Generation of entanglement & suppression of decoherence in ENDOR-based quantum computing
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Transcript of Generation of entanglement & suppression of decoherence in ENDOR-based quantum computing
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Generation of entanglement & suppression of decoherence in ENDOR-ba
sed quantum computing
Robabeh Rahimi1, Akira SaiToh2, and Mikio Nakakara1
1 Department of Physics, Kinki University2 Graduate School of Engineering Science, Osaka University
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2007/9/? IICQI'07, Kish, IRAN 2
Liquid state NMR Quantum ComputingSeems working fine
Drawbacks of NMR quantum computing
• requires number of experiments, molecules
• weak signal intensity
Pseudo-pure states come with some costs!!
Exponential !!
!
Sates in the current NMR experiments separable (non-entangled)
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For NMR Quantum ComputingHigher nuclear spin polarizations are requires
• Directly:
lowering the temperature; mK required!
increasing the magnetic field; current technology• Indirectly:
parahydrogen molecule; a large number of qubits
dynamic nuclear polarization (DNP)
Spin polarization is transferred
from electron spins, with high spin polarization,
to the nuclear spins, with low spin polarizationlow spin polarization.
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Electron spin bus systems forquantum computing
Solid state quantum computingwith a bus spin, an electron spin, coupled to client qubits, many nuclear spins.*
* M. Mehring, J. Mende, Phys. Rev. A 73, 052303 (2006)
solid state
can be cooled to low temperaturewith an available high magnetic field
quantum limit can be achieved
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ENDOR; Electron Nuclear DOuble ResonanceNMR in paramagnetic entities
Pulsed ENDORelectron-nuclear spin manipulation technology
high sensitivity & high polarization from ESR high resolution & nuclear selectivity from NMR
Magnetic Resonasnce Technology: ENDOR = ESR + NMR High sensitivity ( ~ 101-2 GHz) High resolution ( ~ 1 kHz)
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Block Diagram of Pulsed QC-ENDOR Setup
X-band ( 10 GHz) Version:
~ DetectorTWTAPulse Former
RF Generator Nd:YAG LaserRF Amplifier
8 channel
Two Direct Digital Synthesizers
1 kW
300 W, 0.25 150 MHz 500 W, 0.30 35 MHz1000 W, 0.01 250 MHz
50 Hz, 90 mJ (at 532 nm) 1064/532/355/266 nm
High-Speed Digital Oscilloscope
Pulse Programmer
Water-cooling Electromagnet (-1.5~1.5 T)
9.6 GHzMW OSC.
ENDOR Probehead(Dielectric Resonator with RF Coil)Operating at liq. He Temp.
Liq. He Cryostat with a Gas-Flow Controller
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Pulse Electron Multiple Resonance Spectrometers
ESR/ENDOR/ELDOR
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Entanglement & ENDOR
• Pseudo-pure state entanglemententanglement*:
*Mehring et al., PRL. 90, 153001(2003)
(a) (b) (c)
neneP
neneP
neSI
2
1
2
1 )()2/( 2434 MWRF
(a) (b) (c)
1
2
4
3
w24
w12
w34
1
2
4
3
w24
w12
w34
1
2
4
3
w24
w12
w34
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(Pseudo-)Entanglement
ENDOR quantum computing
MW RF1 RF2 Bell state nTPPI
w24 w12 w34 f1 − f2
w24 w34 w12 f1 + f2
w13 w12 w34 f1 + f2
w13 w34 w12 f1 − f2
2
1
2
1
2
1
2
1ESRENDOR
1
2
4
3
w24
w12
w34
w13
RF1 RF2 RF2
echo
MW MW MW
2
2
2
2
1f
2f109
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Malonyl Q-band
1.198898w24
1.198898w24
1.201028w13
B0/T
C
B
A
22.701w34
79.699w12
79.699w12
22.701w34
79.757w12
22.777w34
RF2/MHzRF1/MHz
0 2 4 6 8 10
TPPI Frequency / MHz
21
21
21
|1 − 2 ||1 + 2|
|1||2|1 = -5.2 MHz2 = 1.0 MHz
(Pseudo-)EntanglementENDOR quantum computing
ESRENDOR
1
2
4
3
w24
w12
w34
w13
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DPNO Q-band
11
11
21
21
0 2 4 6 8 10
TPPI Frequency/ MHz
0 2 4 6 8 10
TPPI Frequency/ MHz
1 − 2 ||1 + 2|
|1|
2|
1 = -5.2 MHz2 = 1.0 MHz
00
00
21
21
B0 = 1. 2044T
B0 = 1.2066T
HN IIS MMMS IN IH
21
21 ,1,
21
21 ,1,
21
21 ,1,
21
21 ,1,
21
21 ,0,
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(Pseudo-)EntanglementENDOR quantum computing
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Decoherenceelectron spin with very short decoherence time
Radical T1 /ms
DPNO-d10 42.5
Malonyl radical 91.5
DPNO 392.0
Spin-lattice relaxation time, T1@10K, saturation recovery
Radical T2 /μs
Malonyl radical 5.200 *
DPNO 0.777
DPNO-d10 0.489
Spin-spin relaxation time, T2@10 K , two pulse echo decay
* at 20 K
R. Rahimi, PhD thesis, quant-ph/0609063
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A conventional model of a spin-boson system
On-resonance bosons,if dissipation is ignored,oscillation is found rather than a decay
A dissipative model of a spin-boson system
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System study
CPS HHHH
n
kkk
n
jjjS SSASfH
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bn
lkllP aaH
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as
ssaasC aaSCH
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Spin system Hamiltonian
Boson system Hamiltonian
Spin-boson coupling
For a bosonic mode in resonance with the spinaa aS
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Tk
H
Z BO exp
1 the original density operator
(b) With polarization transfer Tk
H
PO
B
P
eZ
1n
ele
1
(a) Without polarization transfer OO
is the reduced density operator of the electron spin of the original stateele O
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the total entangling operationentU
Q-band ENDOR; 35 GHz
IUIU O entent0
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A dissipative noise model
tiHTk
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p
tttiH eetptpett B
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uu
Tr111
t is a map
tiHt
tiH etett
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Decoherence control
LntxLnL
xLnLtnLVtH x 10 n
XVdtixLnL
nL
exp
xH a Hamiltonian of bang-bang pulses
10 x is a duty ratio
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tVHieU 1tiHeU 2
Time evolution
txLtLxL tΔt
//1
12
0ρtρ Lt
L
at time Lt
111 UUu 222 UUu
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Case without prior polarization transfer
10.0 GHz,1000.1 210 pcc
10.0 GHz,1000.1 610 pcc
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Case without prior polarization transfer
50.0 GHz,1000.1 610 pcc
99.0 GHz,1000.1 610 pcc
Wipe effect
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Case with prior polarization transfer
10.0 GHz,1000.1 210 pcc
10.0 GHz,1000.1 610 pcc
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Case with prior polarization transfer
50.0 GHz,1000.1 610 pcc
99.0 GHz,1000.1 610 pcc
Wipe effect
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Conclusion
-For an electron spin bus system, entanglement is achieved under milder experimental conditions.
-Decoherence control for an electron spin bus system is rather more challenging.
-If the number of qubits is small, we find some regions of parameters, not much far from the currently accessible region of magnetic spectroscopy technology, where the quantum state can be stable.
- A high probability of dissipation of bosons result in slow decoherence, quantum wipe effect.
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work done by
S. Nishida, K. Toyota, D. Shiomi, Y. Morita, A. Ueda, S. Suzuki, K. Nakasuji (Osaka City Univ.) K. Furukawa, T. Nakamura (IMS) H. Hara, P. Carl, P. Höfer (Bruker Biospin Co.)
Masahiro Kitagawa (Osaka Univ.)
Takeji Takui (Osaka City Univ.)
Kazunobu Sato (Osaka City Univ.) Akira SaiToh (Osaka Univ.)
Mikio Nakahara (Kinki Univ.)
RR is supported bySasakawa scientific research grant from the Japan Science Society