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Quantum Simulation of arbitrary Hamiltonians with superconducting qubits

Explore the quantum simulation of arbitrary Hamiltonians using superconducting qubits. Learn about the process, applications, and benefits through collaborations with experts in the field. Experience the accuracy and capabilities of quantum dynamics in molecular collisions and random Hamiltonian simulations.

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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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