Quantum Simulation of arbitrary Hamiltonians with superconducting qubits Colin Benjamin (NISER, Bhubaneswar) Collaborators: A. Galiautdinov, E. J. Pritchett, M. Geller, A. Sornborger and P. C. Stancil (UGA) J. M. Martinis (UCSB) 1

Outline Quantum Simulation Superconducting simulator Quantum statics: Hamiltonian mapping Quantum dynamics Application to-i. Random real Hamiltonian ii. Molecular collisions 2

Introduction Definition: Quantum simulation is a process in which a quantum computer simulates another quantum system(Lloyd, ‘96). Corollary: A classical computer can also simulate quantum systems. 3

Superconducting simulator(1) - 4

Superconducting simulator(2) Hamiltonian Rescaled energies 5

The 1-excitation subspace Superconducting simulator(3) H qc = f’s are function of g’s 6

Mapping(1) Random Hamiltonian Exact mapping: err=||H rand -H qc ||=0 7

Mapping (2) Molecular collision Na(3s)+He  Na(3p)+He err=||H’  H qc ||=0 =|| H’ (t) || / [  0.1 GHz] 8

Quantum dynamics: Molecular Collision(1) distance to time transformation R 2 =b 2 +v 2 t 2, v=1 Time dependent Hamiltonian 9

Quantum dynamics: Molecular Collision(2) Scattering Probabilities 10

Quantum dynamics: Quantum Computer(1) a(t)=e -iH’t a (-∞) =e -i(H’/ )( t) a(- ∞ )  a(t qc )=e -iHqc tqc a(0) dtqc/dt=   tqc(- ∞ )=0 Energy-time rescaling 11

Quantum dynamics: Quantum Computer(2) Scattering probabilities 12

13 Quantum Computer: Fidelity and Leakage Simulation fidelityLeakage

Conclusion 14 proposed a superconducting quantum simulator can simulate any random Hamiltonian -mapping error: zero example simulation of a molecular collision (electron orbital scattering) - 99% fidelity