Download NMR quantum computer

Financial supports from Kinki Univ.,
MEXT and JSPS
Liquid State NMR
Quantum Computing
Mikio Nakahara,
Research Centre for Quantum
Computing, Kinki University, Japan
Physical Realizations of QC @ Tehran,
Jan. 2009
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Plan of Talk
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1. Introduction
2. NMR
3. NMR Hamiltonian
4. Gate Operations
5. Pseudopure State
6. Measurement
7. DiVincenzo Criteria
8. Summary
Physical Realizations of QC @ Tehran,
Jan. 2009
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1. Introduction
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Jan. 2009
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Qubits in NMR Molecule
Trichloroethylene
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Jan. 2009
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Plan of Talk
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1. Introduction
2. NMR
3. NMR Hamiltonian
4. Gate Operations
5. Pseudo-Pure State
6. Measurement
7. DiVincenzo Criteria
8. Summary
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Jan. 2009
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NMR (Nuclear Magnetic Resonance )
=MRI (Magnetic Resonance Imaging)
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NMR
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Schematic of NMR
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Molecules used in NMR QC
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Plan of Talk
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1. Introduction
2. NMR
3. NMR Hamiltonian
4. Gate Operations
5. Pseudopure State
6. Measurement
7. DiVincenzo Criteria
8. Summary
Physical Realizations of QC @ Tehran,
Jan. 2009
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3.1 Single-Qubit Hamiltonian
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Hamiltonian in Rotating Frame
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2-Qubit Hamiltonian
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Plan of Talk








1. Introduction
2. NMR
3. NMR Hamiltonian
4. Gate Operations
5. Pseudopure State
6. Measurement
7. DiVincenzo Criteria
8. Summary
Physical Realizations of QC @ Tehran,
Jan. 2009
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1-Qubit Gates
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Example: Hadamard gate
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Example: Hadamard gate 2
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Selective addressing
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In resonance:
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Jan. 2009
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0.1
1.000
0.995
0.990
0.0
0.1
0.0
0.1
0.1
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0.05
1.000
0.999
0.998
0.00
0.05
0.00
0.05
0.05
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2-Qubit Gates: CNOT
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Plan of Talk
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1. Introduction
2. NMR
3. NMR Hamiltonian
4. Gate Operations
5. Pseudopure State
6. Measurement
7. DiVincenzo Criteria
8. Summary
Physical Realizations of QC @ Tehran,
Jan. 2009
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Spins are in mixed state!
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Preparation of a pseudopure state in
terms of temporal average method
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Temporal average method
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Averaging three contributions
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Plan of Talk








1. Introduction
2. NMR
3. NMR Hamiltonian
4. Gate Operations
5. Pseudopure State
6. Measurement
7. DiVincenzo Criteria
8. Summary
Physical Realizations of QC @ Tehran,
Jan. 2009
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6.1 Free Induction Decay (FID)
|00〉
|01〉
|10〉
|11〉
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Free Induction Decay (FID)
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6.2 Quantum State Tomography
We want to “measure” the density matrix.
 Measure observable such as
magnetizations to find linear combinations
of the matrix elements of the density
matrix.
 Not enough equations are obtained.
 Deform the density matrix with pulses to
obtain enough number of equations.
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2-Qubit QST
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Plan of Talk
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

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
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
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1. Introduction
2. NMR
3. NMR Hamiltonian
4. Gate Operations
5. Pseudopure State
6. Measurement
7. DiVincenzo Criteria
8. Summary
Physical Realizations of QC @ Tehran,
Jan. 2009
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DiVincenzo Criteria for NMR QC
A scalable physical system with well
characterized qubits.
 The ability to initialize the state of the qubits
to a simple fiducial state, such as |00…0>.
 Long decoherence times, much longer than
the gate operation time.
 A “universal” set of quantum gates.
 A qubit-specific measurement capability.
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Scalability
Selective addressing to each qubit
becomes harder and hader as the # of
qubits increases. Limited # of nuclear
spices and overlap of resonance freqs.
 Signal strength is suppressed as the # of
qubits increases. Readout problem.
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Initialization (pseudopure state)
# of steps required to prepare a
pseudopure state increases exponentially
as the # of qubits increases.
 No real entanglement
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Long decoherence time
Decoherence time
 Single-qubit gate operation time
 Two-qubit gate op. time
 May execute Shor’s algorithm for 21=3X7.
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A “universal” set of quantum gates.
One-qubit gates by Rabi oscillation.
 Two-qubit gates by J-coupling.
 Cannot turn off interactions; reforcusing
technique becomes complicated as the #
of qubits increases.
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Measurement capability.
FID is a well-established techunique.
 Quantum State Tomograpy and Quantum
Process Tomography are OK.
 S/N scales as
, which limits
the # of qubits to ~ 10.
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Still…
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NMR QC is commercially available.
It can execute small scale quantum algorithms.
It serves as a test bed for a real QC to come.
May ideas in other realizations are inspired from
NMR.
We use NMR QC to demonstrate theoretical ideas,
such as decoherence suppression, optimal control
of a Hamiltonian etc.
Physical Realizations of QC @ Tehran,
Jan. 2009
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Plan of Talk








1. Introduction
2. NMR
3. NMR Hamiltonian
4. Gate Operations
5. Pseudopure State
6. Measurement
7. DiVincenzo Criteria
8. Summary
Physical Realizations of QC @ Tehran,
Jan. 2009
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Liquid state NMR QC is based on a wellestablished technology. Most of the materials
introduced here have been already known in the
NMR community for decades.
There are still many papers on NMR QC.
It is required to find a breakthrogh for a liquid
state NMR to be a candidate of a working QC.
ENDOR, Solid state NMR…
Thank you for your attention.
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