NV Centers in Quantum Information Technology!

Transcription

1 NV Centers in Quantum Information Technology! De-Coherence Protection & Teleportation! Brennan MacDonald-de Neeve, Florian Ott, and Leo Spiegel!

2 The NV Center! Point Defect in Diamond! Interesting Physics in negatively charged state NV -1! N C Total electron spin S=1! 14 N Nuclear Spin I=1! V C

3 Di Vincenzo Criteria! 1. Well-defined qubits! 2. Initialization! 3. t coherence > t gate operation! 4. Universal set of quantum gates! 5. Qubit specific read-out! 6. Convert from stationary to mobile qubit! 7. Faithful transmission!

4 Relevant Ground State Energy Structure! B 0 = 500 G! 1 e! 2.9 MHz! 1.4 GHz! 0 e! 5.1 MHz! é N! ê N!

5 Relevant Ground State Energy Structure! B 0 = 500 G! 1 e! 2.9 MHz! Electron Spin Modulation:! MW Rabi Driving at 1.4 GHz with driving strength 40 MHz! 1.4 GHz! 0 e! 5.1 MHz! é N! ê N!

6 Relevant Ground State Energy Structure! B 0 = 500 G! 1 e! 2.9 MHz! Electron Spin Modulation:! RF Rabi Driving at 2.9 MHz with Rabi frequency at 30 khz! Electron Spin Modulation:! MW Rabi Driving at 1.4 GHz with Rabi frequency at 40 MHz! 0 e! 1.4 GHz! 5.1 MHz! 2 qubit register! qubit modulation via Rabi driving! entanglement through hyperfine interaction! é N! ê N!

7 Spin Initialization from Excited State! 1) Electron Spin using LASER pumping! 532 nm! S=0! m S =0! m S =+/ 1! N. B. Manson et al. Phys. Rev. B 47, (2006).!

8 Spin Initialization from Excited State! 1) Electron Spin using LASER pumping! 2) Nuclear Spin using LASER pumping at B = 500 G! 532 nm! S=0! m S =0! m S =+/ 1! FIG. 2 (color online). N. B. Manson et al. Phys. Rev. B 47, (2006).! V. Jacques et al. Phys. Rev. Lett. 102, (2011).! Nuclear-spin polarization mechanism.

9 anson 1 s states with m S 5 0. A typical we study, is shown in Fig. 1c B). Under resonant excitation decays with time owing to a tes that induces shelving into l pumping mechanism allows from the data in Fig. 1d, we e m S 5 0 ground state of of the % preparation Intensity A PL Spectrum of optically excited V NV Center:!! m S = 0 is bright (E x )! m S = -1 is dark (A 1 )! b E x MW A 1 Intensity (kct s 1 ) N Read-Out! m 0 S = 0 m S = ± Laser detuning (GHz) Figure 1 Resonant excitation and electronic spin preparation of a E x nitrogen vacancy centre. a, Scanning electron microscope image of a solid A 1 NV A 60 immersion lens representative of those used in the experiments (for details, see Supplementary Information). The overlaid sketch shows the substitutional 20 nitrogen and the adjacent vacancy that form the NV. Inset, scanning confocal L. Robledo et al. Nature 477, microscope image (2011).! of NV A (logarithmic colour scale). kct, 1,000 counts b, Energy levels used to prepare and read out the NV s electronic spin (S 5 1in E x A 1 NV A

10 Fraction of outco deterministic quantum tele- the other spin state (Fig. 1d). This optical pumping mechanism allows re attractive candidates for high-fidelity spin state initialization24,27: (ii) p Fig. = 1 1d, we from the data in ing, their single-shot detec- estimate a preparation error into the ms 5 0 ground state of Hanson d qubits3 6. Here we demon %, which is a drastic reduction of the % preparation nt of a multi-spin quantum 0.6 a b mi = {0, +1} te system by implementing 150 ts states with ms 5 0. A typical es originally developed in preparation s we study, is shown in Fig. 1c y read-out of the electronic N Vvacancy B). Under resonant excitation p=1 PL Spectrum of opticallyv excited 1 centre in diamond, (iii) A1 with Center:! time owing to a 0.2 NV o decays three nearby nuclear spin NVA A NV A NV 0.1 ates that we induces shelving into Ex versely, can distinguish ! al pumping mechanism allows le shot by mapping it onto, Microwave frequency (GHz) 5,8. data ms in = Fig. 0weisshow bright : from 1d, we (Ex)! MW onic spinthe Finally, 10 μm he ms 5 state of (A )! ms = ±1 0 mground = -1 is dark demonstrate initialization, ms = 0 S 1 c Ø Can also be used to read out nread-out of the % preparation in a single experic d mi by using a CNOT gate:!nv B chniques suitable for exten115 b 1,000 mi = 1 pave the way for a test of NV A 0.8 Ex 100 NV A and the implementation of 80 A Ex N 60 ion protocols vacancy centre (NV) in dia-a 1 20 A system for investigating Atate 15 0 Ex 400 ent spin coherence9 12 with a e, the host nitrogen nuclear 200 A1 5 MW isotopic I 5 1) and nearby ±1 ms =the erfine interactions with ms = p=2 g development of few-spin Time (μs) Laser detuning (GHz) ested as building blocks for 0.0,000 mputation18100 and distributed Figure 1 Resonant excitation and electronic spin 0 preparation 5 of a Ex NV A nitrogen vacancy centre. a, Scanning electron microscope image of a solid A1 ications require high-fidelity Counts in N see = 3 repetitions immersion lens representative of those used in the experiments (for details, 60 spins. There ment of multiple Supplementary Information). The overlaid sketch shows the substitutional 40 few-spin sysnt control over 600 nitrogen the adjacent vacancy that form the NV. scanning confocal 20 Figure 3 and Nuclear spin preparation andinset, read-out. a, Measurement-based stsl.for the simultaneous prerobledo et al. Nature 477, (2011).! microscope image of NV A (logarithmic colour scale). kct, 1,000 counts f multi-spin registers, which 4 5 Read-Out! Intensity (kct s 1) Fraction of occurrences Intensity (kct s 1) Intensity spin. Earth s ambient magnetic field of preparation of used a single b, Energy levels to preparen andnuclear read out the NV s In electronic spin (S 5 1 in

11 Decoherence! Decoherence is caused by all the undesired interactions of a quantum state with its environment which shortens its lifetime.!! 1 free evolution 0 P (π/2) x τ (π/2) x τ (µs) G. de Lange et al. Science 330, (2010).! ontrol pulses and NV centers appear as

12 Decoherence! Decoherence is caused by all the undesired interactions of a quantum state with its environment which shortens its lifetime.!! 1 free evolution 0 P (π/2) x τ (π/2) x τ (µs) G. de Lange et al. Science 330, (2010).! ontrol pulses and NV centers appear as Ø Dynamic decoupling: Periodic flipping of the qubit spin state to average out the interactions with the environment.! L. Viola et al. Phys. Rev A 58, 2733 (1998).!

13 Dynamical Decoupling! (a) y (b) y S z S x t t Hahn Echo! S z x S y (c) t/2 y t y t/2 N Carr Purcell Meiboom Gill! S z (d) x y x C n 1 C n 1 C n 1 C n 1 y N XY-4! A. M. Souza et al. Phil. Trans. R. Soc. 370, (2012).!

14 and decoupling. We experimentally demonstrate g a two-qubit register in diamond operating at room uantum tomography reveals that the qubits involved ation are protected as accurately as idle qubits. We rover s quantum search algorithm1, and achieve ticularly promising for the tures12 22, in which differen spins, superconducting res form different functions. D to be decoupled at its own Decoherence in multi-qubit gates! 1) couple to a Qubits Unprotected each other but also quantum gate to environment! e n b c Protected storage: Decoupling e n Protected quantum gate e d NV cen C C N V C n C e 1 Environment Environment 1 Environment Nuclear drivin Gate Decoupling Gate + decoupling z N. van der Sar et al. Nature 484, (2012).! x y R X( ) 14

15 and tion decoupling. and decoupling. We experimentally We experimentally demonstrate demonstrate ticularly ticularly promising promising for thef gusing a two-qubit a two-qubit register register in diamond in diamond operating operating at room at room, in which, in which differen d tures12 22 tures uantum re. Quantum tomography tomography reveals reveals that the that qubits the qubits involved involved spins,spins, superconducting superconducti res ation operation are protected are protected as accurately as accurately as idleasqubits. idle qubits. We We form different form different functions. functid 1, and1, achieve and achieve to be decoupled to be decoupled at its own at its rm rover s Grover s quantum quantum searchsearch algorithm algorithm Decoherence in multi-qubit gates! 2)b Qubits decoupled d c c Protected Protected Protected Protected from each other and quantum storage: storage: quantum gate gate Decoupling Decoupling environment! 1) to b a Qubits a couple Unprotected Unprotected each otherquantum but alsogate quantum gate to environment! e e n n e e n n e e n dnv cenn C C N C n e V C e 1 Environment Environment Environment Environment C 1 1 Environment Environment Nuclear Nuclea drivin Gate Gate decoupling + decoupling Decoupling Decoupling Gate +Gate z N. van der Sar et al. Nature 484, (2012).! x y z y x R X( ) 14 1

16 operation and tion decoupling. and decoupling. and decoupling. We experimentally We experimentally We experimentally demonstrate demonstrate demonstrate ticularly ticularly promising ticularly promising for promi thef ggates using a two-qubit using a two-qubit a register two-qubit register in diamond register in diamond inoperating diamond operating at operating room at room at room, intures which, in which differen, in wh d tures tures uantum erature. re. Quantum tomography Quantum tomography tomography reveals reveals thatreveals the that qubits the that qubits involved the qubits involved involved spins,spins, superconducting spins, superconducti supercon res ation operation gate are operation protected are protected are as protected accurately as accurately as accurately as idleasqubits. idleasqubits. idle Wequbits. We formwe different form form different functions. different functid f 1, and1, achieve and1, achieve and to achieve be decoupled to be decoupled to be at decoupled its own at its perform rm rover s Grover s quantum Grover s quantum search quantum search algorithm search algorithm algorithm Decoherence in multi-qubit gates! 1) to b Protected 2)b Qubits only d dnv cen dn a Qubits a couple a Unprotected b decoupled c c c3) Qubits Protected Protected Unprotected Unprotected Protected Protected Protected each otherquantum but also from each other and quantum decoupled storage: storage: storage: quantum gate quantum gate gate quantum gate quantum gate from gate C C C Decoupling Decoupling Decoupling to environment! environment! environment! N e e e n n e n e e n n e n e e n n C n e V C e e Environment Environment Environment Environment Environment Environment Environment Environment Environment Nuclear Nuclea drivinn Gate Gate Gate Gate +Gate decoupling +Gate decoupling + decoupling Decoupling Decoupling Decoupling z N. van der Sar et al. Nature 484, (2012).! x y z y x RX( x) 14 1

17 Qubit Coupling

18 Qubit Coupling Generally desirable Fast coupling for fast qubit manipulation

19 Qubit Coupling Generally desirable Fast coupling for fast qubit manipulation But we pay a price We also get faster coupling to the environment

20 Fast and Slow Qubits Encode Physical Qubits in:

21 Fast and Slow Qubits Encode Physical Qubits in: atomic states

22 Fast and Slow Qubits Encode Physical Qubits in: atomic states superconducting circuits

23 Fast and Slow Qubits Encode Physical Qubits in: atomic states superconducting circuits quantum dots

24 Fast and Slow Qubits Encode Physical Qubits in: atomic states superconducting circuits quantum dots NV centers

25 Two Qubit Gates

26 Two Qubit Gates Difficult Scenario Using fast qubit as the control bit

27 Two Qubit Gates Difficult Scenario Using fast qubit as the control bit Question Can we use dynamical decoupling to make a gate using the fast qubit as our control bit?

28 Fast and Slow Qubits; NV Centers Fast qubit: electronic spin

29 Fast and Slow Qubits; NV Centers Fast qubit: electronic spin GHz energy splitting

30 Fast and Slow Qubits; NV Centers Fast qubit: electronic spin GHz energy splitting T 2 = 3.5µs ; Rabi 2π pulse: 20ns

31 Fast and Slow Qubits; NV Centers Fast qubit: electronic spin GHz energy splitting T 2 = 3.5µs ; Rabi 2π pulse: 20ns Slow qubit: nuclear spin

32 Fast and Slow Qubits; NV Centers Fast qubit: electronic spin GHz energy splitting T 2 = 3.5µs ; Rabi 2π pulse: 20ns Slow qubit: nuclear spin MHz energy splitting

33 Fast and Slow Qubits; NV Centers Fast qubit: electronic spin GHz energy splitting T 2 = 3.5µs ; Rabi 2π pulse: 20ns Slow qubit: nuclear spin MHz energy splitting T 2 = 5.3ms ; Rabi 2π pulse: 30µs

34 Two Qubit Gates Imagine

35 Two Qubit Gates Imagine

36 Two Qubit Gates Imagine

37 Two Qubit Gates Imagine

38 Two Qubit Gates Imagine

39 Two Qubit Gates Not obvious whether this can work

40 Two Qubit Gates Not obvious whether this can work

41 Building a 2-Qubit Gate Electronic Spin m S = 0 : 0 m S = 1 : 1 Nuclear Spin m I = +1 : m I = 0 :

42 Building a 2-Qubit Gate Electronic Spin m S = 0 : 0 m S = 1 : 1 Nuclear Spin m I = +1 : m I = 0 :

43 Building a 2-Qubit Gate Electronic Spin m S = 0 : 0 m S = 1 : 1 Timescales ( µs ) Nuclear Spin m I = +1 : m I = 0 :

44 Building a 2-Qubit Gate Electronic Spin m S = 0 : 0 m S = 1 : 1 Timescales ( µs ) Nuclear Spin m I = +1 : m I = 0 :

45 Building a 2-Qubit Gate Electronic Spin m S = 0 : 0 m S = 1 : 1 Timescales ( µs ) Nuclear Spin m I = +1 : m I = 0 :

46 Building a 2-Qubit Gate Decoupling Pulse Sequence τ X 2τ Y τ

47 Building a 2-Qubit Gate Decoupling Pulse Sequence τ X 2τ Y τ Electronic Qubit in State 0 exp( iσz θ 0 )exp( iσx 2θ 1 )exp( iσz θ 0 )

48 Building a 2-Qubit Gate Decoupling Pulse Sequence τ X 2τ Y τ Electronic Qubit in State 0 exp( iσz θ 0 )exp( iσx 2θ 1 )exp( iσz θ 0 ) Electronic Qubit in State 1 exp( iσx θ 1 )exp( iσz 2θ 0 )exp( iσx θ 1 )

49 Building a 2-Qubit Gate Special case 1 τ = (2n + 1)π/A

50 Building a 2-Qubit Gate Special case 1 τ = (2n + 1)π/A Example

51 Building a 2-Qubit Gate Special case 1 τ = (2n + 1)π/A Example

52 Building a 2-Qubit Gate Special case 1 τ = (2n + 1)π/A Example

53 Building a 2-Qubit Gate Special case 2 τ = 2nπ/A

54 Building a 2-Qubit Gate Special case 2 τ = 2nπ/A Example

55 Building a 2-Qubit Gate Special case 2 τ = 2nπ/A Example

56 Building a 2-Qubit Gate Special case 2 τ = 2nπ/A Example

57 Building a 2-Qubit Gate Combine special cases 1 and 2 obtain a conditional rotation gate

58 Experimental Results

59 Experimental Results CNOT Gate ( θ = π ) Process fidelity: F p = Tr(χ ideal χ) = 83%

60 Experimental Results CNOT Gate ( θ = π ) Process fidelity: F p = Tr(χ ideal χ) = 83% For a State ψ = α 0 + β 1 ρ = ψ ψ

61 Experimental Results CNOT Gate ( θ = π ) Process fidelity: F p = Tr(χ ideal χ) = 83% For a State ψ = α 0 + β 1 ρ = ψ ψ For an Operator A = αi + βσ x + γσ y + δσ z ε(ρ) = AρA = i,j χ ije i ρe j

62 Testing Gate Robustness Inject noise into the diamond Reduce T 2,SE from 251µs to 50µs

63 Testing Gate Robustness Inject noise into the diamond Reduce T 2,SE from 251µs to 50µs Reduce RF drive power to nuclear spin Gate time increases to 120µs

64 Testing Gate Robustness Inject noise into the diamond Reduce T 2,SE from 251µs to 50µs Reduce RF drive power to nuclear spin Gate time increases to 120µs Single qubit decoupling apply (τ π τ) N

65 Testing Gate Robustness Inject noise into the diamond Reduce T 2,SE from 251µs to 50µs Reduce RF drive power to nuclear spin Gate time increases to 120µs Single qubit decoupling apply (τ π τ) N T 2,N=16 = 234µs

66 Testing Gate Robustness Apply CNOT Input state ( 0 + i 1 ) Desired output state ψ = ( )/ 2

67 Testing Gate Robustness Apply CNOT Input state ( 0 + i 1 ) Desired output state ψ = ( )/ 2

68 Testing Gate Robustness Apply CNOT Input state ( 0 + i 1 ) Desired output state ψ = ( )/ 2 State Fidelity N = 16 : F = ψ ρ ψ reaches 96%

69 Running Grover s Algorithm Recall: Search Algorithm Find entry in list of N elements Number of oracle calls scales as N

70 Running Grover s Algorithm Recall: Search Algorithm Find entry in list of N elements Number of oracle calls scales as N

71 Running Grover s Algorithm

72 Running Grover s Algorithm Final State Fidelity > 90%

73 Summary

74 Summary Can construct 2-qubit gate protected from decoherence

75 Summary Can construct 2-qubit gate protected from decoherence Especially useful when control bit is fast

76 Summary Can construct 2-qubit gate protected from decoherence Especially useful when control bit is fast Achieved process fidelities above 80%, and state fidelities above 90% using an NV center

77 Summary Can construct 2-qubit gate protected from decoherence Especially useful when control bit is fast Achieved process fidelities above 80%, and state fidelities above 90% using an NV center Ultimate goal: < 10 4

78 Quantum Teleportation NV - Centers

79 Framework Unconditional teleportation Any state can be transmitted Remoteness Sender and reciever are reasonably separated (3m)

80 Entanglement Remote entanglement between NV electrons Local entanglement: Spin rotation / Spin-selective excitation Electron-Photon Local entanglement: Quantum interference photon detection Photon-Photon

81 Teleporter Setup Configuration Alice NV-Center: Transmission Qubit (1) Nuclear spin Messenger Qubit (2) Electron spin Bob NV-Center: Reciever Qubit (3) Electron spin Qubits 2 & 3 entangled in i 23

82 Teleporter Setup Initialization Transmission Qubit initialized in 1i 1 Projective measurement of Messenger Prior to entanglement Source State i 1 = 0i 1 + 1i 1 After entanglement to avoid Dephasing

83 Teleporter Setup Final State Final State in Bell basis: i 1 i 23 = 1 2 [ + i 12 ( 1i 3 0i 3 ) + i 12 ( 1i 3 + 0i 3 ) + + i 12 ( 0i 3 + 1i 3 ) + i 12 ( 0i 3 1i 3 )]

84 Teleportation Interaction between Qubits 1 and 2 CNOT followed by /2 Y-rotation of Transmitter Projective measurements Conditional Pauli-rotations

85 Teleportation Interaction Nuclear rotations controlled by Electron excitation level: Controlled /2 Y-rotation (on 1 controlled by 2) Y-rotation (unconditional on 2) Controlled /2 Y-rotation (on 1 controlled by 2) Effectively: /2 Y-rotation (unconditional on 1)

86 Teleportation Interaction Overall state after interaction: R y1 ( / 2 )U CNOT ( i 1 i 23 )= 1 2 [ 11i 12( 1i 3 0i 3 ) + 01i 12 ( 1i 3 + 0i 3 ) + 10i 12 ( 0i 3 1i 3 ) + 00i 12 ( 0i 3 + 1i 3 )]

87 Teleportation Interaction Overall state after interaction: R y1 ( / 2 )U CNOT ( i 1 i 23 )= 1 2 [ 11i 12( xz i 3 ) + 01i 12 ( x i 3 ) + 10i 12 ( z i 3 ) + 00i 12 ( i 3 )]

88 Teleportation Measurement Direct measurement on messenger Projective measurement on transmitter CNOT on 0i 2 electron (on reinitialized messenger, controlled by transmitter) Direct measurement on messenger

89 Teleportation Pauli rotations Depending on measurement: 00i 12 7! 10i 12 7! z 01i 12 7! x 11i 12 7! xz

90 Results Tomography for Y on Bob s side to confirm alignment of reference frames 6 unbiased states transmitted. Fidelity 0.77

91 Outlook Remote Entanglement Mutliple Qubits per node: NV Centers are a good candidate for Quantum networks Entanglement fidelity high enough to close detection loophole of Bell Inequality