Fock-Space Prethermalization: A 72-Qubit Route to Slower Floquet Heating

Every Floquet engineer eventually meets the same enemy: heating. Periodic driving can make quantum matter behave as if it has new interactions, new bands, new symmetries and even new phases of matter. But the drive is also an energy source. If a many-body system keeps absorbing energy from that clock, the carefully engineered state can wash out into a hot, featureless state before it does anything useful.

A recent superconducting-processor experiment points to a fresh way of slowing that failure mode. In “Fock space prethermalization and time-crystalline order on a quantum processor”, Zehang Bao, Zitian Zhu, Yang-Ren Liu, Zixuan Song and a large collaboration report a disorder-free mechanism they call Fock-space prethermalization (FSP). The preprint, first posted in October 2025 and updated in March 2026 as arXiv:2510.24059, uses 72 superconducting qubits to observe a time-crystalline response lasting more than 120 Floquet cycles for generic initial Fock states.

The energy lesson is subtle but powerful: the drive still costs energy, and no thermodynamic law is bypassed. The advance is that the system’s own many-body connectivity can make absorption dramatically slower.

That distinction matters for the quantum-energy community. Floquet protocols are often discussed as routes to better batteries, heat engines, sensors and topological transport. But practical devices need more than exotic dynamics. They need a time window in which the engineered state is stable enough to charge, sense, route heat or process information. Fock-space prethermalization is interesting because it attacks that stability problem at the level of the many-body state space itself.

What is being prethermalized?

In ordinary language, thermalization means “settling down.” In a closed many-body quantum system, it usually means that local observables start looking as though the system has shared energy among all its available degrees of freedom. In a periodically driven system, that process can be brutal: without protection, the drive can eventually heat the system toward an effectively infinite-temperature state where the special Floquet order is gone.

Prethermalization is the useful pause before that final destination. The system behaves for a long time as if it has reached a quasi-steady, organized regime governed by an effective Hamiltonian or an approximate conservation law. It is not truly safe forever, but it can be safe long enough to be useful. Earlier high-frequency Floquet theory, including work by Abanin, De Roeck, Ho and Huveneers, showed how rapid driving can exponentially slow heating in broad classes of interacting systems.

Fock-space prethermalization is different in emphasis. Instead of relying mainly on high-frequency driving or spatial disorder, the Bao collaboration focuses on the connectivity of Fock space: the enormous graph of many-body configurations available to the system. If ordinary real space is where qubits sit, Fock space is the map of all possible bit-string configurations and the drive-induced transitions among them. The paper argues that a kinetic constraint associated with approximately conserved domain-wall numbers divides that graph into many sparse sub-networks. Energy and information then do not spread through configuration space as quickly as they otherwise would.

The experiment: 72 qubits, 120 cycles, site-resolved diagnostics

The primary result is a programmable Floquet experiment on a superconducting quantum processor. The authors prepare generic initial Fock states, apply a repeated drive, and monitor whether the system rapidly thermalizes or remains trapped in a long-lived prethermal regime. Their headline observation is a form of time-crystalline order based on FSP, persisting for more than 120 driving cycles.

That number is not just a scale trophy. Larger processors allow researchers to ask whether the effect is genuinely many-body or merely a short-lived few-qubit oscillation. The paper reports finite-size scaling for domain-wall and Fock-space dynamics by varying system sizes. It also connects the observed crossover behaviour to the eigenstructure of the Floquet unitary — the one-period evolution operator that encodes the whole drive.

The diagnostic piece is especially important. Time-crystal language can be slippery: a system that wiggles for many cycles is not automatically a time crystal. Bao and colleagues identify the underlying kinetic constraint by measuring site-resolved correlators, a way of checking whether the expected domain-wall structure is really present locally rather than inferred from a single global signal. That makes the work more useful as an engineering case study. It does not only say “we saw persistent oscillations”; it asks what microscopic constraint kept the state from heating too quickly.

Why disorder-free matters

Many early discrete time-crystal proposals relied on many-body localization, where disorder plus interactions prevent a driven system from absorbing energy efficiently. The classic theoretical papers by Khemani, Lazarides, Moessner and Sondhi, and by Else, Bauer and Nayak, clarified how a periodically driven system could break discrete time-translation symmetry. Experiments in trapped ions, nitrogen-vacancy centers and superconducting processors then helped turn that idea into a hardware target.

Disorder is useful, but it is not always what an engineer wants. Too much disorder can make a device hard to reproduce, tune, scale or couple to other components. A disorder-free protection mechanism is attractive because it suggests a cleaner design rule: use constraints and graph structure in configuration space to slow thermalization. In that sense, FSP sits beside high-frequency prethermalization and many-body localization as another entry in the Floquet stability toolbox.

For energy applications, the important question is not whether a state lasts forever. It is whether the useful task finishes before heating, noise and measurement backaction erase the ordered dynamics.

What this means for quantum batteries and thermal machines

Floquet.ca has covered several quantum-battery proposals where periodic kicks, long-range interactions or time-crystalline order improve energy storage in model systems. FSP does not by itself build a battery. The experiment is better understood as a control milestone: it shows a route to keeping a driven many-body system organized over many repeated operations. That is precisely the problem any Floquet quantum battery must solve before “fast charging” becomes a device principle rather than a Hamiltonian sketch.

Consider a quantum battery built from spins or qubits. Periodic driving can inject energy coherently and, in ideal models, generate collective charging advantages. But the same drive can create unwanted transitions, dephase stored energy or push the system toward a useless thermal mixture. If Fock-space constraints can be designed into the charger-battery dynamics, they may help separate useful charging pathways from uncontrolled heating pathways. That is a hypothesis, not a demonstrated product — but it is a concrete engineering direction.

The same logic applies to quantum heat engines. Periodically driven thermal machines rely on limit cycles, coherence and controlled energy exchange with reservoirs. A prethermal window can make the difference between a clean engine cycle and a smeared-out transient. Still, the second law remains intact. The external drive is a work resource; reservoirs carry heat and entropy; control electronics and measurements have costs. FSP may improve the lifetime or fidelity of a cycle, but it does not make a beyond-Carnot engine in the naïve sense of free extra work.

A bridge between time crystals and useful Floquet control

The paper also fits into a broader 2026 conversation about time crystals on quantum devices. Gonzalo Camacho and Benedikt Fauseweh’s review “Time Crystals on Quantum Devices” argues that modern platforms now support a more diverse classification: closed and open, discrete and continuous, topological, quasiperiodic, critical and controlled versions. The Bao result is a useful example of why that taxonomy is needed. Its stabilization mechanism is not simply “add disorder and hope localization protects the phase.” It is a kinetic-constraint story in Fock space, implemented on programmable hardware.

For non-specialists, the safest analogy is traffic design. If every road connects to every other road, congestion and spreading happen quickly. If the city plan contains bottlenecks, one-way streets and neighbourhoods with limited exits, motion across the whole map slows down. FSP is not literally traffic, but the intuition helps: the many-body system’s configuration graph is structured so that the drive cannot freely scramble the state across all possibilities at once.

That graph-based viewpoint may become increasingly important as quantum processors mature. The same hardware used for algorithms can emulate quantum materials that would be hard to build in a crystal. Instead of asking only “how many qubits?” researchers can ask “what geometry does the processor create in Hilbert space?” For Floquet engineering, that is a profound shift. The engineered object is not merely a pulse sequence; it is an effective many-body landscape in which energy absorption, information spreading and order formation compete.

What remains open

The result is a preprint, so the usual scientific caution applies: peer review, independent replication and platform comparison will matter. It is also a finite-device experiment. More than 120 cycles on 72 qubits is impressive, but it is not an infinite-time phase transition. The most important next questions are practical:

• Robustness: How sensitive is the FSP regime to calibration errors, noise, qubit loss, pulse imperfections and coupling disorder?
• Transferability: Can similar Fock-space constraints be implemented in trapped ions, Rydberg arrays, cold atoms or photonic platforms?
• Task coupling: Can the protected window improve a specific operation such as sensing, state transfer, battery charging or a thermal-machine cycle?
• Thermodynamic accounting: How much external work and control overhead is required to create and maintain the protected dynamics?

Those questions do not weaken the result. They are the route by which a physics demonstration becomes an engineering principle. In fact, FSP is most exciting when treated as a disciplined anti-hype story. It does not promise perpetual motion or unlimited energy storage. It offers a mechanism for delaying the most common failure mode of driven many-body systems.

The bottom line

Fock-space prethermalization gives Floquet engineers another way to think about stability. Instead of only tuning frequency, adding disorder or leaning on dissipation, one can shape the many-body configuration network so that thermalization is slowed by approximate constraints. Bao and colleagues’ 72-qubit demonstration is therefore more than another time-crystal headline. It is a hardware-scale experiment in energy-flow architecture: controlling how a periodically driven quantum system explores its own possible states.

For quantum energy research, that is exactly the kind of progress to watch. The path to useful quantum batteries, thermal machines and heat-routing devices will likely depend less on one spectacular loophole and more on many careful methods for extending coherent, ordered operation. FSP is one of those methods. It turns the abstract geometry of Fock space into a practical lever against Floquet heating.