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A time crystal is a phase of a matter which is ordered in time, similar to classical crystals which are ordered spatially. In other words, the structure of a time crystal is ever-changing but with some period. In fact, time crystals are quantum systems whose ground states are characterized by periodic motion (so-called non-equilibrium matter), e.g. periodically changing spins in a chain of ions. See more for example here and on Wiki.

Time crystals were proposed in 2012 by Frank Wilczek as a theoretical concept, however, later their existence was proved (see e.g. references on Wiki page). In July 2021, Google claimed that its team prepared the time crystal on Sycamore processor, see the paper Observation of Time-Crystalline Eigenstate Order on a Quantum Processor.

In many articles on time crystals, I see a statement that time crystals can help to design quantum memories (qRAM). I can imagine that the periodic time change can help somehow increase decoherence times which are low in current qRAMs. However, I was not able to find any details on how time crystals can actually help in qRAM design. Could anybody shed more light on this?

Additional question to Google's claim - did they really prepare the time crystal or rather did they simulate a quantum system behaving like the time crystal?

Cross-posted on Physics.SE

EDIT: Just one idea, how time crystals can be used in qRAM. A ground state of a time crystal is characterized by a periodic oscillations. Such oscillations have an amplitude $A$, frequency $f$ and phase $\varphi$. A general qubit state is $\cos(\theta/2)|0\rangle + \sin(\theta/2)\mathrm{e}^{i\varphi}|1\rangle$. If we were able to set amplitude $A = \cos(\theta/2)$ and phase $\varphi$ of the time crystal ground state, we would be able to represent the qubit with the crystal. Since the crystal is in its ground state, it should stay so for very long time. As a result, decoherence time would be elongated significantly. Of course, the crystal is still prone to noise as for example radioactive background can change the crystal state. Hope this is not non-sense.

Martin Vesely
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As @Rohan Mehta said, qRAM has a technical definition that does not apply to this question. The "qRAM" being referred to here is "qubits".

In this talk (1:03:15 - 1:07:40), Wilczek proposes 2 applications of time crystals to quantum computing: As a clock and to mitigate decoherence. Like @Greenstick, I don't know what a time crystal as a QC clock brings to the table, especially since we don't need it for that. On the other hand, time crystals have been used to fight decoherence. In "Creating and controlling global Greenberger-Horne-Zeilinger entanglement on quantum processors", the authors create and manipulate GHZ states encoded in a time crystal. They observe that the time crystal helps increase the state's coherence time.

Victory Omole
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