B O S C H U N D S I E M E N S H A U S G E R Ä T E G R U P P E Frequency locking and error correction based sensing schemes Alex Retzker HUJI PSAS Tuvia Gefen, Nati aharon, Itsik Cohen, Daniel Cohen, Thomas Unden, Prya balasubramanian, Daniel Louzon, Martin Plenio, J.M Cai,Mikhail Lukin, L. Cohen, Y. Pilnyak, D. Istrati, H. S. Eisenberg Christof Wunderlich, Ingo Baumgart and Fedor Jelezko.

Quantum Sensing Quantum sensing scales as: Thus dynamical decoupling is used to increase the coherence time Challenge: increasing the coherence time while reading the signal

Hahn Echo: PSAS2016I I Slide: 3

Carr Purcell – CP: PSAS2016I I Slide: 4 A sequence of echos, i.e., of π pulses focuses the polarization for a long time y z x

Carr Purcell – CP: PSAS2016I I Slide: 5 A sequence of echos, i.e., of π pulses focuses the polarization for a long time y z x π+δΦ y z x 2 δΦ

Improved CPMG: PSAS2016I I Slide: 6 y z x π+δΦ y z x

PSAS2016 I I Slide: 7 Coherent control Timoney et, al., 2007

PSAS2016 I I Folie: 8 Working with ensembles A strong pulse in needed to work on all systems identically

PSAS2016 I I Folie: 9 Power issues The ratio between continuous and pulsed:

PSAS2016 I I Folie: 10 Dynamical Decoupling: Spin locking Dephasing(T2) Rate : Flipping(T1) Rate :

Cohernce time of dressed states Coherence time   20 ms PSAS2016 I I Folie: 11 Data from Wunderlich group

Single drive PSAS I I Folie: 12 Cai et al., New J. Phys (2012)

Carr Purcell – CP: PSAS2016I I Slide: 13 A sequence of echos, i.e., of π pulses focuses the polarization for a long time y z x π+δΦ y z x 2 δΦ

Stable Qubit  Sequential continuous dynamical decoupling PSAS I I Folie: 14 Cai et al., New J. Phys (2012) Plus non-rotating drive terms

PSAS2016 I I Slide: 15 Coherent control Timoney et, al., 2007

Single drive PSAS I I Folie: 16 Cai et al., New J. Phys (2012)

PSAS I I Folie: 17 But if we have more levels maybe we could so something better

Dynamical Decoupling: multi level struture Dephasing(T2) Rate : Quantum Computing-> Sensing N. Timoney, I. Baumgart, M. Johanning, A. F. Varon, Ch. Wunderlich, M. B. Plenio, A. R Nature 476, 185 (2011)

Robust magnetometry Measured Sensitivity by Wunderlich: signal The signal is locked to the frequency and not to Rabi frequency I. Baumgart, J.M. Cai, M. B. Plenio, A. R, C. Wunderlich PRL (2016)

Generalisation to N levels N. Aharon, M. Drewsen, and A.R, PRL 111, (2013) PSAS2016 I I Folie: 20

For NVs PSAS2016 I N. Aharon, I. Cohen, AR in preparation

Dressed states PSAS2016 I Robust qubit (a) (b) N. Aharon, I. Cohen, AR in preparation

Pure dephasing PSAS2016 I N. Aharon, I. Cohen, AR in preparation

With drive of 100MHz PSAS2016 I N. Aharon, I. Cohen, AR in preparation

PSAS I I Folie: 25 Good and bad levels – Error correction Two ‘good’ levels Two ‘sensing’ levels G. Arrad, Y. Vinkler, D. Aharonov, A. R, PRL 112, (2014)

PSAS I I Folie: 26 Good and bad levels Weak coupling to noise Weak coupling to signal Strong coupling to noise Strong coupling to signal Weak coupling to noise Strong coupling to signal G. Arrad, Y. Vinkler, D. Aharonov, A. R, PRL 112, (2014)

General Idea of error correction for quantum computing Code error1 error2 Error N Logical operation PSAS2016 I G. Arrad, Y. Vinkler, D. Aharonov, A. R, PRL 112, (2014)

Error correction – majority vote Regular majority vote code Error1 Error2 Error3

General Idea of error correction for quantum sensing Code error1 error2 Error N Sensing signal However, the sensing signal is weak/slow and the logical operation is strong/fast PSAS2016 I

Advantage – use of protected qubits Code Sensing qubit Good qubits PSAS2016 I

Example: fighting dissipation Using dynamical decoupling have to be faster than Using error correction have to be faster than PSAS2016 I

Example: fighting T1 Using dynamical decoupling have to be faster than Using error correction have to be faster than PSAS2016 I

PSAS2016 I I Folie: 33 Quantum error correction for sensing Sensing qubit Robust qubits Instead of the nine/five qubit code a simpler code with good qubits can be designed The sensing signal is weak/slow and the logical operation is strong/fast

Initial state: Free evolution: Error: Cnot-Gate: Laser: Cnot-Gate: Quantum error correction for bit flip error T. Unden,..A. R, F. Jelezko PRL (2016)

Electron and nuclear spin PSAS2016 I T. Unden,..A. R, F. Jelezko PRL (2016)

With drive of 100MHz PSAS2016 I L. Cohen, Y. Pilnyak, D. Istrati, A. Retzker, H. S. Eisenberg Arxiv (2016)

With drive of 100MHz PSAS2016 I L. Cohen, Y. Pilnyak, D. Istrati, A. Retzker, H. S. Eisenberg Arxiv (2016)

Back to Heisenberg scaling David A. Herrera-Martí, Tuvia Gefen, Dorit Aharonov, Nadav Katz, AR Phys. Rev. Lett. 115, (2015)

Back to Heisenberg scaling Tuvia Gefen, David A. Herrera-Martí, AR Phys. Rev. A 93, (2016)

B O S C H U N D S I E M E N S H A U S G E R Ä T E G R U P P E Thanks a lot for your attention! Diadems IP (FP7) Diadems IP (FP7) CIG Career integration grant CIG Career integration grant

Hahn Echo: PSAS2016I I Slide: 41

Noise sources - mixing PSAS2016 I This state has a Part:

Dressed states – driving fields fluctuations PSAS2016 I Robust qubit

Noise sources – driving fields fluctuations PSAS2016 I The next order shift: Then the noise is:

Magnetic fluctuations PSAS2016 I The rotating frame: Stark Shift

XY8: PSAS2016I I Slide: 46 y z x π+δΦ y z x

CP + Meiboom – Gill = CPMG: PSAS2016I I Slide: 47 y z x π+δΦ y z x

Quantum Sensing of high frequency fields PSAS2016 I

Dressed states – Noise sources PSAS2016 I Deleterious noise at:

PSAS2016 I I Folie: 50 General scheme for the construction of a protected qubit subspace Robust subspace like symmetry protected subspace

Error correction – Shor’s algorithm Bit flip or a phase flip will map this to an orthogonal sub space Shor’s code: For example, phase flip of the first qubit: For example, bit flip of the first qubit:

Dressed states PSAS2016 I Robust qubit N. Aharon, I. Cohen, AR in preparation

Dressed states – Noise sources PSAS2016 I Robust qubit