concatenated composite pulses: toward high-precision quantum gate implementation
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Concatenated Composite Pulses: Toward High-
Precision Quantum Gate Implementation
Mikio NakaharaDepartment of Physics, Kinki University, Japan
Collaborators; M. Bando, U. Gungordu, T. Ichikawa and Y. KondoPhys. Rev. A 84 (2011) 062311.
J. Phys. Soc. Jpn, 82 (2013) 014004. Phys. Rev. A 87 (2013) 022323.
Financial supports from Kinki Univ., MEXT and JPSJ
1. Motivations
NMR QIP in Rio 2013
NMR QIP in Rio 2013
NMR QIP in Rio 2013
2. Hamiltonian with Errors
NMR QIP in Rio 2013
Two types of errors in NMR context
Pulse length error is due to inhomogeneity in the rf field.
Off-resonance error is due to inhomogeneity in the static strong magnetic field.
They distort the NMR spectrum and cause error in gate operations.
NMR QIP in Rio 2013
NMR QIP in Rio 2013
Time-Development Operator with Errors
3. Composite Pulses
NMR QIP in Rio 2013
Idea of Composite Pulses
NMR QIP in Rio 2013
Time-Development Operator with Errors
NMR QIP in Rio 2013
NMR signal in the presence of errors
NMR QIP in Rio 2013
N=2 cases
NMR QIP in Rio 2013
NMR QIP in Rio 2013
T. Ichikawa, M. Bando, Y. Kondo, and M. Nakahara: Phys. Rev. A 84 (2011) 062311.
M. Bando, T. Ichikawa, Y. Kondo and M. Nakahara, J. Phys. Soc. Jpn. 82, 014004 (2013).
Examples
NMR QIP in Rio 2013
NMR QIP in Rio 2013
4. ConCatenated Composite Pulses (CCCP)
NMR QIP in Rio 2013
Shor’s 9-qubit QECC
NMR QIP in Rio 2013
Successful Example (CinSK)
NMR QIP in Rio 2013
Residual Error Preserving Property
NMR QIP in Rio 2013
NMR QIP in Rio 2013
Example
NMR QIP in Rio 2013
NMR QIP in Rio 2013
NMR QIP in Rio 2013
5. Reduced CCCP
NMR QIP in Rio 2013
Example 1; reduced CinSK
NMR QIP in Rio 2013
Example 2; reduced CinBB
NMR QIP in Rio 2013
NMR QIP in Rio 2013
Fidelity Profiles
NMR QIP in Rio 2013
NMR results
NMR QIP in Rio 2013
6. Robust 2-qubit Gates
NMR QIP in Rio 2013
NMR QIP in Rio 2013
NMR QIP in Rio 2013
NMR QIP in Rio 2013
NMR QIP in Rio 2013
6. Summary
NMR QIP in Rio 2013
NMR QIP in Rio 2013
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