Optimized metrological algorithms with a transmon artificial atom: Qubit and qutrit schemes
Perelshtein Michael
Laboratory of Physics of Quantum Information Technology, MIPT NANO Group, Aalto University [email protected] Outline
• Concept of metrology • Transmon artificial atom in a nutshell • Metrology with transmon qubit • Metrology with transom qutrit • Improvement of metrological scheme with qutrit • Decoherence compensating metrological algorithm in a qutrit system Metrology
In the history of science, every time more precise measurements were made possible, new discoveries were made
Standart quantum limit Heisenberg limit Resource: Coherence
No entanglement Phase estimation protocol
x
P E R
Preparation Exposure Readout
Accumulated phase: Measurement error:
Coherence time Transmon device
, Transmon as magnetic field detector
Detector Signal
Optimal DC flux point is not a «Sweet spot» Metrology with transmon qubit
Ramsey interferometry:
z z z z y y y y x x x x
, Metrology with transmon qubit: Experiment
[S. Danilin, A. V. Lebedev, A. Vepsäläinen, G. B. Lesovik, G. Blatter & G. S. Paraoanu, npj Quantum Information 4, 29 (2018)] Metrology with transmon qutrit Qubit: Qutrit:
3 steps P:
E:
R:
[A. R. Shlyakhov, V. V. Zemlyanov, M. V. Suslov, A. V. Lebedev, G. S. Paraoanu, G. B. Lesovik, and G. Blatter, Phys. Rev. A 97, 02115 (2018)] Optimized metrology with transmon qutrit
Universal manipulations:
P: Rf-pulse parameters: If E:
R:
— Fourier-based procedure Learning procedure in a qutrit-based system
— magnetic field distribution
Updated probability distribution after n-th step:
Measure of uncertainty in regard to the value of the field: Optimal procedure in a qubit scheme
Information gain — amount of information learned after n-th step
Case 1: Qubit information gain (Step 1)
Case 2: 1 bit
Case 3: 1 G 0.49 bit Max
Fourier-based procedure is always optimal 0 0.5 1 1.4 a Optimal procedure in a qutrit scheme
Case 1: Optimal: Fourier-based procedure with s f Case 2:
Case 3:
Optimal: Optimized procedure with s1 Optimal procedure in a qutrit scheme
Fouirer-based procedure:
Population in the initial state is 2φ φ φ 2φ φ {1/3, 1/3, 1/3} 0
Optimized procedure in continuous distribution case:
φ φ 2φ Difference in φ phases 2φ φ φ 2φ φ
Difference in population 1/4, 1/4, 0 0, 1/4, 1/4 1/4, 0, 1/4 Decoherence effects in transmon
Lindblad equation
Gaussian noise:
Fourier-based procedure:
Optimal and modified Decoherence compensation in transmon
Compensation
• Always 0% for a qubit 1 G Max
a • Not always 0% for a qutrit Decoherence compensation: M = 3
Optimal: Fourier-based procedure with s f
G 1
1 trit = 1.58 bits
Unambiguous distinction
t, ns Decoherence compensation: Continuous distribution
Optimal (no decoherence): Optimized procedure with
Optimal (with decoherence): Optimized procedure with
G1
0.61 trit = 0.88 bits
0.49 trit = 0.78 bits
t, ns
Decoherence improvement is diminutive 0.3% Decoherence compensation: M = 30
Optimal (no decoherence): Fourier-based procedure with s f
Optimal (with decoherence): Optimized procedure with
G1
0.44 trit = 0.63 bits 1 trit
Optimal interaction time Optimal interaction time 617 ns 6.9 µs
t, ns Decoherence improvement is 7.3% Optimization of qutrit scheme: summary
M = 3 Continuous M = 30 Why qutrit is such an interesting system?
[M. Kitagawa, M. Ueda, Phys. Rev.A 47, 5138 (1993)]
Transformations:
1. Rotations S j 2 2. One-axis twisting S j 3. Two-axis twisting S 2- S2 j i OPEN PROBLEM Conclusion
Metrology Transmon qubit Transmon qutrit
Detector Signal
Resource: Coherence time
Improvement and decoherence compensation in a qutrit Acknowledgments
MIPT Aalto University ETH Zurich
• G. B. Lesovik • G. S. Paraoanu • G. Blatter • A. V. Lebedev • S. Danilin • V. Zemlyanov • N. Kirsanov