# Paper Introduction: Simulation of Melting in a Time Crystal Network.

In this article, we present the results of a quantum computer simulation of melting in a time crystal (time crystal). A time crystal is a system with translational symmetry in the time direction. In other words, it is a system that has robust periodicity under certain conditions. This does not occur spontaneously, but it does appear in special lattices that are realized by applying a potential. One such lattice is the discrete Floquet lattice. This lattice is represented by a periodically varying Hamiltonian

$H_1=\hbar g(1-\epsilon)\sum_l\sigma_l^x ~~(0<t<T_1)$

$H_2=\hbar\sum_{l,m}J_{lm}^z\sigma_l^z\sigma_m^z+\hbar\sum_lB_l^z\sigma_l^z~~(T_1<t<T_2)$

The result is where g is a constant called the g factor, $\epsilon$ is the error rate, and $\sigma_l^z$ and $\sigma_l^x$ are the z and x components of the Pauli matrix, respectively. Also, the period of this Hamiltonian is $T=T_1+T_2$ . On a quantum computer, we will use the effective Hamiltonian instead of this.

$H_{\epsilon,T}^{eff}=\sigma_i\Epsilon_i\mid i\rangle \langle i\mid + \sum_{i,j}K_{ij}\mid i\rangle \langle j\mid$

On a quantum computer, the system is calculated by mapping 0s and 1s in the qubit to upward and downward directions in the quantum spin, respectively, and the network of time crystals is represented by pairs of states in the entangled qubit system. The network of time crystals is represented by a pair of states in an entangled qubit system. Calculations with two different effective Hamiltonians, including the one above, show that the higher the error rate, the more melting of time crystals occurs and the more multiple large time crystals separated by domain walls* are generated. The distribution function of the states with respect to the wavenumber was calculated for 8 to 12 qubits, and the results showed a power distribution for small error rates and a normal distribution for large error rates.

This is an important result for entanglement generation. It may be possible to create arbitrary entangled states with it. I am also curious about how to reverse this process. This is a study that can be simulated well in blueqat, and I would like to reproduce this result when I get a chance.

*Boundary surface separating the structures in the spin system. In this case, it is a boundary that distinguishes a group of entangled states.

[1907.13146] Simulating complex quantum networks with time crystals (arxiv.org)