93 Views

Download Presentation
##### Quantum Control

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**QUANTUM WORLD**Quantum Control Classical Input Preparation Dynamics Readout Classical Output QUANTUM INFORMATION INSIDE**Hilbert spaces are fungible**ADJECTIVE: 1. Law.Returnable or negotiable in kind or by substitution, as a quantity of grain for an equal amount of the same kind of grain. 2. Interchangeable. ETYMOLOGY: Medieval Latin fungibilis, from Latin fung (vice), to perform (in place of). Subsystem division 2 qubits; D = 4 Unary system D = 4**Example: Rydberg atom**http://gomez.physics.lsa.umich.edu/~phil/qcomp.html**A Hilbert space is endowed with structure by the physical**system described by it, not vice versa. The structure comes from preferred observables associated with spacetime symmetries that anchor Hilbert space to the external world. Hilbert-space dimension is determined by physics. The dimension available for a quantum computation is a physical quantity that costs physical resources. Key Question What physical resources are required to achieve a Hilbert-space dimension sufficient to carry out a given calculation? quant-ph/0204157 We don’t live in Hilbert space**Action quantifies the**physical resources. Planck’s constant sets the scale. Hilbert space and physical resources Hilbert-space dimension is a physical quantity that costs physical resources. Single degree of freedom**Hilbert space and physical resources**Primary resource is Hilbert-space dimension. Hilbert-space dimension costs physical resources. Many degrees of freedom Number of degrees of freedom Identical degrees of freedom Hilbert-space dimension measured in qubit units. Scalable resource requirement Strictly scalable resource requirement qudits**x3, p3**Primary resource is Hilbert-space dimension. Hilbert-space dimension costs physical resources. x2, p2 x1, p1 x, p Hilbert space and physical resources Many degrees of freedom**Length**Momentum Action Energy Bohr 3 degrees of freedom Hilbert-space dimension up to n Quantum computing in a single atom Characteristic scales are set by “atomic units”**Length**Momentum Action Energy Bohr Poor scaling in this physically unary quantum computer Quantum computing in a single atom Characteristic scales are set by “atomic units” 5 times the diameter of the Sun**Other requirements for a scalable quantum computer**Avoiding an exponential demand for physical resources requires a quantum computer to have a scalable tensor-product structure. This is a necessary, but not sufficient requirement for a scalable quantum computer. Are there other requirements? DiVincenzo’s criteria DiVincenzo, Fortschr. Phys. 48, 771 (2000) 1. Scalability:A scalable physical system with well characterized parts, usually qubits. 2. Initialization:The ability to initialize the system in a simple fiducial state. 3. Control: The ability to control the state of the computer using sequences of elementary universal gates. 4. Stability:Long decoherence times, together with the ability to suppress decoherence through error correction and fault-tolerant computation. 5. Measurement:The ability to read out the state of the computer in a convenient product basis.**Classical bit**A fewelectronson a capacitor Anelectron spinin a semiconductor Apiton a compact disk Afluxquantumin a superconductor A0or1on the printed page Aphotonof coupled ions A smoke signalrising from a distant mesa Energy levels in an atom Quantum bit Physical resources: classical vs. quantum A classical bit involves many degrees of freedom. Our scaling analysis applies, but with a basic phase-space scale ofarbitrarily small. Limit set by noise,not fundamental physics. The scale of irreducible resource requirements is always set by Planck’s constant.**State Preparation**• Initialization • Entropy Dump Why Atomic Qubits? State Manipulation • Potentials/Traps • Control Fields • Particle Interactions Laser cooling Quantum Optics NMR State Readout • Quantum Jumps • State Tomography • Process Tomography Fluorescence**Designing Optical Lattices**Tensor Polarizability P3/2 3 / 2 - 1 / 2 1 / 2 - 3 / 2 1 ( ) 1 2 2 2 i a = - a d + e s 1 1 ij 0 ij ijk k 3 3 3 3 S1/2 1 / 2 1 / 2 - Effective scalar + Zeeman interaction**Multiparticle Control**Controlled Collisions**+**+ - - 2 G = G ¢ + G £ G ¢ tot dd 2 d 2 d V ~ h ~ G ¢ dd 3 r 3 D (Quasistatic potential) (Dicke Superradiant State) Figure of Merit Dipole-Dipole Interactions • Resonant dipole-dipole interaction**Coupled**Bare Dressed ¢ e e e e e e 1 2 1 2 1 2 V y dd e g g e - ¢ 1 2 1 2 y + D y + ¢ g g 1 2 g g g g 1 2 1 2 Cooperative level shift**r**12 Two Gaussian-Localized Atoms**Atomic Spectrum**“Molecular” Spectrum Three-Level Atoms**“Molecular” Spectrum**Brennen et al. PRA 65 022313 (2002) Molecular Hyperfine Atomic Spectrum 0.8 GHz F=2 5P1/2 F=1 F=2 6.8 GHz 5S1/2 F=1 87Rb**Figure of Merit:**E E 2 E E + - D 11 00 01 c k = = h h G G ij ij Resolvability = Fidelity Controlled-Phase Gate Fidelity**azimuthally symmetric trap**Leakage: Spin-Dipolar Interaction Noncentral force**Suppressing Leakage Through Trap**Energy and momentum conservation suppress spin flip for localized and separated atoms.**Dimer Control**• Lattice probes dimer dynamics • Localization fixes internuclear coordinate**Separated-Atom Cold-Collision**Short range interaction potential, well characterized by a hard-sphere scattering with an “effective scattering length”.**Shape Resonance**Molecular bound state, near dissociation, plays the role of an auxiliary level for controlled phase-shift.**Dreams for the Future**• Qudit logic: Improved fault-tolerant thresholds? • Topological lattice - Planar codes?**http://info.phys.unm.edu/~deutschgroup**I.H. Deutsch, Dept. Of Physics and Astronomy University of New Mexico • Collaborators: • Physical Resource Requirements for Scalable Q.C. Carl Caves (UNM), Robin Blume-Kohout (LANL) • Quantum Logic via Dipole-Dipole Interactions Gavin Brennen (UNM/NIST), Poul Jessen (UA), Carl Williams (NIST) • Quantum Logic via Ground-State Collisions René Stock (UNM), Eric Bolda (NIST)