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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.

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    $\begingroup$ I have no expertise on time crystals or the nitty gritty of building quantum hardware, so caveat emptor. That said, I imagine they may be useful as a clock, possibly to to aid in error correction. How they would practically differ from an atomic clocks (which have many similarities to analog quantum simulators from what I understand) is less clear to me. I suppose they've been realized on a "digital" quantum computer (Sycamore), so maybe that's one benefit. Having the computational clock integrated versus controlling it fully classically does seem useful, but again I couldn't say exactly why. $\endgroup$
    – Greenstick
    Aug 16, 2021 at 19:49
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    $\begingroup$ Revising the above comment based on a re-read. When I said clock, I meant one used to schedule gates, but this doesn’t actually make sense. In particular, the clock has to be fundamentally classical given that the pulse generators controlling the quantum gates (and thus error correction, too) are themselves classical and driven by a classical controller. Perhaps it’s possible that a time crystal could be used as an “inertial” quantum component to stabilize computations passively or even store information, but again, not a hardware expert. $\endgroup$
    – Greenstick
    Sep 10, 2021 at 20:06

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