Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Slide 29Slide 30Slide 31Slide 32Slide 33Slide 34Slide 35Slide 36Slide 37Slide 38Slide 39Slide 40Slide 41Slide 42Slide 43Slide 44Slide 45Slide 46Slide 47Slide 48Slide 49Slide 50Slide 51Slide 52Slide 53Slide 54Slide 55Slide 56Slide 57Slide 58Slide 59Slide 60Slide 61Slide 62CSEP 590tv: Quantum ComputingDave BaconAug 17, 2005Today’s MenuQuantum Computing implementationsQuantum Error CorrectionQuantum CryptographyQuantum Information and Black Holes…AdministriviaTurn in the take home final. Let out a deep breath.If you are taking the 1 week extension which is an extension to Monday, please let me know via email.Fill out course evaluations at end of class.But What Will It Look Like?Solid StateAtomicMolecularPhoton Basedsuperconducting circuitselectron spin in Phosphorus doped Siliconquantum dotsdefects in diamondscavity QEDneutral atoms in optical latticesion trapslinear optics plus single photon devicesLiquid NMR (no longer?) Pics: Mabuchi (Caltech), Orlando (MIT)DiVincenzo’s CriteriaDavid DiVincenzo1. Well defined qubits in a scalable architecture2. The ability to initialize the system to a fixed wave function.3. Have faster control over the system than error processes in the system.4. Have the ability to perform a universal set of quantum gates.5. Have the ability to perform high quality measurementsIon Trap2 9Be+ Ions in an Ion Trap Oscillating electricfields trap ionslike charges repelWhere’s the Qubit?EnergyorbitalsEach ion = 1 qubit1. Well defined qubits Scalable?. Well defined qubits in a scalable architectureSolid state qubits seem to have a huge advantage for scalability.MeasurementEnergylaserdecayDetecting florescence implies in state 0 99.99% efficiency5. Have the ability to perform high quality measurements Single Qubit OperationsEnergyLaser 1Laser 2Allows any one qubit unitary operationsInitializationlaserdecayLaser 1Laser 2measureIf not in zero state, flip2. The ability to initial the system to a deterministic state. Universal Computers1. Turing machine reads state of tape at current position.2. Based on this reading and state of machine, Turing machine writes new symbol at current position and possibly moves left or right.Certain Turing machines can perform certain tasks.A Universal Turing Machine can act like any other possible Turing machine (i.e. it is programmable)Universal Quantum ComputerU(2)Universal Quantum Computer•a quantum computer which can be programmed to perform any algorithmic manipulation on quantum information.Set of Universal Quantum Gates•a set of operations/gates which, acting on the quantum information, can be used to implement (to any desired accuracy) any unitary evolution of the quantum info.The Royal King and Queen of Universal Quantum GatesCNOT and 1-qubit rotationsstationaryCoupling Two Qubitssloshing modeThese modes can be used as a bus between the qubits.4. Have the ability to perform a universal set of quantum gates What is the Problem?Real quantum systems are open quantum systems!systemenvironmentQuantum systems readily couple to an environment… System decoheres:qubits01bits50% 0 50% 1The Decoherence Problem (1996)Quantum Classical3. Have faster control over the system than error processes in the system.The ProblemDecoherence is a lot like classical noise, BUT:Yingyang of quantum computingStrong coupling to environment causes decoherenceStrong coupling to control devices needed to enactcomputationsQuantum Computing is BunkWays Quantum Computers Fail to Quantum ComputeQuantum Computing Disappearing Actqubits disappear (leakage of computing states)Lack of Unitary Controlattempting to apply unitary evolution U instead results in Vor (worse) results in non-unitary evolutionDecoherence Measurements are faultymeasurement result is noisy, incorrect result obtainedThe Quantum Solution (1995-96)Threshold Theorem:Error RateQCIon Trap ParametersDecoherence rate for qubits: 1 minutesGate speed: 10 microsecondsDecoherence rate for bus: 100 microseconds to 100 millisecondsMeasurement errors: 0.01%3. Have faster control over the system than error processes in the system. State of the ArtNIST BoulderA Critical GhostAll papers on quantum computing should carry a footnote: “This proposal, like all proposals for quantum computation, relies on speculative technology, does not in its current form take into account all possible sources of noise, unreliability and manufacturing error, and probably will not work.”Rolf Landauer IBMNature abhors a quantum computer?•Maintenance of giganto-coherence?•Faulty quantum gates?•Do we understand the physics of quantum errors in the system?Analog ComputersCompute by adding, multiplying real infinite precision numbers.This can be used to solve NP complete problems in polynomialtime!This, however is NOT a realistic model of computation.Why? Infinite precision is requires, as far as we know, infiniteresources! Noise destroys the speedup.Is quantum computing an analog computer? The resolution of this is the subject of quantum error correction.Don’t Eat That Appleplus: simpleminus: unrealisticplus: essential ideasLucifer’s channel:IdentityThe Story of the GhostRolf Landauer IBMYou are protecting your quantum information against a crazy noise model! Z1Z2? If this is all nature can throw at you, then pigs can fly.Noisy Cell PhoneHello? Hello? Hello? Hello?I have a flat tire. I said, I have a flat tire! A flat tire.No, I’m not trying to flatter you..No, you’re not getting fatter. I have a flat tire! Communication over a noisy CHANNEL can be overcome viaENCODING“Hello?” = “Hello? Hello? Hello? Hello?” [using redundancy to encode “Hello”]Simple Repetition Code0101Binary Symmetric Channelpp1 p1 pbNo encoding:Probability of error = pmeasureencodeb b b bEncoding (n=3): measuredecodeand correctProbability of errorEncode:n copies1994 Reasons to be a PessimistMeasurement destroys coherence:How can one decode without destroying the information?No cloning:Quantum Cloning Machine“A single quantum cannot be cloned,” Wootters and Zurek, Nature, 1982No quantum repetition code:Unrealistic Realistic Channel0 000, 1 111WWCCD? (What Would Classical Coders Do?)00bbbbmeasureencode decodeerror fix100 111101 110
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