quantum simulation of arbitrary hamiltonians with superconducting qubits colin benjamin (niser,...
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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
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Outline
• Quantum Simulation
• Superconducting simulator Quantum statics: Hamiltonian
mapping Quantum dynamics
• Application to-i. Random real Hamiltonian ii. Molecular collisions
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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 .
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Superconducting simulator(1)
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Superconducting simulator(2)
Hamiltonian
Rescaled energies
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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
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Mapping(1)
• Random Hamiltonian
• Exact mapping:
err=||Hrand-Hqc||=0
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Mapping (2)
• Molecular collision
• Na(3s)+HeNa(3p)+He
• err=||H’ Hqc||=0
=|| H’ (t)|| /[0.1GHz]
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Quantum dynamics: Molecular Collision(1)
distance to time transformation R2 =b2+v2t2, v=1
Time dependent Hamiltonian
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Quantum dynamics: Molecular Collision(2)
Scattering Probabilities
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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
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Quantum dynamics: Quantum Computer(2)
Scattering probabilities
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Quantum Computer: Fidelity and Leakage
Simulation fidelity Leakage
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Conclusion
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• proposed a superconducting quantum simulator
• can simulate any random Hamiltonian -mapping error: zero• example simulation of a molecular
collision (electron orbital scattering) - 99% fidelity