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## Wiring up a Quantum Computer

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**Wiring up a Quantum Computer**Paola CappellaroQuantum Engineering Group - MIT**Distributed quantum computing**• Modular, hybrid architecture for quantum computing • quantum registers for simple algorithms and local memory • quantum wires to connect the registers**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) Quantum Information Transport**State-Transfer in spin chains**• Flip-flops transport a single-spin excitation |0 0 0 0 0 0 0 0〉 • Similar to spin-waves driven by Heisenberg exchange Hamiltonian • Most common model is the xx-Hamiltonian 1 1**Optimal Transport**• Perfect transport for F Spin # 5 10 15 20**Optimal Transport**• Perfect transport for F Spin N Spin 1 Time**Dispersive Transport**• Limited fidelity for F Spin # 5 10 15 20**Dispersive Transport**• Limited fidelity for F Spin 1 Spin N Time**Transport Fidelity**Optimal couplings Equal couplings A. Ajoy, P. Cappellaro, to appear in Phys. Rev A**ImplementationsNuclear spins in apatite crystalsElectronic**spins in diamond Nuclear spins in apatite crystals**Simulation with NMR**• Nuclear spins in regular crystal • Advantages: • Well-defined geometry • Good control • Long coherence times • Challenges: • No single-spin addressability**FluorApatite**• Single-crystal, Ca5F(PO4)3 • Quasi-1D system: • Ratio of couplings: Cin/Cx= Dx3/din340 Bz 19F spin ½ • Generate the transport interaction • Prepare the initial state**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**Create DQ-Hamiltonian**• Rotate the natural dipolar interaction • On average we obtain z 2t t/2 t/2 x y**Create DQ-Hamiltonian**• More complex sequence ➙better approximation**Create Initial State**• Initial state: thermal state, • Leave just one spin polarized: • Spin 1 has just 1 neighbor ➙different evolution Px x-polarization: t***Chain Ends Selection**• Simple control scheme • Similar scheme for readout of end-chain spins • NMR spectrum of the two initial states**Transport**• Compare dynamics of Thermal vs. End Chain E/E T/T E/T T/E**Transport**• Compare dynamics of Thermal vs. End Chain E/E T/T E/T T/E G. Kaur, P. Cappellaro, arXiv:1112.0459**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**ImplementationsNuclear spins in apatite crystalsElectronic**spins in diamond Electronic spins in diamond**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, 025014(2011)**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.**Complex Networks**• Randomly distributed spins in a lattice • Distance-dependent interactions • Network represented by adjacency matrix**Weak Coupling**• Couple the end-spins only very weakly: • Information is slowly transported from 1 ➙ N irrespective of details in the fast bulk dynamics**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**High spatial resolution**• Optical control with STED techniques: • Donut beam switches off signal from other spins • Increase the spatial resolution to ~10nm • … more complex setup**Higher spatial resolution**• Nano-scale magnetic field control • Fabrication of small circuit to create • Static magnetic fields and gradients • High-power microwave/radiofrequency fields**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**Funding**NSF DMR MISTI AFOSR YIP Publications A. Ajoy and P. Cappellaro, "Mixed-state quantum transport in correlated spin networks” Phys. Rev. A 85, 042305 (2012) G. Kaur and P. Cappellaro, "Initialization and Readout of Spin Chains for Quantum Information Transport" arXiv:1112.0459 (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. 13 103015 (2011) P. Cappellaro, L. Viola, C. Ramanathan, "Coherent state transfer via highly mixed quantum spin chains” Phys. Rev. A 83, 032304 (2011)**Alex Cooper**Gary Wolcowitz Clarice Aiello Masashi Hirose Thanks! Honam Yum Ashok Ajoy GurneetKaur Jonathan Schneider Martin Goycoolea