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Quantum Information: From Optics to the Real World

Learn about the exciting field of quantum information and its applications in the real world. Topics covered include quantum foundations, nonlinear optics, quantum computation, quantum communication, and quantum metrology.

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Quantum Information: From Optics to the Real World

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  1. Quantum information: from the optics laboratory to the “real” world Kevin Resch IQC, Dept. of Physics University of Waterloo

  2. Institute for Quantum Computing • 14 faculty • 6 post-docs • ~50 students Always looking for more! Founded 2001 at University of Waterloo Waterloo, Ontario http://www.iqc.ca/

  3. Optical quantum information Talk Outline Quantum Information Quantum Foundations Nonlinear Optics Quantum Computation Quantum Communication Quantum Metrology Free-space entanglement distribution Entanglement Purification Measurement-induced nonlinearity Interference-enhanced nonlinearity One-way quantum computation Linear optics entangling gates Classical analogues of quantum interference Tomography Weak measurement Multipartite entanglement Nonlocality tests

  4. Quantum information Quantum bits can be 0 or 1 but also superpositions bit: 0 or 1 qubit: |0 + |1 |1 = |V |1 |0 |0 = |H Atomic Levels Photon Polarization

  5. Familiar quantum features Uncertainty principle W. Heisenberg Position Momentum No-cloning theorem Dieks Wootters Zurek

  6. …leads to ultimate cryptosystem “X” “P” An eavesdropper must make measurements to learn about the state, but cannot do so without disturbance (HUP) Attemptingeither strategy will lead to errors in the detected signal Single photons are sent in one of two noncommuting basis states Nor can the eavesdropper make identical copies of the state and make measurements on them (no-cloning) C. Bennett, G. Brassard 1984

  7. More quantum features • Superposition • A quantum system can be in many states at the same time Interference

  8. …more powerful computers ψ Measurement results are random, except that interference (+clever algorithms) can reduce wrong answers A computer takes some input state to an output state A Quantum computer takes a superposition of all possible inputs state to a superposition of all possible output states Feynman Deutsch

  9. Entanglement • Separable states (not entangled) An entangled state “Bell state” Foundation for most quantum information protocols

  10. t t t2 t1 |D> |R> Optical photons as qubits Spatial modes • Polarization i = + |V> |H> Time-bin Freq. encoding

  11. Optical photons as qubits The Ugly The Bad The Good • Single-qubit operations • Low decoherence • High speed • Perfect carriers of quantum information Easy to lose a photon No natural interactions/weak nonlinearities means 2-qubit operations are hard Linear optics proposals for scalable quantum computing are extremely complicated (~50-1000s of ancillas/elements per CNOT)

  12. Entangled Photon Source Parametric Down-conversion “blue” photon two “red” photons c(2) wpump=ws + wi Phase matching: kpump=ks + ki

  13. Entangled Pair H-Photon Confused Correlated V-Photon Type-II Down-conversion

  14. Recent source advancements • High-power UV laser diodes (cheap, easy to use -> UG lab!) • Efficient single-mode coupling (long-distance, low divergence, free-space) • 4-, 5-, and 6-photon entanglement • Controllable entanglement – fundamental tests and quantum computing

  15. Number of photons entangled Entangling measurements Source Brightness Downconversion Atomic Cascade State of the art

  16. Long-distance Entanglement distribution Quantum source

  17. Not Pictured here: FS1&2: Michael Taraba FS2: Bibiane Blauensteiner, Alessandro Fedrizzi, Christian Kurtsiefer, Tobias Schmitt-Manderbach, Henning Weier, Harald Weinfurter Zeilinger Group

  18. Distributing Entanglement • Photons are the ideal carriers • Practical quantum communication needs shared entanglement over long distances • Challenges: High efficiency (no cloning) and high background rejection (single photons)

  19. Entanglement takes to the air 500m 150m Donau (Danube)

  20. Quantum correlations • A “Bell experiment” • Local properties (ex. A=+1, A’=-1, B=+1, B’=+1) A(B+B’)+A’(B-B’) = ±2 • CHSH-Bell inequality (req. 16 measurements) S = |<AB+AB’+A’B-A’B’>| ≤ 2 • QM allows S = 2√2 = 2.83 +1 +1 -1 -1 Source Set {A, A’} Set {B, B’}

  21. Freespace 1 Results Measured S = 2.4 ± 0.1 (larger than 2 indicates entanglement) • Two links 500m & 100m • ~10 coincidences/s • SMF-SMF coupling • Time-stable channel Polarization correlations Science (2003)

  22. The next step • 500m to 7.8km (the atmosphere straight up is 7.3km thick) • No more cable • Light passed over a city – likely real-world scenario

  23. Source telescope From Source 15cm

  24. Receiver/Movie Test Range Laser source FS1 Atmospheric fluctuations 4 km

  25. H V PBS -45o λ/2 45o PBS 50/50 To detector Receiver module

  26. UV BBO Practicalities • Absence of good single-photon sources • Can use quantum randomness to select state: • Triggered single photons, reduced “empty” pulses |0> and double photons |2> • Laser frequency monitoring unnecessary PBS 45/-45 Alice HWP BS -45 PBS (HV) 45 V H

  27. Entanglement takes to the air – again! Freespace 2 7.8km

  28. HWPs BOB ALICE PBS Pol. B 45 BS DC Free-space (Quantum Channel) A V 135 PBS HWP PBS H Pol. 45 Time-tagging BS V 135 PBS H GPS Rb-clock Time-tagging GPS, Rb clock Public Internet (Classical Channel) V I E N N A ALICE 7.8km BOB

  29. Freespace 2 Results S = 2.27±0.019 > 2 Quantum Correlations! Two links 7.8 km and 10-4km 25 ccps found over time tags/internet Single-mode fibre to spatial-filter coupling 14-σ Bell violation, all 16 meas. taken simultaneously Optics Express (2005)

  30. Remaining challenges • Longer distances, Higher bit rates • Active components to compensate atmosphere • Long-distance quantum interference (repeaters) • Full cryptography, different protocols • Moving targets (satellites, airplanes)

  31. IQC free-space experiment • Gregor Weihs • Raymond Laflamme • Chris Erven

  32. One-way quantum computation with a multi-photon cluster state “1”

  33. Photonic one-way quantum computation Philip Walther (ViennaHarvard) Terry Rudolph (Imperial) Emmanuel Schenck (ViennaENS) Vlatko Vedral (Leeds) Markus Aspelmeyer (Vienna) Harald Weinfurter (LMU, Munich) Anton Zeilinger (Vienna)

  34. Readout (measure final qubits) Initialization (prepare a “cluster state”) Algorithm (single-qubit measurements) Readout (classical bits) Algorithm (dynamics) Initialization (all qubits |0) QC - Circuit vs. One-way model One-way model Circuit Model “1” |0 Unitary “1” |0 “0” |0 “1” |0 H X Physical qubit Raussendorff & Briegel, PRL 86, 5188 (2001) Optics: Neilsen; Browne/Rudolph

  35. 00 01 10 11 00 01 10 -11 |+ |+ |+ |+ One-way quantum computing • Cluster states can be represented by graphs Entanglement “bond” CPHASE |+ |+

  36. |ψ> |+> If “0”, do nothing If “1”, apply NOT (bit flip) This is an example of Feed-forward 2 0 1 1 2 Qubit 2 is HRz(α)|ψ> 2 Form a cluster state 1 2 Measure Qubit 1 in B(α) B(α) = {|0 + eiα|1, |0 - eiα|1} 2 Processing encoded information • How measurement can compute Equivalent quantum circuit Rz(α) H |ψ>

  37. More general computations Number of operations Readout Number of encoded qubits

  38. Making cluster states |ψ> = |HHHH>+|HHVV> +|VVHH>-|VVVV>

  39. V V V H H H Polarizing Beam-splitter • Quantum “parity check” V polarization H polarization

  40. The four-photon cluster Quantum state tomography Reconstructed density matrix Fidelity = 63%

  41. Clusters to circuits • Horizontal bond: Rz(-a) H 1:B(a) Vertical bond: 1:B(a) Rz(-a) H Rz(-b) H 2:B(b)

  42. Clusters to circuits One-qubit computations • Multiple circuits using a single cluster • Different order of measurements Two-qubit computations

  43. Single & two-qubit operation Two-qubit operations Single-qubit rotations Separable Entangled Fid ~ 83-86% Fid = 93% Tangle = 0 Fid = 84% Tangle = 0.65

  44. Grover’s Algorithm Hard Easy Best Classical: O(N) queries Quantum: O(√N) queries Sorted database Unsorted database L.K. Grover, Phys. Rev. Lett.79, 325-328 (1997).

  45. Conclusions and Future directions • First demonstration of one-way quantum computation using cluster states • Experimental • Larger cluster states = more complex circuits • Feed-forward – two types – easy and hard • Theoretical • Different geometries and measurements • Higher dimensions

  46. Summary • “Real” world • First experiments demonstrating free-space entanglement distribution • Ideal world • First demonstration of Cluster State Quantum Computing – including the first algorithm

  47. Clusters/Grover’s Algorithm 90% correct computational output First algorithm in the cluster model

  48. Mean Grover’s algorithm Interference “Inversion about the mean” amplifies the correct element and reduces the others • Quantum parallelism • GA initializes the qubits to equal superposition of all possible inputs On a query to the black box (quantum database/phonebook), the sign of the amplitude of the special element is flipped Ampl 000 100 111 Element

  49. THANK YOU!

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