IIITH research reveals quantum thermal behavior can emerge from low-complexity dynamics

In everyday life, objects equilibrate with the environment. “A steaming cup of tea left on your desk eventually reaches room temperature, losing almost all memory of how it was heated,” says Prof. Shantanav Chakraborty, Center for Quantum Science and Technology, IIITH. 

He is referring to the process known as thermalization in Physics, where many-particle systems evolve towards equilibrium. “Here, only a few coarse properties, like temperature or energy, matter, and the fine details of the past are effectively forgotten”.

Quantum thermalization explained
According to the professor, quantum physics can mimic thermalization but in an intriguing manner. “A large quantum system can be in a perfectly well-defined pure state, evolving deterministically under Schrödinger’s equation, and yet any small part of it can still look completely random and ‘thermal’”, he says. 

In the quantum setting, an external “environment” is not required for the system to thermalize. To understand this, one must consider a system made of many quantum particles, which is isolated from any external environment. 

“Even then this system can thermalize. If you look at the state of the whole system, it is “pure” (which means it is not interacting with any external environment). However, some of the particles of this system itself act as the “bath” (another term for “environment”).” 

What this means is that even though the system as a whole is “pure”, the rest of the particles (the ones not included in this “bath”) look thermal — meaning, random. So, one would have no idea about what the local state of the system actually is – just like we lose information of how a cup of tea was heated (in the microwave oven or on the stove top). It has equilibrated with its environment. This is quantum thermalization.

Deep thermalization
Recently, experiments with highly controllable quantum devices, such as programmable arrays of ultracold atoms or trapped ions, have revealed something even stranger. These platforms let you prepare large, interacting quantum states, evolve them for a short time, and then measure individual particles one by one. 

When experimentalists did this, they saw not only ordinary thermalization, but a stronger effect dubbed deep thermalization. Here, you don’t just ask whether a small subsystem looks thermal before any measurements. You first measure part of the system, collapsing those particles, and then look at the state of the remaining particles conditioned on the outcomes. 

Deep thermalization, which is stronger than standard thermalization, implies that even after this invasive measurement, the leftover state still looks, in a very precise statistical sense, as if it came from a completely random quantum state.

What makes this surprising is how quickly the experiments seem to reach this regime. In many setups, deep-thermal behaviour appears after relatively shallow evolution: a modest number of time steps or circuit layers. 

By contrast, the leading theoretical models that try to explain deep thermalization have mostly relied on extremely complex, long-time dynamics. They invoke random quantum circuits that approximate so-called Haar-random states or high-order “designs”, which in rigorous constructions typically require very large depths and enormous entanglement. 

“There was a clear tension: nature seemed to get deep thermalization “on the cheap,” while our clean mathematical models insisted it should be expensive,” remarks Prof. Chakraborty.

Computational deep thermalization
Prof. Chakraborty, in collaboration with Soonwon Choi (MIT), Soumik Ghosh (U. Chicago), and Tudor Giurgică-Tiron (QuICS, U. Maryland), offered a resolution to this puzzle. Their research sheds new light on how and why large quantum systems can look strikingly “thermal” after surprisingly short times. 

The researchers show that a strong form of apparent randomness seen in modern quantum simulators – deep thermalization – does not necessarily emerge from high complexity or chaos, but from fundamental limits on what even quantum computers can efficiently detect. 

This work, titled Fast Computational Deep Thermalization, was published in Physical Review Letters, one of the leading physics journals.

What is the work about?
The researchers propose that deep thermalization, at least in many situations, is not purely a statement about intrinsic physical chaos, but also about the limits of computation. They introduce the idea of computational deep thermalization: a quantum state is deeply thermal not because it is literally indistinguishable from a random state in an absolute sense, but because no realistic observer has the computational power to notice that it isn’t. 

Here, “realistic” means any observer that can be modelled as an efficient quantum computer – something that runs in polynomial time and may even have access to many copies of the state. If every such observer fails to distinguish a given ensemble of states from truly random thermal states, then, operationally, those states are deeply thermal.

How they did it?
To make this idea concrete, the researchers constructed a family of highly structured quantum states using shallow, local quantum circuits. These states are generated by circuits of low depth and have minimal entanglement, far less than in the complex states produced by chaotic evolution or fully random circuits. 

Yet, under standard assumptions from post-quantum cryptography, the team proves that to any efficient quantum observer, these states are indistinguishable from genuinely random, “infinite-temperature” equilibrium states – even if that observer is allowed to perform measurements and has access to many copies of the state.

More strikingly, the researchers show that if one now mimics what the experiments do – measure a large subset of the qubits and condition on the outcomes – the remaining qubits still look random in exactly the same strong sense, for almost every way of splitting the system and the bath. In other words, these simple, low-entanglement states exhibit deep thermalization, but for fundamentally computational reasons.

Revisiting the cup of tea 
In the case of ordinary thermalization, when you leave the cup of tea unattended long enough, and take a sip after a while, it tastes like room-temperature tea. In the case of deep thermalization, long after the tea has cooled, if multiple people taste spoonfuls of the tea and probe at it, the leftover tea is still uniform and at room-temperature. 

“In the quantum case, “taking spoonfuls” corresponds to measuring part of the system. Quantum deep thermalization means that even after you measure a large part of the system and use that information, the remaining part still looks random and thermal,” explains Prof. Chakraborty.

Implications and outlook
Seen through this lens, the tension between experiment and theory becomes less mysterious. Experiments can reach deep-thermal-looking states quickly because they do not need to generate truly Haar-random states or enormous entanglement; they only need to generate enough structured pseudorandomness that no physically reasonable observer, classical or quantum, can tell the difference. 

The computational assumptions in the work “do the trick”: they explain how deep thermalization can emerge after short timescales, without invoking prohibitively complex chaotic dynamics.

According to the Professor, this perspective blurs the boundary between physics and computer science. It suggests that part of what physicists call thermalization, and especially deep thermalization, may be as much about what is computationally feasible to detect as it is about microscopic dynamics. 

“The results point toward a universe that can look random and chaotic, not necessarily because it truly is, but, because even the most powerful quantum computers we can realistically build would struggle to prove otherwise.”