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Quantum Simulation of arbitrary Hamiltonians with superconducting qubits

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). Outline. Quantum Simulation

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Quantum Simulation of arbitrary Hamiltonians with superconducting qubits

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  1. 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)

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

  3. 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 .

  4. Superconducting simulator(1) -

  5. Superconducting simulator(2) Hamiltonian Rescaled energies

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

  7. Mapping(1) • Random Hamiltonian • Exact mapping: err=||Hrand-Hqc||=0

  8. Mapping (2) • Molecular collision • Na(3s)+HeNa(3p)+He • err=||H’/l- Hqc||=0 l=|| H’ (t)|| /[h0.1GHz]

  9. Quantum dynamics: Molecular Collision(1) Time dependent Hamiltonian • distance to • time transformation • R2 =b2+v2t2, v=1

  10. Quantum dynamics: Molecular Collision(2) Scattering Probabilities

  11. Quantum dynamics: Quantum Computer(1) Energy-time rescaling • a(t)=e-iH’t a(-∞) =e-i(H’/l)(lt) a(- ∞) a(tqc)=e-iHqc tqca(0) • dtqc/dt=l, tqc(- ∞)=0

  12. Quantum dynamics: Quantum Computer(2) Scattering probabilities

  13. Quantum Computer: Fidelity and Leakage Simulation fidelity Leakage

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

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