Post on 14-Apr-2018
7/29/2019 Effects of magnetic tensions on topological quantum memories
1/26
Saeed S. Jahromi, K.N.Toosi University Of Technology, Iran
M. Kargarian, University Of Texas at Austin, USA
K. P. Schmidt, TU Dortmund, Germany
SF. Masoudi, K.N.Toosi University Of Technology, Iran
Effects of magnetic tensions on topological quantum memories
Quantum Information Conference, 4-5 Sep. 2013, Shahrood, Iran.
7/29/2019 Effects of magnetic tensions on topological quantum memories
2/26
2Saeed S. Jahromi
Outline
Topological Order
Quantum Computation
Error Correcting Quantum Codes
Color Code
Perturbed Topological Color Code with Magnetic Field
Phase diagram
Discussion and results
7/29/2019 Effects of magnetic tensions on topological quantum memories
3/26
3Saeed S. Jahromi
Topological Order
Order
Symmetry
Breaking
Non-Symmetry
Breaking
Landau Theory of
Phase Transition
Quantum
Liquid
String-Net
Condensation
Topological
Order
7/29/2019 Effects of magnetic tensions on topological quantum memories
4/26
4Saeed S. Jahromi
Quantum Computation
Quantum
Computation
Quantum
Bits
Error
Correction
Unitary
Operation
Computational
Basis
Quantum
Gates
7/29/2019 Effects of magnetic tensions on topological quantum memories
5/26
5Saeed S. Jahromi
Errors in Quantum Computation
DecoherencePhase FlipBit Flip
Search for systemswhich are intrinsically robust against errors.
States carrying non local degrees of freedom.
We can put the quantum information on global degrees of freedom.
Topological Systems
7/29/2019 Effects of magnetic tensions on topological quantum memories
6/26
6Saeed S. Jahromi
Error Correcting Quantum Codes
Fault-Tolerant Quantum Computation
Topological Properties protects the system against Errors
Toric Code Color Code
A.Yu. Kitaev, Annals of Physics 303 2-30 (2003). H. Bombin, Phys.Rev.Lett. 97 180501 (2006).
7/29/2019 Effects of magnetic tensions on topological quantum memories
7/26
7Saeed S. Jahromi
Topological Color code
H. Bombin, M.A. Martin-Delgado, Phys.Rev.Lett. 97 180501 (2006).
H. Bombin, M.A. Martin-Delgado, Phys. Rev. A 77, 042322 (2008).
7/29/2019 Effects of magnetic tensions on topological quantum memories
8/26
8Saeed S. Jahromi
String Operators
7/29/2019 Effects of magnetic tensions on topological quantum memories
9/26
9Saeed S. Jahromi
Ground State
X.G. Wen, Quantum Field Theory of Many-body Systems, Oxford Univ. Press, (2004).
String-net Condensation
7/29/2019 Effects of magnetic tensions on topological quantum memories
10/26
10Saeed S. Jahromi
Global String Operators
There are another kind of strings which are closed but are not product of
pluquette operators
Global Strings (Fundamental non-contractible loops )
7/29/2019 Effects of magnetic tensions on topological quantum memories
11/26
11Saeed S. Jahromi
Topological Degeneracy
7/29/2019 Effects of magnetic tensions on topological quantum memories
12/26
12Saeed S. Jahromi
Excitations
Excitations are created at the end points of open strings
7/29/2019 Effects of magnetic tensions on topological quantum memories
13/26
13Saeed S. Jahromi
Topological Color Code in magnetic field
7/29/2019 Effects of magnetic tensions on topological quantum memories
14/26
14Saeed S. Jahromi
Continuous Unitary Transformations (CUTs)
7/29/2019 Effects of magnetic tensions on topological quantum memories
15/26
15Saeed S. Jahromi
Continuous Unitary Transformations (CUTs)
F.J. Wegner, Ann. Phys. (1994)
S.D. Glazek and K.G. Wilson, Phys. Rev. D (1994)
The basic idea is to unitarily transform the
initial problem in a continuous fashion.
7/29/2019 Effects of magnetic tensions on topological quantum memories
16/26
16Saeed S. Jahromi
Perturbative Continuous Unitary
Transformations (PCUT)
A. Mielke, EPJB (1998)
C. Knetter and G. S. Uhrig, EPJB (2000)
7/29/2019 Effects of magnetic tensions on topological quantum memories
17/26
17Saeed S. Jahromi
Perturbative Continuous Unitary
Transformations (PCUT)
A. Mielke, EPJB (1998)
C. Knetter and G. S. Uhrig, EPJB (2000)
Quasiparticle conserving Generator
7/29/2019 Effects of magnetic tensions on topological quantum memories
18/26
18Saeed S. Jahromi
Single parallel field
S. S. Jahromi, M. Kargarian, S. F. Masoudi, K. P. Schmidt,
Phys. Rev. B 87, 094413 (2013).
Mapped to Baxter-Wu model in transverse magnetic field
7/29/2019 Effects of magnetic tensions on topological quantum memories
19/26
19Saeed S. Jahromi
Phase Transition
S. S. Jahromi, M. Kargarian, S. F. Masoudi, K. P. Schmidt,
Phys. Rev. B. 87, 094413 (2013)
7/29/2019 Effects of magnetic tensions on topological quantum memories
20/26
20Saeed S. Jahromi
Physical Measurement
7/29/2019 Effects of magnetic tensions on topological quantum memories
21/26
21Saeed S. Jahromi
Two Parallel field (x,z)
7/29/2019 Effects of magnetic tensions on topological quantum memories
22/26
22Saeed S. Jahromi
Transverse field (y)
7/29/2019 Effects of magnetic tensions on topological quantum memories
23/26
23Saeed S. Jahromi
Transverse field (y)
7/29/2019 Effects of magnetic tensions on topological quantum memories
24/26
24Saeed S. Jahromi
Transverse field (y)
7/29/2019 Effects of magnetic tensions on topological quantum memories
25/26
25Saeed S. Jahromi
Conclusion
Color Code in a single parallel magnetic field is mapped to the
Baxter-Wu model in transverse field.
The problem was solved by mapping the perturbed Hamiltonian to
a quasiparticle conserving effective Hamiltonian, using PCUT
The topological phase of TCC breaks down to a polarized phase
via a first order phase transition in all of the field directions.
TCC in transverse field conserves the parity of the number of
quasiparticles on the plaqquests.
Color Code is More robust than Toric code in parallel fild
7/29/2019 Effects of magnetic tensions on topological quantum memories
26/26
Thanks For Your Attention