Molecular prototypes for spin-based CNOT and SWAP quantum logic gates
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1 Bellaterra: anuary 2011 Architecture & Design of Molecule Logic Gates and Atom Circuits Molecular prototypes for spin-based CNOT and SWAP quantum logic gates Fernando LUIS Instituto de Ciencia de Materiales de Aragón (Zaragoza, Spain)
2 Outline Molecular design of CNOT and SWAP quantum gates Tb 2 Integration of SMM into superconducting microdevices
3 Outline Molecular design of CNOT and SWAP quantum gates Tb 2 Integration of SMM into superconducting microdevices
4 Quantum computers Quantum processing of information Bit Qubit 1 Richard Feynman,
5 Molecular qubits Unitary operations Single qubits Chemically synthesized Scalability Identical entities 1 Read-out 0 R b rf Carry magnetic moment S m= Initialization m=+10
6 Molecular qubits Unitary operations Single qubits 1 Cr 7 Ni, S = 1/2 A. Ardavan et al. Phys. Rev. Lett. 98, (2007) 0 S. Bertaina et al. Nature 453 (2008) V 15, S = 1/2
7 CNOT (universal) quantum logic gate control target
8 CNOT quantum logic gate control target 1. Two qubits 2. Coupling 3. Asymmetry
9 D. Aguilà et al, Inorg. Chem. 49 (2010) 6784 G. Aromí, D. Aguilà, P. Gámez, F. Luis, and O. Roubeau, Chem. Soc. Rev., (2012), DOI: /C1CS15115K Molecular design Dinuclear [Tb] 2 complex Linked to three asymmetric H 3 L ligands Two anisotropic spins in different coordinations
10 Definition of qubit states [LaTb] = 6, g = 3/2
11 T(emu K/ Oe mol Tb) Definition of qubit states [LaTb] = 6, g = 3/ eff g B 2 T eff eff g B 1 m = 0 m = ±4 Tb D = 19 K T(K) m = ±5 m = ±6 180 K! H anis DS 2 z g B H x x H y y H z z Two states
![c p /R Definition of qubit states [LaTb] = 6, g = 3/2 Y 10 0 LaTb H 10-1 H = 0 0 H = 0.125 T 0 H = 0.](/docs-images/88/114753316/images/12-1.jpg "25 T m = 0 m = ±4 Tb 10-2 Debye H 1 10 m6 T (K) g H 0 H = 0.")
12 c p /R Definition of qubit states [LaTb] = 6, g = 3/2 Y 10 0 LaTb H 10-1 H = 0 0 H = T 0 H = 0.25 T m = 0 m = ±4 Tb 10-2 Debye H 1 10 m6 T (K) g H 0 H = 0.5 T 0 H = 1 T B z z m = ±5 m = ±6 Two states m = -6 2g H cos Y B m = +6
13 T(emu K/ Oe mol Tb) Coupling between the Tb 3+ qubits [Tb] [LaTb] 8 [Tb] 2 2 T eff H exch T(K) ex z1 z2 AF coupling
14 c p /R c p /R Coupling between the Tb 3+ qubits 10 0 [LaTb] [Tb] Tb nuclear spins Debye T (K) 10 0 [Tb] 2 ex K 10-1 = 4 ex 2 = 2.14 K H exch T (K) ex z1 z2
15 T(emu K/ Oe mol Tb) Magnetic asymmetry min (13 1mHz mk) 10 1/2 f μ B Hz 1MHz SQUID (dc) 15.8 mhz 1.58 Hz 158 Hz 15.8 khz 5 ex = K = T(K)
16 T(emu K/ Oe mol Tb) T(emuK/Oe mole Tb 2 ) Magnetic asymmetry mhz 1.58 Hz 158 Hz 15.8 khz dc 0 H = 0.1 T SQUID (dc) 15.8 mhz 1.58 Hz 158 Hz 15.8 khz T(K) 5 ex = K = T(K)
17 T(emu K/ Oe mol Tb) T(emuK/Oe mole Tb 2 ) Magnetic asymmetry mhz 1.58 Hz 158 Hz 15.8 khz dc 0 H = 0.1 T SQUID (dc) 15.8 mhz 1.58 Hz 158 Hz 15.8 khz ex = K = 66 deg T(K) T(K) ex = K = 0 = 66 degrees Noncollinear anisotropy axes z 2 z 1
18 M( B /Tb 2 molecule) T(emuK/Oe mole Tb 2 ) Magnetic asymmetry mhz 1.58 Hz 158 Hz 15.8 khz dc 0 H = 0.1 T T(K) z 2 z Hall T = 0.26 K Hall T = 2.0 K SQUID T = 2.0 K = 66 degrees 2 theory T = 0.26 K = 66 o 0 = 0 o H (T) Noncollinear anisotropy axes
19 c p /R c p /R c p /R Magnetic asymmetry 1 Experiment 0 H = theory: = 0 0 H = T 0 H = 0.25 T 0 H = 0.5 T z 1 z theory: = 66 deg. 0 H = 0 0 H = T 0 H = 0.25 T 0 H = 0.5 T = 66 degrees H = 0 0 H = T 0 H = 0.25 T 0 H = 0.5 T T(K) Noncollinear anisotropy axes
20 Heterometallic clusters [LaEr] Er 3+ = 15/2, g = 6/5 [CeEr] Ce 3+ = 5/2, g = 6/7 [CeY]
21 All ingredients are met! Tb 1 Non-collinear easy axes or different ions 99.99% lie in the ground state below 20 K Tb 2 z Tb 1 Tb 2 m = 0 m = ±4 Antiferromagnetic exchange below 3 K x y 180 K! m = ±5 m = ±6 two qubits interaction = 66 deg
22 Energy(K) 0 H (T) [Tb] 2 as a CNOT logic gate ) ( z z z z hf z z z z B z z ex m I I A H H g H CNOT
23 Energy(K) EPR signal (a.u.) Implementation by EPR CNOT T = 6 K = 9.8 GHz X-band H (T) H (T) CNOT transitions are not forbidden
24 F. Luis et al, Phys. Rev. Lett. 107, (2011). Energy(K) EPR signal (a.u.) T = 6 K = 9.8 GHz H (T) H (T) SWAP gate operations are also possible!
25 Intensity (a.u.) echo intensity (a.u.) Quantum coherence? (X-band pulsed EPR) Tb 2 : m = -6 m = +6 ECHO? NOT OBSERVED Ce 2 : m = -1/2 m = +1/2 OBSERVED!! CNOT 8.0x T 1 = 1 s T 2 = 250 ns x H(G) time(ns)
26 Outline Molecular design of CNOT and SWAP quantum gates Tb 2 Integration of SMM into superconducting microdevices
27 Hybrid quantum computation architectures Magnetic qubits as hardware for quantum computers.. Tejada, E. M. Chudnovsky, E. del Barco,. M. Hernandez and T. P. Spiller, Nanotechnology 12 (2001) Cavity QED Based on Collective Magnetic Dipole Coupling: Spin Ensembles as Hybrid Two-Level Systems. Atac Imamoglu, PRL 102, (2009) Molecule-based qubits and qugates Superconducting circuits
28 The goal: maximizing the flux coupling 1. Scaling down the dimensions of the loop 2. Playing with the sample position!!! The first challenge is the placement of a single nanoparticle close to the nanosquid while achieving sufficient magnetic coupling between the particle and the device C. P. Foley and H. Hilgenkamp. Supercond. Sci. Technol. 22, (2009).
29 M Martínez-Pérez,. Sesé, F. Luis, D. Drung and T. Schurig Rev. Sci. Instrum. 81, (2010) The device: microsquid ac susceptometer
30 (F 0 Oe/ B A) d coupled n i Cross-section view B i P P
31 The tool: Dip pen nanolithography AFM Tip Water Meniscus Writing Direction Substrate
32 The sample: ferritin-based nanomagnets (CoO) CoO 2 nm sized Antiferromagnetic particle ~ 12 B
33 Height (nm) Au Au SiO 2 Cross-sectional view Al Nb ~10 nm Section (μm)
34 Direct deposition on the most sensitive areas 10 5 molecules/dot
35 M.. Martínez-Pérez, E. Bellido, R.. De Miguel,. Sese, A. Lostao, C. Gómez-Moreno, D. Drung, T. Schurig, D. Ruiz-Molina, and F. Luis, APL. 99, (2011) Detection of the linear response of a SMM monolayer ' [emu/mol(clus)oe] Hz 2.1 khz 72 khz T (K) Sensitivity 10 2 B /Hz 1/2
36 Mn 12 Gd 2
37 Towards the implementation of quantum computation architectures Magnetic qubits as hardware for quantum computers.. Tejada, E. M. Chudnovsky, E. del Barco,. M. Hernandez and T. P. Spiller, Nanotechnology 12 (2001) Cavity QED Based on Collective Magnetic Dipole Coupling: Spin Ensembles as Hybrid Two-Level Systems. Atac Imamoglu, PRL 102, (2009) Molecule-based qubits and qugates DPN!!! Superconducting circuits
38 CONCLUSIONS [LnLn ] clusters, designed and synthesized via coordination chemistry, meet the following ingredients proper definition of qubit states weak AF coupling between qubits magnetic asymmetry molecular prototypes for CNOT quantum gates SWAP gate operations can be performed in the same molecule Dip pen nanolithography offers a very attractive tool to integrate molecular qubits into superconducting microdevices: towards the implementation of quantum architectures
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