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)

n 3 000 , 001 , 010 , 011 , 100 , 101 , 110 , 111

111 2

011 , 101 , 110

001 , 010 , 100

000

0

3

2

1

1

132

12233

f

gf

ggf

Hqc=

f’s are function of g’s6

Mapping(1)

• Random Hamiltonian

• Exact mapping:

err=||Hrand-Hqc||=0

7

Mapping (2)

• Molecular collision

• Na(3s)+HeNa(3p)+He

• err=||H’ Hqc||=0

=|| H’ (t)|| /[0.1GHz]

8

Quantum dynamics: Molecular Collision(1)

distance to time transformation R2 =b2+v2t2, 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(tqc)=e-iHqc tqca(0)

• dtqc/dt=tqc(- ∞)=0

Energy-time rescaling

11

Quantum dynamics: Quantum Computer(2)

Scattering probabilities

12

13

Quantum Computer: Fidelity and Leakage

Simulation fidelity Leakage

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