Wiring up a Quantum Computer Paola Cappellaro Quantum Engineering Group - MIT

P. Cappellaro — Modular, hybrid architecture for quantum computing – quantum registers for simple algorithms and local memory Distributed quantum computing – quantum wires to connect the registers

P. Cappellaro — Q UANTUM I NFORMATION T RANSPORT

P. Cappellaro — Q UANTUM I NFORMATION T RANSPORT I-mode at Alcator C-mod: Turbulent-Transport In High-Performance, ITER Relevant Plasmas (A. White) Strain Coupling to the Reactivity and Transport Properties of Solid Oxide Fuel Cell Materials (B. Yildiz) Beyond Multigroup: An Alternative for the Energy Treatment in Radiation Transport (B. Forget)

P. Cappellaro — State-Transfer in spin chains Flip-flops transport a single-spin excitation | 〉 – Similar to spin-waves driven by Heisenberg exchange Hamiltonian – Most common model is the xx-Hamiltonian 11

P. Cappellaro — Optimal Transport Perfect transport for F Spin #

P. Cappellaro — Optimal Transport Perfect transport for Time F Spin 1 Spin N

P. Cappellaro — Dispersive Transport Limited fidelity for F Spin #

P. Cappellaro — Dispersive Transport Limited fidelity for F Spin 1 Spin N Time

P. Cappellaro — Transport Fidelity Optimal couplingsEqual couplings A. Ajoy, P. Cappellaro, to appear in Phys. Rev A

P. Cappellaro — I MPLEMENTATIONS Nuclear spins in apatite crystals Electronic spins in diamond Nuclear spins in apatite crystals

P. Cappellaro — Nuclear spins in regular crystal Advantages: – Well-defined geometry – Good control – Long coherence times Challenges: – No single-spin addressability Simulation with NMR

P. Cappellaro — BzBz Single-crystal, Ca 5 F(PO 4 ) 3 Quasi-1D system: – Ratio of couplings: C in /C x = D x 3 /d in 3  40 FluorApatite 1.Generate the transport interaction 2.Prepare the initial state 19 F spin ½

P. Cappellaro — Create Transport Hamiltonian xx-Hamiltonian usually is not available – Use coherent control to create (on average) the transport Hamiltonian – Constraints on control (collective rotations) DQ-Hamiltonian simulates transport

P. Cappellaro — Create DQ-Hamiltonian Rotate the natural dipolar interaction On average we obtain t/2 2t x z y

P. Cappellaro — Create DQ-Hamiltonian More complex sequence ➙ better approximation

P. Cappellaro — Initial state: thermal state, Leave just one spin polarized: – Spin 1 has just 1 neighbor ➙ different evolution t*t* PxPx Create Initial State x-polarization:

P. Cappellaro — Simple control scheme – Similar scheme for readout of end-chain spins Chain Ends Selection NMR spectrum of the two initial states

P. Cappellaro — Transport Compare dynamics of Thermal vs. End Chain T/T E/E T/EE/T

P. Cappellaro — Transport Compare dynamics of Thermal vs. End Chain T/T E/E T/EE/T G. Kaur, P. Cappellaro, arXiv:

P. Cappellaro — Outlook Investigate deviations from ideal behavior – and devise methods to still achieve transport. Full control of chain end spins in FAp with high proton defect density – Universal control of the entire chain – Direct readout of transport New playground for non-equilibrium many- body physics and simulation

P. Cappellaro — I MPLEMENTATIONS Nuclear spins in apatite crystals Electronic spins in diamond Electronic spins in diamond

P. Cappellaro — Nitrogen spin chains Precise implantation of nitrogens in diamond – Some are converted to NV – Leftovers nitrogen impurities NV addressed optically – sub-diffraction limit Nitrogen spins act as spin-chain wires P.Spinicelli et al., New J. Phys. 13, (2011)

P. Cappellaro — Nitrogen spin chains Challenges – Implantation is not precise enough ➞ Study transport in complex 3D networks – NV spins are still too close-by for confocal microscopy ➞ Use (1) sub-diffraction-limit (STED) techniques to address them, combined with (2) microwave control.

P. Cappellaro — Complex Networks Randomly distributed spins in a lattice – Distance-dependent interactions – Network represented by adjacency matrix

P. Cappellaro — Weak Coupling Couple the end-spins only very weakly: – Information is slowly transported from 1 ➙ N irrespective of details in the fast bulk dynamics

P. Cappellaro — Speed vs. Fidelity Transport in ANY network, but compromise: – Setting the end-spins on resonance with a collective bulk mode increases the speed – Off-resonance condition yields higher fidelity 25 nitrogens (1ppm), ~40nm

P. Cappellaro — High spatial resolution 1.Optical control with STED techniques: Donut beam switches off signal from other spins Increase the spatial resolution to ~10nm … more complex setup

P. Cappellaro — Higher spatial resolution 2.Nano-scale magnetic field control Fabrication of small circuit to create – Static magnetic fields and gradients – High-power microwave/radiofrequency fields

P. Cappellaro — Conclusions – A different type of transport Quantum wires are a key ingredients for a distributed, scalable quantum computer Spin chains and networks can be used as wires to transport quantum information – Perfect transport conditions – Experimental implementations

P. Cappellaro — Funding NSF DMR MISTI AFOSR YIP Publications A. Ajoy and P. Cappellaro, "Mixed-state quantum transport in correlated spin networks” Phys. Rev. A 85, (2012) G. Kaur and P. Cappellaro, "Initialization and Readout of Spin Chains for Quantum Information Transport" arXiv: (To appear in New J. of Phys.) C. Ramanathan, P. Cappellaro, L. Viola and D.G. Cory, "Experimental characterization of coherent magnetization transport in a one- dimensional spin system” New J. Phys (2011) P. Cappellaro, L. Viola, C. Ramanathan, "Coherent state transfer via highly mixed quantum spin chains” Phys. Rev. A 83, (2011)

P. Cappellaro — Clarice Aiello Masashi Hirose Ashok Ajoy Honam Yum Alex Cooper Gurneet Kaur Thanks! Martin Goycoolea Jonathan Schneider Gary Wolcowitz