University:
Boston University
Course:
CAS PY 105 | Physics 1
Academic year:

2020
Views:

144

Pages:

22
Author:

Jamison Harrison

On the IBM Q “Johannesburg” device i : i-th physical qubit : coulings between qubits On the IBM Q “Johannesburg” device 0 3 1 2 5 4 On the IBM Q “Johannesburg” device 0 3 1 2 5 4 On the IBM Q “Johannesburg” device 0 3 1 2 5 4 On the IBM Q “Johannesburg” device 0 3 1 2 5 4 On the IBM Q “Johannesburg” device 0 1 3 2 5 4 On the IBM Q “Johannesburg” device PD of measuring the state |ψ>=e^(-iHBt)x e^(-iHXYt)e^(-iHEt)|0 > with t=0.1 IBM Q Exact Error mitigation noisy circuit mitigation operation Error ε is mitigated with its inverse operation ε-1 Error mitigation Mitigated Trotter: Mathematical Formalism of Error mitigation Error modeling: Measurement of noisy circuit Characterization of the noise Measurement of the state UρiU†with some basis |k> and ref state ρi Mathematical Formalism of Error mitigation Error modeling: From experiments Want Computable Measurement of noisy circuit Characterization of the noise Measurement of the state UρiU†with some basis |k> and ref state ρi Mathematical Formalism of Error mitigation Error modeling: From experiments Want Computable Measurement of noisy circuit Characterization of the noise Measurement of the state UρiU†with some basis |k> and ref state ρi Mathematical Formalism of Error mitigation Compute the mitigation operation: -1 Since ε ○ ε is identity, Want Known Mathematical Formalism of Error mitigation -1 Now we know ε . It can be expressed as Mathematical Formalism of Error mitigation -1 Now we know ε . It can be expressed as We approximate this by taking only the diagonal elements for simplicity: Mathematical Formalism of Error mitigation Ideal probability measuring x can be obtained from the LC of the noisy circuits with some additional Pauli: Error mitigation In our case, we have multiple mitigation operations, but the idea is the same. On the IBM Q “Johannesburg” device PD of measuring the state |ψ>=e^(-iHBt)x e^(-iHXYt)e^(-iHEt)|0 > with t=0.1 With mitigation No mitigation On the IBM Q “Johannesburg” device PD of measuring the state |ψ>=e^(-iHBt)x e^(-iHXYt)e^(-iHEt)|0 > with t=0.1 With mitigation Exact What I have to work on from now ● Pauli Twirling to restrict ε-1 to have exactly only diagonal elements d+1-dim Gravity d-dim GT What I have to work on from now ● Pauli Twirling to restrict ε-1 to have exactly only diagonal elements ● Does there exist a duality to a strongly coupled spin system? Analogous to Ads/CFT duality: d+1-dim Gravity Weak Coupling LGT d-dim GT Strong Coupling Spin System Summary ● Investigated the lattice gauge theory (2+1d U(1) theory) model on a spin basis. ● Constructed an optimized quantum circuit for it. ● Tested it on a noisy quantum device with the noise mitigation which gave improvements in the simulation result.