Discrete Time Crystals
In NISQ ERA

Defined using symmetry. Consider Hamiltonian Dynamics. (continuous time transnational symmetry).

But operator dynamics shows distinct (and sufficiently robust) periods (against perturbation, de-phasing).

Discrete Time Crystals

Play the same game in Floquet.

Consider a quantum system (tunable using some parameters) that has period T.

The system is said to undergo a spontaneous time transnational symmetry breaking if the correlators of the system exhibits dynamics with a period nT n \in \mathcal{N}, for an extended range of the tunable parameters.

Classical, Equilibrium systems disallow. No free lunch. [Watanabe et. al.]

X kicks

Random ZZ gates (Ising Even)

XX+YY Interactions (\theta)

Background Z fields

Dynamical

Signatures:

Eigenstate

Signatures:

Geometry:

We can play this game in 3 levels too. Consider a spin-1 chain instead. The relevant kick is one that permutes 0->1, 1->2, 2->1.

Again MBL (of correct symmetry) is needed to escape heating up till infinite temperature.

This kick is similar to the RX(4\pi/3).

One can show this kick is unique for a given level. So the only (1-body) kicks that work in three level are all similar to RX(4\pi/3)

So: Underlying Hilbert space dimensions seems to be mapped to the periodicity one can achieve.

But one can reduce a spin 1 chain to a chain of two qubits. (with one extra dimension of patching)

Note that now we have 4 body gates (for the disoder) and the rotations are two body gates. These 4 body gates can be reduced to 6 CNOTS and few rotations. So efficient.

Turns out if one uses the original spin-1/2 brickwall and the reduced three level kick, one still has a stable DTC. (note this brickwall does not have correct symmetry conditions).

Why is this stable?

Geometry+Criticality

collaboration with Maxime Debertolis

Does not look the same.

Turns out no.

Different co-efficents. Different Universility classes

David Luitz