Optimized metrological algorithms with a transmon artificial atom: and schemes

Perelshtein Michael

Laboratory of Physics of 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:

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 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 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