What’s a Time Crystal?

UPDATE 23 FEBRUARY 2024: In the couple of years since researchers on the Google Quantum AI team and colleagues at multiple institutions realized a 20 qubit time crystal on Google’s Sycamore quantum computer (original story, below), other groups have exceeded the feat. Most notably, physicists at the University of Melbourne managed a 57-qubit time crystal in 2022, more than twice as large as the Google group’s effort.

Later in 2022, another group at the University of Hamburg managed to produce a continuous time crystal. Earlier attempts, including those from the Melbourne group and Google group, had created discrete time crystals driven by a periodic system—the practical gist being that the time crystal had to be cut off from the system that instigated it and protected from decaying (which ultimately happened regardless). A continuous time crystal, in contrast, should prove more robust against such decay.

Despite these triumphs, time crystals still remain very much in the realm of hard physics. Physicists continue to explore their nature. Applications remain a long ways away, although time crystals still seem to be a potential candidate for memory in quantum computers someday. —IEEE Spectrum

Original article from 9 December 2021 follows:

First conceived of a decade or so ago, a time crystal is a new kind of matter that bears an uncanny resemblance to a perpetual motion machine. Its parts can theoretically move in a repeating cycle without consuming energy for eternity, like a watch that runs forever without any batteries.

Scientists have raced to create this novel phase of matter for years. Now researchers at Google Quantum AI and their colleagues reveal they have created time crystals using Google’s Sycamore quantum computing hardware, findings they detailed online Nov. 30 in the journal Nature.

Whereas classical computers switch transistors either on or off to symbolize data as ones and zeroes, quantum computers use quantum bits, or qubits that, because of the nature of quantum mechanics, can exist in a state of superposition where they are both 1 and 0 simultaneously. By linking qubits together via a quantum effect known as entanglement, a 300-qubit quantum computer theoretically could perform more calculations in an instant than there are atoms in the visible universe. In 2019, Google argued it used Sycamore to display “quantum primacy,” finding answers to problems no classical computer could ever solve.

In the new study, the researchers used a 20-qubit system not for computation, but to realize time crystals. To find out more, we spoke with Google staff research scientist Kostyantyn Kechedzhi and Google senior research scientist Xiao Mi, who conducted much of the research on the theoretical and experimental sides, respectively. The conversation has been edited for length and clarity.

IEEE Spectrum: What is a time crystal?

Kostyantyn Kechedzhi: A crystal is a system of many atoms that, due to mutual interactions, organize themselves into a periodic pattern in space. A time crystal is a quantum system of many particles that organize themselves into a periodic pattern of motion—periodic in time rather than in space—that persists in perpetuity.

Spectrum: What might you compare time crystals to in nature?

Kechedzhi: Persistent periodic motion is very familiar in nature. A system of two massive objects attracting each other due to gravity is the simplest example—the two objects move around the common center of mass following strictly periodic orbits. At first sight, this might seem like an example of a time crystal. However, the key novelty of a time crystal is the periodic motion of a system of many objects interacting with each other.

A system of many interacting objects demonstrates an entirely different behavior compared with just two massive objects orbiting each other—instead of repeated patterns, the motion continually changes. For instance, in the solar system, planets follow trajectories that are approximately periodic, but the true behavior of planets is chaotic, which means a small deviation of a planet from its path today will result in a completely reshaped trajectory over time, albeit billions of years.

The second law of thermodynamics postulates that systems of many interacting objects tend toward more disorder, which appears in contradiction with the strictly periodic motions of a time crystal. Nonetheless, a system of many interacting quantum objects could demonstrate periodic motion without violating the second law of thermodynamics due to a fundamentally quantum phenomenon called many-body localization.

A time crystal is a quantum system of many particles that organize themselves into a periodic pattern of motion—periodic in time rather than in space—that persists in perpetuity.

Spectrum: So in your new work, you created a periodically driven many-body localized time crystal. This is a time crystal consisting of many parts whose activity is driven by an externally applied cyclic series of pulses. And by localization, you mean that physical laws act in the specific locale of this time crystal to help keep it stable and from dissipating energy?

Kechedzhi: Yes. A key property of a localized quantum system of many objects is that a sufficiently weak external pulse or force applied to any one of the objects will affect its neighbors, but will not be felt across the entire system. In this sense, the system’s response is localized. In contrast, in a chaotic system, a small disturbance is felt across the entire system. The phenomenon of localization prevents absorption of energy from the external drive.

Spectrum: How comparable are your time crystals to perpetual motion machines?

Kechedzhi: The time crystals observed in our experiment do not absorb any net energy from the pulses used to drive their behavior. This is perhaps why they are often compared to perpetual motion machines.

However, perpetual motion machines are expected to produce work without an energy source, which would violate the laws of thermodynamics. In contrast, the motion of a time crystal does not produce work without an energy source and therefore does not violate physical laws.

Spectrum: Do your time crystals break down over time?

Kechedzhi: Our processor is not 100% isolated from the environment, and this weak coupling to the environment introduces a finite “extrinsic” lifetime of the time crystal. In other words, after a sufficiently long time, the order is lost and the periodic pattern no longer repeats itself.

Spectrum: What applications might time crystals have?

Kechedzhi: A time crystal is, like ferromagnetism or superconductivity, an example of spontaneous symmetry breaking, or spontaneous order. For instance, a ferromagnet is essentially a system of much smaller magnets whose magnetic poles all point in a single direction, and in this sense are ordered. Symmetry is said to be “spontaneously” broken in such a state, since in normal matter the poles all point in random directions. Stable examples of spontaneous symmetry breaking, as seen in ferromagnetism or the vanishing electrical resistance of a superconductor, often have significant technological value.

Spontaneous symmetry breaking is associated with equilibrium. For instance, think of liquid water freezing into a crystal when brought to a stable low temperature. A remarkable property of the time crystal we observed is its spontaneous order despite it being driven out-of-equilibrium. This observation opens the door to identifying other out-of-equilibrium states of quantum matter with novel types of order.

Google Sycamore chip.Google Quantum AI

Spectrum: What about time crystals has proven difficult to research, and why?

Kechedzhi: The challenge is the isolation of quantum matter from its environment is never perfect.

Spectrum: Why use a quantum computer to help create time crystals?

Xiao Mi: Quantum computers are the platform of choice to realize time crystals because they have precisely calibrated quantum logic gates.

Spectrum: A quantum logic gate is the quantum computing version of the logic gates that conventional computers use to perform computations?

Mi: Yes. Quantum logic gates allow the many-body interactions that are necessary for time crystals to exist to be implemented with very high precision.

Previous studies on time crystals were all performed on so-called quantum simulators. These platforms lack the precision of quantum computers. As a result, many of these experiments were later found to be flawed due to unintended interactions.

Spectrum: What did you show in your new study?

Mi: We engineered quantum circuits that have the types of interactions that are theoretically expected to lead to a time crystal. We then collected data from these quantum circuits and used a variety of techniques to verify that our data are consistent with time-crystalline behavior. This included three things:

1. Any decay or “melting” of time-crystalline order was only induced by external decoherence, not the internal dynamics of our system.
2. The signature of a time crystal was present regardless of the initial state of the system.
3. We could determine the boundary of the time crystal phase—that is, where it “melted.”

Quantum logic gates allow the many-body interactions that are necessary for time crystals to exist to be implemented with very high precision.

Spectrum: What do you personally find most interesting about these results?

Mi: Understanding the behavior of interacting particles near the critical point of phase transitions—for example, the melting temperature of ice into water—is a longstanding problem in physics and still holds many unresolved puzzles for quantum systems. We were able to characterize the phase transition point between the time crystal and quantum chaotic states. This is a very promising direction for early applications of quantum processors as a tool for scientific research, where modest size systems of dozens or hundreds of qubits could already provide new experimental information about the nature of phase transitions.

Spectrum: How might time crystals lead to better quantum computers?

Mi: Having an object like a time crystal that is stable against experimental interference may help design quantum states that are long-lived, a crucial task for the future improvement of quantum processors.

Spectrum: Another time crystal was created using qubits by researchers at Delft University of Technology in the Netherlands. How would you distinguish your work from theirs?

Kechedzhi: The Delft experiment implemented some of the protocols outlined in our earlier theoretical work, which distinguish many-body localized time crystals from so-called pre-thermal time crystals observed in recent years. Whereas pre-thermal time crystals are characterized by finite intrinsic lifetimes, many-body localized time crystals are characterized by a diverging—that is, infinitely long—intrinsic lifetime.

The exceptional flexibility of our processor allowed us to demonstrate that time crystal dynamics persist over a range of system parameters. One consequence of that is our observation of the phase transition between the time crystal and the chaotic behavior. The presence of the phase transition suggests that time crystal is a distinct state of matter from the more ubiquitous chaotic many-body state, including pre-thermal time crystals.

Crucially, the protocol we describe in our new study is scalable—it can be easily applied to a larger quantum processor. This is a result of further theoretical analysis significantly improving our prior work on which the Delft experiment was based. In the future, I can see our experiment repeated on larger and larger systems.

Spectrum: What specific directions do you think your research might go from here?

Kechedzhi: One of our goals is to develop our processor into a scientific tool for physics and chemistry. The key challenge is reducing the error in the device. This is key for future applications of quantum processors and realization of fault-tolerant quantum computation. It needs to be addressed through improvements in the hardware, algorithmic error mitigation strategies and fundamental understanding of the role of noise in many-body quantum dynamics.