Time Independent Universal Computing with Spin Chains: Quantum Plinko Machine

We present a scheme for universal quantum computing using XY Heisenberg spin chains. Information is encoded into packets propagating down these chains, and they interact with each other to perform universal quantum computation. A circuit using g gate blocks on m qubits can be encoded into chains of length $O(g^{3+\delta} m^{3+\delta})$ for all $\delta >0$ with vanishingly small error.