pulse methods for preserving quantum coherences t. s. mahesh
DESCRIPTION
Pulse Methods for Preserving Quantum Coherences T. S. Mahesh Indian Institute of Science Education and Research, Pune. Criteria for Physical Realization of QIP. Scalable physical system with mapping of qubits A method to initialize the system Big decoherence time to gate time - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/1.jpg)
Pulse Methods for Preserving Quantum Coherences
T. S. Mahesh
Indian Institute of Science Education and Research, Pune
![Page 2: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/2.jpg)
Criteria for Physical Realization of QIP
1. Scalable physical system with mapping of qubits
2. A method to initialize the system
3. Big decoherence time to gate time
4. Sufficient control of the system via time-dependent Hamiltonians
(availability of universal set of gates).
5. Efficient measurement of qubits
DiVincenzo, Phys. Rev. A 1998
![Page 3: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/3.jpg)
Contents1. Coherence and decoherence
2. Sources of signal decay
3. Dynamical decoupling (DD)
4. Performance of DD in practice
5. Understanding DD
6. DD on two-qubits and many qubits
7. Noise spectroscopy
8. Summary
![Page 4: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/4.jpg)
Contents1. Coherence and decoherence
2. Sources of signal decay
3. Dynamical decoupling (DD)
4. Performance of DD in practice
5. Understanding DD
6. DD on two-qubits and many qubits
7. Noise spectroscopy
8. Summary
![Page 5: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/5.jpg)
Closed and Open Quantum System
EnvironmentEnvironment
Hypothetical
![Page 6: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/6.jpg)
Coherent Superposition
| = c0|0 + c1|1, with |c0|2 + |c1|2 = 1
An isolated 2-level quantum system
rs = || = c0c0*|0 0| + c1c1
*|1 1|+
c0c1*|0 1| + c1c0
*|1 0|
c0c0* c0c1
*
c1c0* c1c1
*
Density Matrix
Coherence
Population
=
![Page 7: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/7.jpg)
Effect of environmentQuantum System – Environment interaction Evolution U(t)
|0|E |0|E0
|1|E |1|E1
U(t)
U(t)
||E = (c0|0 + c1|1)|E U(t)
c0|0|E0 + c1|1|E1
System Environment
System Environment
System Environment
Entangled
![Page 8: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/8.jpg)
Decoherencer = ||E |E|
= c0c0*|0 0||E0 E0| + c1c1
*|1 1||E1 E1| +
c0c1*|0 1||E0 E1| + c1c0
*|1 0||E1 E0|
rs = TraceE[r] = c0c0*|0 0| + c1c1
*|1 1|+
E1|E0 c0c1*|0 1| + E0|E1 c1c0
*|1 0|
c0c0* E1|E0 c0c1
*
E0|E1 c1c0* c1c1
*
=Coherence
Population
|E1(t)|E0(t)| = eG(t)
Coherence decays irreversibly
Decoherence
![Page 9: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/9.jpg)
Contents1. Coherence and decoherence
2. Sources of signal decay
3. Dynamical decoupling (DD)
4. Performance of DD in practice
5. Understanding DD
6. DD on two-qubits and many qubits
7. Noise spectroscopy
8. Summary
![Page 10: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/10.jpg)
Signal Decay
Time Frequency
13-C signal of chloroformin liquid
Signal x
![Page 11: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/11.jpg)
Signal Decay
IncoherenceDecoherence
DepolarizationAmplitude decay
Phasedecay
T1 process
T2 process
Relaxation
![Page 12: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/12.jpg)
Signal Decay
IncoherenceDecoherence
DepolarizationAmplitude decay
Phasedecay
T1 process
T2 process
Relaxation
![Page 13: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/13.jpg)
Incoherence
Individual (30 Hz, 31 Hz)
Net signal – faster decay
Time
![Page 14: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/14.jpg)
Hahn-echo or Spin-echo (1950)
y
t t
+ d
d
y
Symmetric distribution of pulses removes incoherence
Signal
Echo
/2-x
![Page 15: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/15.jpg)
Signal Decay
IncoherenceDecoherence
DepolarizationAmplitude decay
Phasedecay
T1 process
T2 process
Relaxation
![Page 16: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/16.jpg)
2
2
1
10
10
1
0 00 00 0 0 0
0 0 0 0 0
x Tx x
y y yTeq
z z z zT
M M Md M M Mdt
M M M M
M
eqzM
T1
Time to reach equilibrium, (energy of spin-system is not conserved)
T2Lifetime of coherences, (energy of spin-system is conserved)
Bloch’s Phenomenological Equations (1940s)
![Page 17: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/17.jpg)
Bloch’s Phenomenological Equations (1940s)
2
2
1
10
10
1
0 00 00 0 0 0
0 0 0 0 0
x Tx x
y y yTeq
z z z zT
M M Md M M Mdt
M M M M
M
eqzM
1
2
2
exp)0()(
exp)0()(
exp)0()(
TtMMMtM
TtMtM
TtMtM
eqzz
eqzz
yy
xx
Solutions in rotating frame:
eqzM
0
0
![Page 18: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/18.jpg)
Signal Decay
IncoherenceDecoherence
DepolarizationAmplitude decay
Phasedecay
T1 process
T2 process
Relaxation
![Page 19: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/19.jpg)
Effect of environment
r r’ = E(r)
= ∑ Ek r Ek†
k(operator-sum representation)
![Page 20: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/20.jpg)
Amplitude damping (T1 process, dissipative)
E0 = p1/2 1 00 (1g1/2
E1 = p1/2 0 g1/2
0 0
E2 = (1 p)1/2 (1g1/2 0 0 1
E3 = (1 p)1/2 0 0
g1/2 0
r = p 00 1 p
Asymptotic state (t , g 1 :
g(t) is net damping : eg., g(t) = 1 et/T1
In NMR, p =
~ 0.5 + 104
1 1 + eE/kT
E(r) = ∑ Ek r Ek†
k
![Page 21: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/21.jpg)
M(t) = 1 2exp( t/T1)
Amplitude damping (T1 process, dissipative)
Measurement of T1: Inversion Recovery
Equilibrium
Inversion
t
![Page 22: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/22.jpg)
Signal Decay
IncoherenceDecoherence
DepolarizationAmplitude decay
Phasedecay
T1 process
T2 process
Relaxation
![Page 23: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/23.jpg)
Phase damping (T2 process, non-dissipative)
E0 = 1 00 (1g1/2
r = a 00 1-a
Stationary state (t , g 1 :
g(t) is net damping : eg., g(t) = 1 et/T2
E1 = 0 00 g1/2
r(t) = a bb* 1-a
E(r) = ∑ Ek r Ek†
k
![Page 24: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/24.jpg)
Bloch’s equation : dMx(t) Mx(t) dt T2
=
Solution : Mx(t) = Mx(0) exp( t/T2)
Transverse magnetization: Mx(t) Re{r01(t)}
Phase damping (T2 process, non-dissipative)
Spin-SpinRelaxation
Signal envelop: s(t) = exp( t/T2)
FWHH = /T2
![Page 25: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/25.jpg)
Contents1. Coherence and decoherence
2. Sources of signal decay
3. Dynamical decoupling (DD)
4. Performance of DD in practice
5. Understanding DD
6. DD on two-qubits and many qubits
7. Noise spectroscopy
8. Summary
![Page 26: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/26.jpg)
Carr-Purcell (CP) sequence (1954)
y
t
Signal
t
/2y
tt
y
tt
y
t
Shorter t is better (limited by duty-cycle of hardware)
H. Y. Carr and E. M. Purcell, Phys. Rev. 94, 630 (1954)
![Page 27: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/27.jpg)
Meiboom-Gill (CPMG) sequence (1958)
x
t
Signal
t
/2y
tt
x
tt
x
t
Robust against errors in pulse !!!
S. Meiboom and D. Gill, Rev. Sci. Instrum. 29, 688 (1958)
![Page 28: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/28.jpg)
CPMG
t t
t t
t t
t t
Sampling points
Dynamical effects are minimized Dynamical decoupling
time1 2 3 4
j = T(2j-1) / (2N) Linear in j
Time
Signal
CPNopulse
HahnEcho
CPMG
S. Meiboom and D. Gill, Rev. Sci. Instrum. 29, 688 (1958)
![Page 29: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/29.jpg)
Dynamical Decoupling (DD)
Optimal distribution of pulses for a system with dephasing bath
T = total time of the sequence
N = total number of pulses
j = T sin2 ( j /(2N+1) )
PRL 98, 100504 (2007)Götz S. Uhrig
Uniformly distributed pulsesCPMG (1958):
Uhrig 2007 (UDD):
![Page 30: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/30.jpg)
Carr Purcell Sequence
j = T(2j-1) / (2N) Linear in jWas believed to be optimal for N flips in duration T
1 2 3 4
5 6 70time
Carr & Purcell, Phys. Rev (1954) .Meiboom & Gill, Rev. Sci. Instru. (1958).
1
3
4
5
6
70time
Uhrig Sequence
2
j = T sin2 ( j /(2N+1) )
Uhrig, PRL (2007)
T
T
Proved to be optimal for N flips in duration T
![Page 31: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/31.jpg)
Hahn-echo (1950)
CPMG (1958)
PDD (XY-4) (Viola et al, 1999)
UDD (Uhrig, 2007)
Dynamical Decoupling (DD)
CDDn = Cn = YCn−1XCn−1YCn−1XCn−1
C0 = t(Lidar et al, 2005)
![Page 32: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/32.jpg)
Contents1. Coherence and decoherence
2. Sources of signal decay
3. Dynamical decoupling (DD)
4. Performance of DD in practice
5. Understanding DD
6. DD on two-qubits and many qubits
7. Noise spectroscopy
8. Summary
![Page 33: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/33.jpg)
ION-TRAP qubits
M. J. Biercuk et al, Nature 458, 996 (2009)
DD performance
![Page 34: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/34.jpg)
Time (s) Time (s)
DD performanceElectron Spin Resonance(g-irradiated malonic acidsingle crystal)
J. Du et al, Nature461, 1265 (2009)
![Page 35: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/35.jpg)
13C of Adamantane
Dieter et al, PRA 82, 042306 (2010)
Solid State NMR
DD performance
![Page 36: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/36.jpg)
Dynamical Decoupling in Solids
D. Suter et al,PRL 106, 240501 (2011)
13C of Adamantane
![Page 37: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/37.jpg)
Contents1. Coherence and decoherence
2. Sources of signal decay
3. Dynamical decoupling (DD)
4. Performance of DD in practice
5. Understanding DD
6. DD on two-qubits and many qubits
7. Noise spectroscopy
8. Summary
![Page 38: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/38.jpg)
Spin in acoherent
state
Randomlyfluctuating local fields
Sources of decoherence – dipole-dipole interaction
![Page 39: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/39.jpg)
Spin loosescoherence
Randomlyfluctuating local fields
Sources of decoherence – dipole-dipole interaction
![Page 40: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/40.jpg)
Source of Phase-damping – chemical shift anisotropy
B0
![Page 41: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/41.jpg)
Redfield Theory: semi-classical
System - > Quantum, Lattice - > Classical
],[ rr Hidtd
Completely reversibleNo decoherence
System
System+Random field(coarse grain)
eqRHidtd
rrrr
,
![Page 42: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/42.jpg)
Local field X(t)
time
G(t) = X(t) X*(t+t) = dx1 dx2 x1 x2 p(x1,t) p(x1,t | x2, t)
Auto-correlation function
Fluctuations have finite memory: G(t) = G(0) exp(|t|/ tc)
tc Correlation Time
Auto-correlation
Spectral density J() = G(t) exp(-it) dt = G(0) 2tc
1+ 2tc2
![Page 43: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/43.jpg)
Spectral density
J()
tc = 1
G(0) 2tc
1+ 2tc2
J() =
rr
,)( XXJdtd
(after secular approximation)
![Page 44: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/44.jpg)
Spectral density
J()
tc = 1
G(0) 2tc
1+ 2tc2
J() =
1T1
J(2) + J()
J(2) + J() + J(0)1T2
3 8
15 4
3 8
Dipolar Relaxation in Liquids
G = d2 J() 2
0
c0c0
* eGt c0c1*
eGt c1c0* c1c1
*
![Page 45: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/45.jpg)
Effect of decoupling pulses L. Cywinski et al, PRB 77, 174509 (2008).M. J. Biercuk et al, Nature (London) 458, 996 (2009)
0
exp(-i H(t) dt ) Magnus expansion
Time-dependent Hamiltonian
![Page 46: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/46.jpg)
Filter Functions
|x(t)|= e(t)
Cywiński, PRB 77, 174509 (2008)M. J. Biercuk et al, Nature (London) 458, 996 (2009)
F()
t
= F() d2 J() 2
0
F(t)
Fourier Transform of Pulse-train
![Page 47: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/47.jpg)
J(t)
Modified Spectral density: J’() = J() F()
Residual area contributes to decoherence
Filter Functions
Cywiński, PRB 77, 174509 (2008)M. J. Biercuk et al, Nature (London) 458, 996 (2009)
= F() d2 J() 2
0
![Page 48: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/48.jpg)
Contents1. Coherence and decoherence
2. Sources of signal decay
3. Dynamical decoupling (DD)
4. Performance of DD in practice
5. Understanding DD
6. DD on two-qubits and many qubits
7. Noise spectroscopy
8. Summary
![Page 49: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/49.jpg)
Two-qubit DD
![Page 50: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/50.jpg)
Wang et al, PRL 106, 040501 (2011)
Two-qubit DDElectron-nuclear entanglement(Phosphorous donors in Silicon)
No DD PDD
![Page 51: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/51.jpg)
S. S. Roy & T. S. Mahesh, JMR, 2010
Fidelity = 0.995
Two-qubit DD – in NMR Levitt et al, PRL, 2004
|00
|11
|01 |10
Eigenbasis of Hz
90x , , , 90y , 12J
Hamiltonian: H = h1Iz1 + h2Iz
2+ hJ I1 I2
Hz HE
Eigenbasis of HE
|01−|102
|01+|102
|00 |11
![Page 52: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/52.jpg)
5-chlorothiophene-2-carbonitrile
Two-qubit DD – in NMR
2 ms 2 ms
27sj = Nt sin2 ( j /(2N+1) )t = 4.027 ms
![Page 53: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/53.jpg)
UDD-7 on 2-qubits
SingletFidelity
S. S. Roy, T. S. Mahesh, and G. S. Agarwal,Phys. Rev. A 83, 062326 (2011)
![Page 54: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/54.jpg)
Entanglement
Product state
0110
01+10
0011
00+11
UDD-7 on 2-qubits
S. S. Roy, T. S. Mahesh, and G. S. Agarwal,Phys. Rev. A 83, 062326 (2011)
![Page 55: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/55.jpg)
Dynamical Decoupling in Solids
CPMG
UDD
RUDD
Abhishek et al
Uhrig, 2011
![Page 56: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/56.jpg)
Dynamical Decoupling in Solids1H of Hexamethylbenzene
Abhishek et al
DD on single-quantum coherences
![Page 57: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/57.jpg)
Dynamical Decoupling in Solids
1H of Hexamethyl Benzene
Abhishek et al
No DD RUDD
![Page 58: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/58.jpg)
2q 4q 6q 8q
Abhishek et al
Dynamical Decoupling in Solids
![Page 59: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/59.jpg)
Contents1. Coherence and decoherence
2. Sources of signal decay
3. Dynamical decoupling (DD)
4. Performance of DD in practice
5. Understanding DD
6. DD on two-qubits and many qubits
7. Noise spectroscopy
8. Summary
![Page 60: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/60.jpg)
Noise Spectroscopy Alvarez and D. Suter,arXiv: 1106.3463 [quant-ph]
|x(t)|= e(t)
F(t)
(t) = F(t) d2 J(t) 2
0
![Page 61: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/61.jpg)
Contents1. Coherence and decoherence
2. Sources of signal decay
3. Dynamical decoupling (DD)
4. Performance of DD in practice
5. Understanding DD
6. DD on two-qubits and many qubits
7. Noise spectroscopy
8. Summary
![Page 62: Pulse Methods for Preserving Quantum Coherences T. S. Mahesh](https://reader035.vdocument.in/reader035/viewer/2022081512/56816497550346895dd66d3b/html5/thumbnails/62.jpg)
Summary
1. Dynamical decoupling can greatly enhance the coherence times,
some times by orders of magnitude
2. Various types of pulsed DD sequences are available. Best DD depends
on the spectral density of the bath, the state to be preserved, robustness
to pulse errors, etc.
3. Filter-functions are useful tools to understand the performance of DD.
4. DD on large number of interacting qubits also shows improved performance.