Exploration and Control of Condensed Exploration and Control of Condensed Matter Qubits Qubits Matter 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 Long-Term Results: Control and manipulation of quantum states Quantum computer - exponential speedups - breaks modern cryptography - quantum cryptography to the rescue ... Quantum computation and cryptography New quantum science
Nanoscience Operates at the Physical Limit of 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 Information Based on Molecular Populations Quantum Phenomena
Requirements for Computation/Communication • A physical system providing a scalable collection of qubits |1> |0> • Ability to initialize qubits in a known starting state • Long decoherence time, much longer than the gate operation time (T d /t g ~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
Condensed Matter Qubits “Scalable” - architecture, nanofabrication, nanoscale synthesis,... + Main issues: I) Measurement, Control II) Decoherence III) Entanglement Experiment: 1) 31 P Dopant atoms - Davis UCB Collaboration Between 2) Magnetic adsorbates - Crommie Physics, Chemistry, EECS: 3) Peapod Nanotubes - Zettl 4) SC Flux rings - Clarke Theory: 1) Decoherence, control - Whaley 2) Control - Sastry
Theory • New perspectives in coherent control - optimal control: - time - universality - minimal decoherence - perfect entanglers - gate sequences - feedback Whaley, Sastry • Overcoming decoherence - decoherence-free subspaces - fault tolerance, error thresholds - error correction and feedback stabilization • Encoding for optimization - encoded universality (single physical interaction)
Decoherence-free subspaces/subsystems: DFS condition for unitary evolution on a subspace: ~ ~ = S i c i α α α α = ⊗ ∑ H I S B with the system-bath interaction α α α • 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)
exploiting DFS for Quantum Computation degeneracy implies safety • robust to perturbing interactions Bacon et al, Phys Rev A 60 1944 (1999) • combine with quantum error correction - concatenated DFS-QECC Lidar et al, Phys Rev Lett 82 14556 (1999) • compute on a DFS, e.g., exchange-only QC Bacon et al, Phys Rev Lett 85 1758 (2000) • fault tolerant computation possible on DFS Kempe et al, Phys Rev A 63 042307 (2001) make use of physics of decoherence mechanisms - symmetry first!
Heisenberg exchange interaction � � = σ ⋅ σ E i j , i j • E is universal with encoding* • introduce tensor structure, eg. blocks with 3 qubits *,** • 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 *Kempe, Bacon, Lidar, Whaley, Phys. Rev. A 63 :042307 (2001) **DiVincenzo, Bacon, Kempe, Burkard, Whaley, NATURE 408 339 (2000)
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)
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