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This 4 page Class Notes was uploaded by Ransom Blanda on Monday October 19, 2015. The Class Notes belongs to CSCI 4967 at Rensselaer Polytechnic Institute taught by Staff in Fall. Since its upload, it has received 26 views. For similar materials see /class/224851/csci-4967-rensselaer-polytechnic-institute in ComputerScienence at Rensselaer Polytechnic Institute.
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Date Created: 10/19/15
Quantum Computationquot Lecture 7 Quantum Circuits 1 Notes taken by David Cerna October 31 2007 Summary This lecture was on the following topics i Quantum Finite Automata ii Fundamental Difference in Computation iii Models of Quantum Computation iV Quantum circuit model Topic 1 In this topic we went over how to show a normal automata using matrices Then how to show a probalistic automata the same way This lead into the quantum automata Topic 2 and 3 This was a basic overveiw of the Church Turing Deutsch theorem and The classical models of computa tion brought to quantum light Topic 4 This last topic dives into quantum circuitry which we only brie y talked about a couple of weeks earlier Such topics that were coved were the controllednot get the toffoli gate and removing garbadge also known as noise from a quantum circuit system 1 Quantum nite automata 11 How to put a automata in matrices we could represent an automata with matrices by representing a step with a matrix such as 10 00 Malollel11l The 2 matrices show the acceptance of values A and B in picture As you can see a DFA when put in this form is a matrix of size N IN were N is the number of nodes in the DFA The columns have to be unit vectors This stems from computation theory where the DFA needs a transition for every imput value 12 Nondeterministic DFA These types of automata are the same as DFA without unit vector columns Also as we saw with the last model DFAs we could only have one path per value In a NFA the paths per value can be anything such as this matrix 1 M l21 Lecture Notes for a course given by Stephen F Bush at RPI mu Ammmwmwmmmmcmmgmanm s Mmmmwgqmmmmzpmsmmun Mn 9 Imam m Mzkingkhng pmhl39micwikhNFAs Eweweww mmmv usmmmsy cmmmmwm haymm Examp n M 5 2 5 a mem yumamuspnmmhwzceyedwmzymu swsemxtau nwm mummummsmm a gawmwywmmmwmmmwmkssm Ammuxsnmm mhtw mum ammm mm 4 M Human mm mmymmehuwaen kqmmvemm MWAxsmm kqummmmmmnmmxwe 9r kwmsammmmnsamxs shk mmmmmwm ammxsmmmmaingmwmwk a z J waqmsmww mw immunng z mammal Difference in Computation u Churchhiring mi ammmssmymmmmmmm 22 mth up Cm wejmy m elmch mngmzr mm mm H was mm m yum2 mqm mmms n my mmMmmmmx m m mma m m m Mm gmmm mammwmk mumsmnmxgmubwgmm 23 ChurchThringDeutsch principle Any physical procress can be represented on a quantum computer The idea is to get to the ChurchTuringDeutsch principle through the laws of physics This has not been done yet an excellent research project 24 Quantum models of computation The rst model that was derived was the quantum turing machine Which is much like the normal turing machine The more covenient model is the quantum circuit model Which is What the next section is on 3 Quantum circuits To the 2 circuit models classical and is the chart 31 quantum logic gates Here are the different types of quantum logic gates pauli gates l 0 0 7239 l 0 Xeio liefiz oiXeio all Hadamard Gate Puts the qubits into the bell basis i0gti1gt i0gtiilgt Hi0gt7Hi1gtT l 0 7 mboxH 7 0 1 phase gate P0gt0gt P1gti1gt l 0 io 2 i controllednot gate 0 c OCH 0 0 l 0 0 0 0 l 0 0 l 0 controlledphase gate and toffoli gate The controll phase gate is simple if the control bit is a zero then it is the I gate and if control bit is an one then it is the Z gate The control phase gate is really just the Z gate is t A 71 c t The toffoli gate is like the controllednot gate except it has 2 control bits and it only ips the nal bit When both of the prior bits are ones So it is a controlledcontrollednot gate using all the gates named here we can make classical computer circuits in a quantum computer The quantum circuits also give us the added reversablity and garbadge collection to clean up the channels
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