Generation and Generation and suppression of decoherence suppression of decoherence in NMR quantum computerin NMR quantum computer

Mikio Nakahara (Kinki University)Mikio Nakahara (Kinki University)in collaboration within collaboration with

Yasushi Kondo, Shogo Tanimura, Sachiko Kitajima, Yasushi Kondo, Shogo Tanimura, Sachiko Kitajima,

Chikako Uchiyama and Fumiaki ShibataChikako Uchiyama and Fumiaki Shibata

J. Phys. Soc. Jpn., 76, 074002 (2007).J. Phys. Soc. Jpn., 76, 074002 (2007).

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Plan of the talk 1. Introduction

2. A Brief Introduction to Decoherence

3. Liquid-state NMR Quantum Computer (QC)

4. Artificial decoherence and its suppression4.1 Generation of artificial relaxation

4.2 Demonstration of bang-bang control

4.3 Theoretical Analysis

5. Decay of Entanglement due to Noise

6. Summary

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1.1. Introduction: DiVincenzo CriteriaIntroduction: DiVincenzo Criteria

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2. Brief Introduction to Decoherence

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Example: Phase-Flip channel

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Bloch vector

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Alternative Formalism (ours)

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Phase-Flip channel vs phase decoherence in NMR

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Probability distributions

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3. Liquid State NMR Quantum Computer3. Liquid State NMR Quantum Computer

systemsystem

environmentenvironment

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HamiltonianHamiltonian

13C

H

Cl

Cl

Cl

1111

22

22

systemsystem

environmentenvironment

qubit 1qubit 1

qubit 2qubit 2

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Spin flip = Telegraph noise

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4.1 Decoherence in Quantum Channel

Quantum Channel

Noise (environment)

Loss of Information

Alice Bob

4. Generation of Artificial Decoherence

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4.2 Qubit Under RTN

111122

22

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Experimental Procedure

+

-

+ +

+

+

+ + +-

--

----

-

reference pulsesreference pulses

random pulsesrandom pulses

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Artificial Transverse Relaxation:Experimental Results

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4.3 Suppression of Decoherence Spin Spin EchoEcho

Cancellation fails if noise Cancellation fails if noise

changes during the cyclechanges during the cycle..

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F. K. Wilhelm and K. Semba, in F. K. Wilhelm and K. Semba, in PHYSICAL REALIZATIONS OF PHYSICAL REALIZATIONS OF QUANTUM COMPUTING: Are the DiVincenzo Criteria Fulfilled in 2004QUANTUM COMPUTING: Are the DiVincenzo Criteria Fulfilled in 2004??

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Artificial Transverse Relaxation+Bang-Bang control

+ + + -+---

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Suppression of artificial transverse relaxation

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5 Theoretical Analysis5 Theoretical Analysis5.1 Without BB pulses5.1 Without BB pulses

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5.2 With BB Pulses

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Suppression of artificial transverse relaxation

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6. Decoherence in Entangled Pair

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Hamiltonian and Initial State

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With Bang-Bang PulsesWith Bang-Bang Pulses

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Example:

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SummarySummary

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Two-spin molecule as a system and its environment

EnvironmentEnvironment

systemsystem• System• Environment• Interaction in between

→→ 　　 Natural DecoherenceNatural Decoherence

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Artificial decoherence (our case)Artificial decoherence (our case)

environmentenvironmentsystem 2system 2

system 1system 1

~

+ stochastic classical field on the subsystem 2Teklemariam et al, Phys. Rev. A 67, 062316 (2003)

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Simulation of Artificial Relaxation