Ion Trap Quantum ComputerIon Trap Quantum Computer

Two Level Atom as a qubitTwo Level Atom as a qubitElectron on lower orbit

Electron on higher orbit

Ion Trap Quantum Ion Trap Quantum ComputerComputer

Ion TrapsIon Traps

• Ions Ions in a radio frequency in a radio frequency trap trap interactinteract by exchanging by exchanging vibrational excitations. vibrational excitations. Each ion can be Each ion can be controlledcontrolled by a polarized, properly by a polarized, properly focused laser beamfocused laser beam..

• Picture shows the electrode Picture shows the electrode structure.structure.

• The electrode is 1mm The electrode is 1mm thick.thick.

Linear ion trapLinear ion trap

Linear ion trap computerLinear ion trap computer

ion

Laser pulses

electrodes

Research in NIST

Quantum CNOT gate on beril ion in the trapQuantum CNOT gate on beril ion in the trap

Linear ion trapLinear ion trap

Silicon Based Quantum ComputerSilicon Based Quantum Computer

Optical Quantum Optical Quantum ComputerComputer

What about scaling?What about scaling?• 1-7 qubits using NMR 1-7 qubits using NMR

technologytechnology• 1-2 qubits using ion traps1-2 qubits using ion traps• 1-2 qubits using various other 1-2 qubits using various other

quantum technologiesquantum technologies• Scaling is very hard!Scaling is very hard!• Is the problem technical or Is the problem technical or

fundamental?fundamental?

Technical or Fundamental?Technical or Fundamental?

• Noise, “decoherence”, imprecision are Noise, “decoherence”, imprecision are detrimentaldetrimental

• Similar problems exist in “classical” Similar problems exist in “classical” systemssystems

• Theory of Theory of linear error correctionlinear error correction and and fault fault tolerant computingtolerant computing can be generalised to can be generalised to the quantum setting (Shor, Steane, etc.)the quantum setting (Shor, Steane, etc.)

• Using Using “reasonable” physical“reasonable” physical modelsmodels, , there exist fault-tolerant schemes for there exist fault-tolerant schemes for scalablescalable quantum computing quantum computing

Quantum CircuitsQuantum CircuitsQuantum Quantum Error-CorrectionError-Correction Circuit Circuit• ProblemProblem: State |: State | = = aa|0|0 + + b b |1|1 is degraded by noise is degraded by noise

• SolutionSolution Encode in a suitable EC code such as the 5-bit code: Encode in a suitable EC code such as the 5-bit code:|0|0 = |00000 = |00000 + |11000 + |11000 + |01100 + |01100 + |00110 + |00110 + |00011 + |00011 + |10001 + |10001 – |10100– |10100 – |01010 – |01010 – |00000 – |00000 – |10010 – |10010 – |01001 – |01001 – – |11110|11110 – |01111 – |01111 – |10111 – |10111 – |11011 – |11011 – |11101 – |11101 |1|1 = = |11111|11111 + |00111 + |00111 + |10011 + |10011 + … + …

SummarySummary

SummarySummary

• Quantum Computers are a natural Quantum Computers are a natural generalisation of “classical” computersgeneralisation of “classical” computers

• Quantum algorithmsQuantum algorithms: Factoring, Discrete : Factoring, Discrete log, Hidden Subgroup, Hidden Affine log, Hidden Subgroup, Hidden Affine Functions, Searching, CountingFunctions, Searching, Counting

• Small implementations existSmall implementations exist• Scaling is difficult, but Scaling is difficult, but seemsseems to be a to be a

technological (technological (not fundamentalnot fundamental) problem) problem

ReferencesReferences

• 1: Chuang, Issac and Gershenfeld, Neil; “Quantum Computing With 1: Chuang, Issac and Gershenfeld, Neil; “Quantum Computing With Molecules”; Molecules”; Scientific AmericanScientific American: June 1998.: June 1998.

• 2: Hey, Anthony; 2: Hey, Anthony; Possible Technologies for Quantum ComputersPossible Technologies for Quantum Computers; May 1998; ; May 1998; http://www.ecs.soton.ac.uk/~ajgh/quantrep.htmlhttp://www.ecs.soton.ac.uk/~ajgh/quantrep.html

• 3: 3: Nuclear Magnetic Resonace Quantum ComputersNuclear Magnetic Resonace Quantum Computers; ; http://www.qubit.org/research/NMR/index.htmlhttp://www.qubit.org/research/NMR/index.html;;Mar 2001.Mar 2001.

• 4: 4: Quantum Computing Experiment At Los AlamosQuantum Computing Experiment At Los Alamos; ; http://p23.lanl.gov/Quantum?qcexper.htmlhttp://p23.lanl.gov/Quantum?qcexper.html; ; Jan 2001.Jan 2001.

• 5: 5: QUIC MilestonesQUIC Milestones; ; http://theory.caltech.edu/~quic/milestones.htmlhttp://theory.caltech.edu/~quic/milestones.html;;Mar 2001.Mar 2001.

• 6: 6: Simple Quantum GatesSimple Quantum Gates; http:/www.qubit.org/intros/comp/inset2.html; ; http:/www.qubit.org/intros/comp/inset2.html; Mar 2001.Mar 2001.

• 7: Waldtrop, M; “Quantum Computing”; 7: Waldtrop, M; “Quantum Computing”; Technology ReviewTechnology Review; May/June 2000.; May/June 2000.

• Five-qubitFive-qubit computer (contd.) computer (contd.)– Molecule with Molecule with 5 flourine atoms5 flourine atoms

whose whose spinsspins implement the implement the qubitsqubits– Experimental 5-qubit circuit to find Experimental 5-qubit circuit to find

the the order of a permutationorder of a permutation

Physical Implementation: NMRPhysical Implementation: NMR

measurements

Quantum Fourier

Transform