* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Presentation (PowerPoint File)
Topological quantum field theory wikipedia , lookup
Density matrix wikipedia , lookup
Atomic orbital wikipedia , lookup
Quantum electrodynamics wikipedia , lookup
Path integral formulation wikipedia , lookup
Bra–ket notation wikipedia , lookup
Quantum dot wikipedia , lookup
Probability amplitude wikipedia , lookup
Quantum field theory wikipedia , lookup
Measurement in quantum mechanics wikipedia , lookup
Wave–particle duality wikipedia , lookup
Relativistic quantum mechanics wikipedia , lookup
Atomic theory wikipedia , lookup
Coherent states wikipedia , lookup
Particle in a box wikipedia , lookup
Matter wave wikipedia , lookup
Quantum entanglement wikipedia , lookup
Bohr–Einstein debates wikipedia , lookup
Quantum fiction wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Many-worlds interpretation wikipedia , lookup
Orchestrated objective reduction wikipedia , lookup
Bell's theorem wikipedia , lookup
Quantum decoherence wikipedia , lookup
Copenhagen interpretation wikipedia , lookup
Renormalization wikipedia , lookup
Scalar field theory wikipedia , lookup
Symmetry in quantum mechanics wikipedia , lookup
Quantum group wikipedia , lookup
Quantum computing wikipedia , lookup
Renormalization group wikipedia , lookup
Quantum key distribution wikipedia , lookup
Hydrogen atom wikipedia , lookup
Quantum machine learning wikipedia , lookup
EPR paradox wikipedia , lookup
History of quantum field theory wikipedia , lookup
Interpretations of quantum mechanics wikipedia , lookup
Quantum teleportation wikipedia , lookup
Canonical quantization wikipedia , lookup
Quantum state wikipedia , lookup
Quantum Control Classical Input Preparation in QUANTUM WORLD Dynamics out Readout Classical Outp QUANTUM INFORMATION INSIDE Q.C. Paradigms Paradigm Unitary Gates Measurement Prior Hilbert Entang. Space Standard Circuit Yes No No Yes N 0108020 No Yes No Yes R&B 0010033 No Yes Yes Yes KLM Yes Yes No Yes 0006088 Hilbert spaces are fungible ADJECTIVE: ETYMOLOGY: 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. 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 We don’t live in Hilbert space 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. What physical resources are required to achieve a Hilbert-space dimension sufficient to carry out a given calculation? quant-ph/0204157 Hilbert space and physical resources Hilbert-space dimension is a physical quantity that costs physical resources. Single degree of freedom Action quantifies the physical resources. Planck’s constant sets the scale. 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 Hilbert-space dimension measured in qubit units. Identical degrees of freedom Scalable resource requirement Strictly scalable resource requirement qudits Hilbert space and physical resources Primary resource is Hilbert-space dimension. Hilbert-space dimension costs physical resources. Many degrees of freedom x3, p3 1 0 0 101 11 0 111 0 00 1 011 0 1 x 1 , p1 0 1 0 x 2 , p2 0 1 1 0 000 1 001 2 010 3 011 4 100 5 101 6 110 7 111 x, p Quantum computing in a single atom Characteristic scales are set by “atomic units” Length Momentum Action Energy Bohr Hilbert-space dimension up to n 3 degrees of freedom 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 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. Physical resources: classical vs. quantum Classical bit A few electrons on a capacitor A pit on a compact disk A classical bit involves many degrees of freedom. Our scaling analysis applies, but with a basic phase-space scale of arbitrarily small. Limit set by noise, not fundamental physics. A 0 or 1 on the printed page A smoke signal rising from a distant mesa The scale of irreducible resource Quantum bit requirements is always set by An electron spin in a semiconductor Planck’s constant. A flux quantum in a superconductor A photon of coupled ions Energy levels in an atom 0 1 Why Atomic Qubits? State Preparation • Initialization • Entropy Dump Laser cooling State Manipulation • Potentials/Traps • Control Fields • Particle Interactions Quantum Optics NMR State Readout • Quantum Jumps • State Tomography • Process Tomography Fluorescence Optical Lattices Designing Optical Lattices Tensor Polarizability P3/2 -3/ 2 -1/2 1 S1/2 1/2 1 3 2 3 1 U(x) - ij E i* (x)E j (x) 4 -1/2 2 3 3/2 1 1 ( ij - 0 2 d ij i e ijk s k ) 3 1/2 Effective scalar + Zeeman interaction U(x) U0 (x) - Beff (x) U0 (x) ~ E(x) 2 Beff (x) ~ i(E* E ) Lin--Lin Lattice e1 e2 -k k U 0 ~ E(x) ~ e1 e2 cos(2kz) cos cos(2kz) 2 Quic kTime™ and a Animation dec ompres sor are needed to see this picture. Beff ~ E (x) E(x) ~ e1 e2 sin( 2kz) sin sin( 2kz)e z * /3 /2 Multiparticle Control Controlled Collisions Dipole-Dipole Interactions • Resonant dipole-dipole interaction + - d V dd ~ 3 r 2 (Quasistatic potential) + - G tot G G dd 2G 2 d hG~ 3 D (Dicke Superradiant State) Figure of Merit 3 Vdd ~ G r Cooperative level shift Bare Coupled g1e2 g1g2 Eg g 1 2 e1e2 e1e2 e1e2 e1g2 Dressed Vdd D g1g2 g1g2 2 / 2 s (D - iG) sVd (D - Vdd (r ) / ) i(G Gdd (r )) / 2 Two Gaussian-Localized Atoms r12 Three-Level Atoms “Molecular” Spectrum Atomic Spectrum E 1 e 0 e d2 d1 D d3 d4 L 11 01 , 10 00 r Molecular Hyperfine “Molecular” Spectrum Atomic Spectrum 0.8 GHz F=2 F=1 F=2 F=1 5P1/2 1 1- 6.8 GHz 0 0 - 5S1/2 87Rb Brennen et al. PRA 65 022313 (2002) Controlled-Phase Gate Fidelity Figure of Merit: E11 E00 - 2E01 DEc hGij hGij Resolvability = Fidelity Controlled-Phase Gate Fidelity D/G (103 ) zo / F 0.05 D L 104 G I L 3.2 kW/cm 2 Dz/z0 DC D L F 0.99 I C 10I L Dz / z0 0.3 1 / 0.1( osc / 2 ) 144 kHz Leakage: Spin-Dipolar Interaction d1 d2 - 3(d1 er )(d2 er ) V r3 Noncentral force D(m f 1 m f 2 ) 0 azimuthally symmetric trap f 2,m f 1 f 2,m f -1 f 2,m f 0 f 2,m f 0 m f -1 mf 0 m f 1 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 H H1 H 2 Vint (r) H cm H rel prel 1 2 2 H rel r - Dr Vint (r) 2 2 4 2 (3) Vint (r) aeff dreg (r) m Short range interaction potential, well characterized by a hard-sphere scattering with an “effective scattering length”. Energy Spectrum aeff 0.5z0 0 5 4 E Energy 3 2 1 TextEnd 0 -1 -2 0 1 2 Separation Dz z0 3 4 5 Shape Resonance Quic kTime™ and a Animation dec ompres sor are needed to see this pic ture. 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)