External Fields Force Entanglement in Quantum Systems Previously Thought Separate

External fields influence entanglement and computational complexity within high-temperature Gibbs states, a model for understanding quantum matter at thermal equilibrium. Ainesh Bakshi and Xinyu Tan at NYU and MIT show that these external fields generate entanglement even in systems initially considered separable, with a specific relationship between field strength and inverse temperature. A key method for efficiently preparing these Gibbs states using a quasi-local Lindbladian achieves mixing in a time proportional to the logarithm of system size and desired accuracy. The findings also reveal conditions under which sampling from these states becomes classically challenging, suggesting potential avenues for achieving quantum advantage through state preparation

Field-resonant Lindbladians enable Gibbs state preparation under external perturbations

A quasi-local Lindbladian forms the core of this work, representing a carefully constructed set of rules governing quantum system evolution over time. It can be conceptualised as a recipe for evolving the system, accounting for both desired changes and inevitable imperfections arising from interactions with the environment. Lindbladians are mathematically expressed as a generator of a completely positive trace-preserving map, ensuring the evolution remains physically plausible and preserves probabilities. Unlike previous methods for preparing Gibbs states, which represent snapshots of a system at a specific temperature, this Lindbladian functions effectively even when external forces are applied, something that typically disrupts existing algorithms. Traditional approaches often rely on the assumption of isolated systems, neglecting the influence of external perturbations. This new method explicitly incorporates these perturbations into the evolution process. Its effectiveness stems from being ‘field-resonant’, meaning its internal parameters are specifically tuned to the strength of the external field and the local energy levels of the quantum system. This tuning ensures that the Lindbladian’s dynamics align with the imposed external field, facilitating efficient state preparation. The resulting quantum Gibbs sampler is capable of functioning even with external fields, efficiently preparing Gibbs states at high temperatures. The precise form of the Lindbladian involves a sum of local operators, each acting on a few qubits, ensuring its quasi-local nature and facilitating efficient simulation on classical computers for verification purposes. The design prioritises minimising the number of terms while maintaining accuracy in representing the desired Gibbs state.

External fields induce entanglement and computational hardness in high-temperature Gibbs states

Entanglement measures now demonstrate a reversal of prior limitations, as external fields induce entanglement in high-temperature Gibbs states previously considered separable, at a crossover scale of approximately $h\asymp β^{-1} \log(1/β)$. Here, $h$ represents an upper bound on any on-site potential, quantifying the strength of the external field, and $β$ is the inverse temperature, related to the system’s thermal energy. Until now, systems below this threshold were incapable of supporting entanglement through external field application. This implies that a certain minimum field strength, scaling logarithmically with the inverse temperature, is required to overcome the thermal decoherence and establish non-local correlations. This new quasi-local Lindbladian, a method for evolving quantum systems, efficiently prepares these states in $\mathcal{O}(\log(n/ε))$ time, where $n$ is the system size and $ε$ represents the desired accuracy. This logarithmic scaling is particularly significant, as it suggests that the preparation time grows very slowly with increasing system size, making it potentially scalable to larger quantum systems. Furthermore, for inverse temperatures β less than 1, sampling from these Gibbs states with external fields is classically hard, suggesting potential for quantum computational advantage. This classical hardness is predicated on the assumption that certain computational problems, such as approximating the partition function, are intractable for classical algorithms. These Gibbs states exhibited entanglement when subjected to fields exceeding the aforementioned crossover scale, re-establishing entanglement in high-temperature Gibbs states previously thought to be fundamentally separable. However, current findings focus on specific, simplified models and do not yet demonstrate a pathway to practical quantum advantage on complex, real-world materials. The models employed are typically spin systems with limited connectivity, and extending these results to more realistic materials with complex interactions remains a significant challenge.

Entanglement generation in thermal states offers pathways towards practical quantum computation

Quantum systems are increasingly being focused on for computational tasks, but preparing the necessary quantum states remains a formidable challenge. Many quantum algorithms require highly entangled states as input, and creating these states efficiently is a major bottleneck in the development of quantum technologies. This work addresses that challenge by demonstrating a method for creating entanglement, a key resource for quantum computing, in high-temperature Gibbs states, even when those states initially lack it. The ability to generate entanglement at relatively high temperatures is particularly appealing, as it reduces the need for expensive and complex cryogenic cooling systems. The proof of classical hardness, an important step towards demonstrating a quantum advantage, currently relies on unproven assumptions within computational complexity theory, introducing a degree of uncertainty regarding the practical realisation of these findings. Specifically, the hardness results depend on the validity of conjectures such as the hardness of approximating the partition function, which remain open problems in computer science. Despite this, acknowledging that establishing a definitive quantum advantage hinges on resolving open questions in computer science does not diminish the significance of this work. It provides a concrete pathway for exploring potential quantum advantages in state preparation and sampling.

Demonstrating entanglement generation within high-temperature Gibbs states, systems mirroring materials at everyday temperatures, expands the scope of potential quantum devices beyond the extremely cold environments typically required. Traditionally, maintaining quantum coherence requires extremely low temperatures to suppress thermal noise. External forces typically complicate the behaviour of quantum systems, yet this research reveals a surprising outcome: these forces can actually generate entanglement within high-temperature Gibbs states, systems which model materials at thermal equilibrium. This is significant because previously these states were considered incapable of supporting such connections between particles, challenging established understanding of how temperature and external influence interact. The team developed a new technique, a quasi-local Lindbladian, to efficiently prepare these entangled states, a key step towards utilising them in quantum technologies. The Lindbladian’s efficiency is crucial for scaling up the system size and exploring more complex quantum phenomena. Further research will focus on extending these findings to more realistic materials and investigating the potential for utilising these entangled states in specific quantum algorithms.

The research demonstrated that external fields can induce entanglement in high-temperature Gibbs states, systems that model quantum matter at thermal equilibrium. This is important because these states were previously thought to be incapable of supporting entanglement, expanding the possibilities for quantum devices beyond extremely cold temperatures. Researchers also developed a quasi-local Lindbladian capable of efficiently preparing these entangled states in approximately log(n/ε) time. The authors intend to extend these findings to more realistic materials and explore potential applications in quantum algorithms.