal state. Strikingly, this acceleration is determined solely by the initial temperature of the system, and the relaxation is confirmed to be a genuine cooling process via the effective steady-state temperature.

Quantum Mpemba Effect in Open Systems

This research demonstrates the quantum analogue of the Mpemba effect, termed the canonical quantum Mpemba effect, using a carefully engineered open quantum system. Scientists investigated a single qubit coupled to two independent thermal baths, allowing precise control over the system’s relaxation dynamics. The team defined an effective steady-state temperature, crucial for identifying genuine cooling processes. This effective temperature minimizes the distance to the steady state, providing a robust metric for assessing relaxation behavior. To demonstrate the effect, the researchers established criteria requiring both relaxation trajectories to be cooling processes, with the initial higher temperature exceeding both the lower initial temperature and the effective steady-state temperature.

They then confirmed that a higher initial temperature suppresses the slowest relaxation mode, resulting in exponentially accelerated cooling. This acceleration is a defining characteristic of the canonical quantum Mpemba effect. To realize this effect experimentally, the team proposed a quantum collision model implemented via a classical-quantum hybrid algorithm. This algorithm emulates the dissipative dynamics originating from a thermal initial state, leveraging current quantum simulation technologies. The method involves preparing the qubit in a thermal state, allowing it to undergo a collision process, and then resetting ancillas repeatedly to accurately simulate the desired dynamics. This innovative approach allows for precise control and measurement of the relaxation process, confirming the existence of the canonical quantum Mpemba effect and paving the way for further exploration of anomalous relaxation dynamics in quantum systems.

Open Quantum System Simulation on NISQ Hardware

This document provides supporting evidence for a research project that combines theoretical development with practical implementation on a noisy intermediate-scale quantum (NISQ) device. The goal is to simulate the dynamics of an open quantum system, a system interacting with its environment, using a hybrid classical-quantum approach. It validates the theoretical model and demonstrates the feasibility of simulating open quantum systems on current quantum hardware. The core theoretical framework is the quantum collision model, which represents the continuous interaction between a system and its environment as a series of discrete collisions, allowing for a more tractable simulation.

The researchers decompose the initial thermal state into a combination of pure states and combine the results of quantum simulations to reconstruct the evolution of the original thermal state. Quantum computations are performed on a real quantum computer, acknowledging the presence of noise and limitations. A method called Suzuki-Trotter decomposition is used to approximate the time evolution operator, essential for implementing the dynamics on a quantum computer. Rigorous analysis of the errors introduced by these approximations and the noise in the quantum hardware is also included. The team found that a variant of the second-order Suzuki-Trotter scheme provides the best balance between accuracy and computational cost, particularly for strong dissipation rates, interleaving the system-environment interaction with the free evolution of the system.

The researchers demonstrate the hybrid classical-quantum approach by simulating the time evolution of a thermal state on a NISQ device. The experimental results agree with classical simulations, validating the experimental setup and the hybrid approach. Increasing the number of experimental repetitions reduces the error between the experimental and simulation results, as expected. Detailed analysis of the population of energy levels and the error between experiment and simulation confirms the accuracy of the findings. This research validates the quantum collision model and demonstrates that the combination of classical and quantum computation is a viable strategy for simulating open quantum systems on NISQ devices. The optimized Suzuki-Trotter scheme represents an advancement in the techniques for simulating quantum systems on NISQ devices.

Faster Cooling From Higher Temperatures Demonstrated

Scientists have demonstrated a quantum analogue of the Mpemba effect, a counterintuitive phenomenon where a hotter system can cool faster than a colder one. This research establishes the ‘canonical quantum Mpemba effect’ within a dissipative qubit system, revealing that the relaxation dynamics of a thermal state with a higher initial temperature can proceed exponentially faster than those starting from a colder temperature. Importantly, this acceleration depends solely on the initial temperature. Within a specific temperature range, termed the ‘Mpemba zone’, the relaxation dynamics exhibit a marked acceleration as the initial temperature increases.

This work provides a quantum counterpart to the well-known classical Mpemba effect, highlighting the fundamental role of temperature in anomalous relaxation dynamics and offering a practical experimental scheme for its realization using superconducting qubits. The authors acknowledge that their findings are currently limited to a single qubit system and that further research is needed to extend these observations to more complex, many-body quantum systems. They suggest that future work could explore the potential for applying these findings to understand anomalous non-equilibrium phenomena in broader contexts.