The Quantum Game of Life

Undergraduate Research Project by Patrick Rall

Advised by Nicole Yunger Halpern and Ning Bao

John Preskill Theoretical Physics Group, IQIM, Caltech

What are cellular automata?

Example: Conway's Game of Life

Figure 1: Conway's Game of Life

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Conway's Game of Life simulated with various initial states. Initial states are presented in red for {{ showtime }} ms, then simulated for {{ simcycle}} iterations with {{ simtime}} ms per iteration.

Uses of cellular automata


Outline for Quantum Cellular Automata

Quantum Bits or Qubits

  • Superposition of states:

$|\Psi\rangle = c_0|0\rangle + c_1|1\rangle$ where $c_0,c_1 \in \mathbb{C}$

  • Helpful geometric picture: Bloch sphere

$|\Psi\rangle = \sin(\theta)|0\rangle + \cos(\theta) e^{i\phi} |1\rangle$ where $\theta \in (0,\pi)$ and $\phi \in (0,2\pi]$

Figure 2: Bloch Sphere

Quantum Cell Colors

Figure 3: Bloch Sphere Color Mapping

Quantum Cell Colors

Figure 4: Bloch Sphere Examples

Quantum Update Rules: My Approach

Figure 6: Quantum One-Dimensional Block Cellular Automata

Demonstration: Quantum Block Cellular Automata

Entanglement Measures

Figure 7: Entangled state

$\mathcal{I}_{ij} = S_{ij} - S_i - S_j$

Demonstration: Mutual Information Networks

Conclusion

Collaboration with Colorado School of Mines

Future Directions

Thank you for your attention!

Acknowledgments

References