Quantum experiments at the IBM's NISQ machines

Condensed matter presents clear thermodynamical phases. The last two hundred years have been devoted to studying the phases of matter in its various forms with ever growing experimental and theoretical tools.

Now, new research is unveiling yet new phases of matter. But in the time domain. How can phases be defined when things are evolving? One situation is when the evolution is under a periodic driving. This seemingly simple situation gives rise to an unexpected new set of phenomena. One of them is the time crystal.

A time crystal shows extraordinary properties. By definition, a time crystal is a state of matter that is being driven under a periodic time-dependent field with a given frequency. Suprisingly, the natural frequency of the time cyrstal is a different frequency! Indeed, the periodicities displayed by the time crystal are subharmonic (the driving frequency divided by some integer number). This is similar to the crystalline phase in that the interactions between the atoms forming the crystal, do not present any periodicy, yet the arrangement of the atoms in the crystal lead to well defined spatial periodicities. The appearing phase thus present a regularity that is an emerging property.

Furthermore the subharmonic response of the time crystal is rigid. This means that if the driving is not perfect, the time crystal still presents the subharmonic periodicity. This is a property of the many-body interactions creating the time crystal. In the absence of these interactions, the time crystal does not develop a subharmonic frequency.

Despite of the continuous drive, the time crystal does not blow up. It does not heat up. There is no entropy exchange. We are in a crypo equilibrium. This is reminiscent of the Rabi oscillations of a two-level system. We can drive the system, and the system just oscillates in resonance with the field.  But this is quite mind boggling for a macroscopic system. How come the system does not obey the eigenstate thermalization hypotesis? Because the time-crystal phase appear if the interactions governing the system are disordered! The disorder gives rise to localization, to many-body localization. The time-crustal phase, is actually a many-body localized phase with a subharmonic periodicity.

In our group, we are exploring how to create time cyrstals using atoms. But before that, we can simulate them in a quantum computer. This is our BasQ project.

Thanks to the revolutionary properties of the new IBM Heron processors (NISQ computers), we can run experiments that create a time crystal in many qubits of the NISQ processor. Here you have the results of a time crystal created with 100 qubits disordered Ising interactions between qubits over 50 cycles. Quite an achievement!

All qubits are initialize in the state 1, and in one cycle they flip to -1 as you can see. The oscillations continue. Little by littel, decoherence and noisy qubits reduce the signal. But the signature of the time crystal is perfectly mantained over 50 cycles. This is more clearly see if we Fourier transform the signal for each qubit as shown in the next figure:

where frequency 26 corresponds to half the driving frequency. Now, we can start simulating time crystals!