Exploration and Control of Condensed Exploration and Control of - - PowerPoint PPT Presentation

Exploration and Control of Condensed Exploration and Control of Condensed Matter Matter Qubits Qubits

NSF-ITR medium group - new award 2002

• K. B. Whaley

Chemistry

• M. F. Crommie

Physics

• J. Clarke

Physics

• J. C. Davies

Physics

• A. Zettl

Physics

• S. Sastry

Electrical Engineering and Computer Science

Grand Challenge:

Quantum Processing

Control and manipulation

• f quantum states

Quantum computation and cryptography New quantum science

Long-Term Results:

Quantum computer

• exponential speedups
• breaks modern cryptography
• quantum cryptography to the

rescue ...

Nanoscience Operates at the Physical Limit

• f Information Processing

Scanning probe microscopies Writing with atoms Entangled quantum states and teleportation Natural nanostructures: enzymes, DNA Artificial nanostructures: nanotubes, nanocrystals, organic dendrimers Nanoscale architectures: microfluidics, nanopores, membranes

Information Based on Quantum Phenomena Information Based on Molecular Populations

• A physical system providing a scalable collection
• f qubits
• Ability to initialize qubits in a known starting state
• Long decoherence time, much longer than the

gate operation time (Td/tg~10,000)

• A universal set of quantum gates
• Individual qubit measurement capability
• Ability to interconvert stationary/flying qubits
• Ability to faithfully transmit flying qubits

DiVincenzo 1995, 2001

|1> |0>

Requirements for Computation/Communication

UCB Collaboration Between Physics, Chemistry, EECS:

Condensed Matter Qubits

+

“Scalable” - architecture, nanofabrication, nanoscale synthesis,... Main issues: I) Measurement, Control II) Decoherence III) Entanglement Experiment: 1) 31P Dopant atoms - Davis 2) Magnetic adsorbates - Crommie 3) Peapod Nanotubes - Zettl 4) SC Flux rings - Clarke Theory: 1) Decoherence, control - Whaley 2) Control - Sastry

• New perspectives in coherent control
• optimal control:
• time
• universality
• minimal decoherence
• perfect entanglers
• gate sequences
• feedback
• Overcoming decoherence
• decoherence-free subspaces
• fault tolerance, error thresholds
• error correction and feedback stabilization
• Encoding for optimization
• encoded universality (single physical interaction)

Theory

Whaley, Sastry

Decoherence-free subspaces/subsystems:

• collective decoherence

Zanardi & Rasetti Mod. Phys. Lett. B 11, 1085 (1997) Lidar, Chuang, & Whaley PRL 81, 2594 (1998)

• modulated (striped) collective decoherence
• K. Brown, unpublished
• correlated errors

Lidar, Bacon, Kempe, Whaley PRA 63, 022306 (2001)

• generalization to subsytems

Knill et al. PRL 84, 2525 (2000)

∑ ⊗ =

α α α

B S HI

DFS condition for unitary evolution on a subspace:

α α α α

i c i S ~ ~ =

with the system-bath interaction

exploiting DFS for Quantum Computation

degeneracy implies safety make use of physics of decoherence mechanisms - symmetry first!

• robust to perturbing interactions
• combine with quantum error correction -

concatenated DFS-QECC

• compute on a DFS, e.g., exchange-only QC
• fault tolerant computation possible on DFS

Bacon et al, Phys Rev A 60 1944 (1999) Lidar et al, Phys Rev Lett 82 14556 (1999) Bacon et al, Phys Rev Lett

85 1758 (2000)

Kempe et al, Phys Rev A

63 042307 (2001)

Heisenberg exchange interaction

• E is universal with encoding*
• introduce tensor structure, eg. blocks with 3 qubits*,**

*Kempe, Bacon, Lidar, Whaley, Phys. Rev. A 63:042307 (2001) **DiVincenzo, Bacon, Kempe, Burkard, Whaley, NATURE 408 339 (2000)

, i j i j

σ σ = ⋅ E

• efficient implementation

numerical search for optimal gates**

serial coupling - 19 operations for CNOT, 4 operations for 1-qubit parallel coupling - 7 operations for CNOT, 3 operations for 1-qubit

Semiconductor nanostructures as spintronic materials (DARPA/ARO)

• Experiments (Awschalom, UCSB):
• long lifetimes (100 ns)
• multiple g-factors
• Theory:
• tight binding atomistic analysis
• linear optics, surface reconstruction (1995-99)
• g-factors, magneto-optical properties
• local spin densities, nanocrystal spin exchange
• functional design of coupled nanostructures
• Eg. - calculations of g-factors shows strong effect of shape

(dot/rod) on anisotropy, consistent with multiple g-factors observed for specific sizes

• J. Schrier (POSTER)