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

Wiring up a Quantum Computer

Paola CappellaroQuantum 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 —

QUANTUM INFORMATION TRANSPORT

P. Cappellaro —

QUANTUM INFORMATION TRANSPORT

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

|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

P. Cappellaro —

Optimal Transport

• Perfect transport for

5 10 15 20

F

Spin #

P. Cappellaro —

Optimal Transport

• Perfect transport for

Time

F

Spin 1Spin N

P. Cappellaro —

Dispersive Transport

• Limited fidelity for

5 10 15 20

F

Spin #

P. Cappellaro —

Dispersive Transport

• Limited fidelity for

F

Spin 1 Spin N

Time

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Transport Fidelity

Optimal couplings Equal couplings

A. Ajoy, P. Cappellaro, to appear in Phys. Rev A

P. Cappellaro —

IMPLEMENTATIONSNuclear spins in apatite crystalsElectronic spins in diamondNuclear 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 —

Bz

• Single-crystal, Ca5F(PO4)3

• Quasi-1D system:– Ratio of couplings:

Cin/Cx = Dx3/din

3 40

FluorApatite

1. Generate the transport interaction2. Prepare the initial state

19F 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 t/22tx

z

y

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Create DQ-Hamiltonian

• More complex sequence ➙ better approximation

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• Initial state: thermal state, • Leave just one spin polarized:– Spin 1 has just 1 neighbor ➙ different

evolution

t*

Px

Create Initial State

x-polarization:

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• Simple control scheme– Similar scheme for readout

of end-chain spins

Chain Ends Selection

• NMR spectrum of the two initial states

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Transport• Compare dynamics of Thermal vs. End Chain

T/T E/E

T/EE/T

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Transport• Compare dynamics of Thermal vs. End Chain

T/T E/E

T/EE/T

G. Kaur, P. Cappellaro, arXiv:1112.0459

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 —

IMPLEMENTATIONSNuclear spins in apatite crystalsElectronic spins in diamondElectronic spins in diamond

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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)

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

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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

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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 DMRMISTIAFOSR 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)

P. Cappellaro —

Clarice Aiello

Masashi Hirose

Ashok Ajoy Honam Yum

Alex Cooper

Gurneet Kaur

Thanks!

MartinGoycoolea

Jonathan Schneider

Gary Wolcowitz