Financial supports from Kinki Univ MEXT and JPSJ

Financial supports from Kinki Univ. , MEXT and JPSJ Concatenated Composite Pulses: Toward High-Precision Quantum Gate Implementation Mikio Nakahara Department of Physics, Kinki University, Japan Collaborators; M. Bando, U. Gungordu, T. Ichikawa and Y. Kondo Phys. Rev. A 84 (2011) 062311. J. Phys. Soc. Jpn, 82 (2013) 014004. Phys. Rev. A 87 (2013) 022323.

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 n n n 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

Time-Development Operator with Errors NMR QIP in Rio 2013

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

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). NMR QIP in Rio 2013

Examples NMR QIP in Rio 2013

NMR QIP in Rio 2013

4. Con. Catenated Composite Pulses (CCCP) NMR QIP in Rio 2013

Shor’s 9 -qubit QECC NMR QIP in Rio 2013

Successful Example (Cin. SK) 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 Cin. SK NMR QIP in Rio 2013

Example 2; reduced Cin. BB 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