1. Ion Trap Quantum Computer

2. Two Level Atom as a qubit Electron on lower orbit Electron on higher orbit

3. Ion Trap Quantum Computer

4. Ion Traps Ions in a radio frequency trap interact by exchanging vibrational excitations. Each ion can be controlled by a polarized, properly focused laser beam.Ions in a radio frequency trap interact by exchanging vibrational excitations. Each ion can be controlled by a polarized, properly focused laser beam. Picture shows the electrode structure.Picture shows the electrode structure. The electrode is 1mm thick.The electrode is 1mm thick. Linear ion trap

5. Linear ion trap computer ion Laser pulses electrodes Research in NIST

7. Quantum CNOT gate on beril ion in the trap Linear ion trap

13. Silicon Based Quantum Computer

14. Optical Quantum Computer

16. What about scaling? 1-7 qubits using NMR technology1-7 qubits using NMR technology 1-2 qubits using ion traps1-2 qubits using ion traps 1-2 qubits using various other quantum technologies1-2 qubits using various other quantum technologies Scaling is very hard!Scaling is very hard! Is the problem technical or fundamental?Is the problem technical or fundamental?

17. Technical or Fundamental? Noise, “decoherence”, imprecision are detrimentalNoise, “decoherence”, imprecision are detrimental Similar problems exist in “classical” systemsSimilar problems exist in “classical” systems Theory of linear error correction and fault tolerant computing can be generalised to the quantum setting (Shor, Steane, etc.)Theory of linear error correction and fault tolerant computing can be generalised to the quantum setting (Shor, Steane, etc.) Using “reasonable” physical models, there exist fault-tolerant schemes for scalable quantum computingUsing “reasonable” physical models, there exist fault-tolerant schemes for scalable quantum computing

18. Quantum Circuits Quantum Error-Correction Circuit Problem: State |  = a|0  + b |1  is degraded by noiseProblem: State |  = a|0  + b |1  is degraded by noise Solution Encode in a suitable EC code such as the 5-bit code:Solution Encode in a suitable EC code such as the 5-bit code: |0  = |00000  + |11000  + |01100  + |00110  + |00011  + |10001  – |10100  – |01010  – |00000  – |10010  – |01001  – |11110  – |01111  – |10111  – |11011  – |11101  |1  = |11111  + |00111  + |10011  + …

19. Summary

20. Summary Quantum Computers are a natural generalisation of “classical” computersQuantum Computers are a natural generalisation of “classical” computers Quantum algorithms: Factoring, Discrete log, Hidden Subgroup, Hidden Affine Functions, Searching, CountingQuantum algorithms: Factoring, Discrete log, Hidden Subgroup, Hidden Affine Functions, Searching, Counting Small implementations existSmall implementations exist Scaling is difficult, but seems to be a technological (not fundamental) problemScaling is difficult, but seems to be a technological (not fundamental) problem

21. References 1: Chuang, Issac and Gershenfeld, Neil; “Quantum Computing With Molecules”; Scientific American: June 1998.1: Chuang, Issac and Gershenfeld, Neil; “Quantum Computing With Molecules”; Scientific American: June 1998. 2: Hey, Anthony; Possible Technologies for Quantum Computers; May 1998; http://www.ecs.soton.ac.uk/~ajgh/quantrep.html2: Hey, Anthony; Possible Technologies for Quantum Computers; May 1998; http://www.ecs.soton.ac.uk/~ajgh/quantrep.html http://www.ecs.soton.ac.uk/~ajgh/quantrep.html 3: Nuclear Magnetic Resonace Quantum Computers; http://www.qubit.org/research/NMR/index.html;3: Nuclear Magnetic Resonace Quantum Computers; http://www.qubit.org/research/NMR/index.html; http://www.qubit.org/research/NMR/index.html Mar 2001. 4: Quantum Computing Experiment At Los Alamos; http://p23.lanl.gov/Quantum?qcexper.html;4: Quantum Computing Experiment At Los Alamos; http://p23.lanl.gov/Quantum?qcexper.html; http://p23.lanl.gov/Quantum?qcexper.html Jan 2001. 5: QUIC Milestones; http://theory.caltech.edu/~quic/milestones.html;5: QUIC Milestones; http://theory.caltech.edu/~quic/milestones.html;http://theory.caltech.edu/~quic/milestones.html Mar 2001. 6: Simple Quantum Gates; http:/www.qubit.org/intros/comp/inset2.html;6: Simple Quantum Gates; http:/www.qubit.org/intros/comp/inset2.html; Mar 2001. 7: Waldtrop, M; “Quantum Computing”; Technology Review; May/June 2000.7: Waldtrop, M; “Quantum Computing”; Technology Review; May/June 2000.

22. Five-qubit computer (contd.)Five-qubit computer (contd.) –Molecule with 5 flourine atoms whose spins implement the qubits –Experimental 5-qubit circuit to find the order of a permutation Physical Implementation: NMR measurements Quantum Fourier Transform