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