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.