implementation - qudev.phys.ethz.ch · qip ii : quantum algorithms with sc qubits | 4/7/17 | 2 §...
TRANSCRIPT
|| 4/7/17QIPII:QuantumalgorithmswithSCqubits 1
§ Introduction§ Superconductingqubits
§ Quantumalgorithms
§ Deutsch-Jozsa
§ Groversearch
§ Implementation§ Superconductingqubits
§ Properties
§ Methods
§ Modernalgorithmsandtheirimplementation
Outline
|| 4/7/17QIPII:QuantumalgorithmswithSCqubits 2
§ 1992, Deutsch-Jozsa [1] : solves a black-box problem which probably requiresexponentially many queries to the black box for any deterministic classical computer
§ 1993, Simon [2]: equivalent to [1] from another oracle
§ 1995, Shor [3]: solves the integer factorization problem, discrete log problem
§ 1997, Grover [4]: Quantum database search algorithm
§ 1998, Jones & Mosca [5]: First experimental demonstration of a quantum algorithm. Aworking 2-qubit NMR quantum computer used to solve Deutsch's problem
TimelineofQuantumAlgorithms
[1]Deutsch,D.andJozsa,R.(1992),ProceedingsoftheRoyalSocietyofLondonA(439-553)[2]Simon,D.R.(1995), FoundationsofComputerScience,1996,35th AnnualSymposium(116-123)[3]Shor,P.W.(1997),SIAMJournalonComputing26(1484-1509)[4]Grover,L.K.(1996),28th AnnualACMSymposiumontheTheoryofComputing(212)[5]Jones,J.A.et.al.(1998),Nature393(344-346)
|| 4/7/17QIPII:QuantumalgorithmswithSCqubits 3
§ Step-by-step procedure, where each of the steps can be performed on a QuantumComputer
§ Make use of quantum features such as superposition and entanglement
§ Can be based on quantum Fourier transform (Deutsch-Jozsa, Simon), amplitudeamplification (Grover), quantum walks (Triangle Finding Problem, Element DistinctnessProblem)
QuantumAlgorithms
|| 4/7/17QIPII:QuantumalgorithmswithSCqubits 4
§ Reducedsensitivitytochargenoise
§ IncreasesratioofJosephsonenergytochargingenergy,usingalargeshuntingcapacitor
§ Coherencetimes~𝜇𝑠
SuperconductingQubits:TheTransmon
*
*
*AdaptedfromQIPII‘17LectureNotes,foundinhttp://www.qudev.ethz.ch/content/QSIT14/QSITNotes.pdf (26Mar2017,9pm)
|| 4/7/17QIPII:QuantumalgorithmswithSCqubits 5
§ Task:Solveblackboxproblem
§ Deterministic:alwaysproducesasolution,andthesolutioniscorrect
§ Limitedpracticalapplicationbutshowsthatquantumcomputerscansolvesuchproblemswithnoerror
Deutsch-Jozsa Algorithm
Deutsch,D.andJozsa,R.(1992),ProceedingsoftheRoyalSocietyofLondonA(439-553)
|| 4/7/17QIPII:QuantumalgorithmswithSCqubits 6
§ Hadamard transformations on 𝑛 zeros,formingallpossibleinputs,andasingle1,whichwillbetheanswerqubit
§ Runthefunctiononce;thisXORstheresultwiththeanswerqubit
§ Hadamards onthe 𝑛 inputsagain,andmeasuretheanswerqubit
Deutsch-Jozsa Algorithm- Steps
Deutsch,D.andJozsa,R.(1992),ProceedingsoftheRoyalSocietyofLondonA(439-553)
|| 4/7/17QIPII:QuantumalgorithmswithSCqubits 7
§ Task:Inanunstructureddatabaseof𝑁 elements,retrievetheonethatsatisfiesagivencondition.
§ Classically𝑁/2itemshavetobequeriedonaverage,Grover’ssearchreducesthisto𝑁�
§ Thesecretliesinamplitudeamplification,whichboostsprobabilityoffindingcorrectstate
Grover’sAlgorithm
Grover,L.K.(1996),28th AnnualACMSymposiumontheTheoryofComputing(212)
|| 4/7/17QIP II : Quantum algorithms with SC qubits 8
§ StatePreparation:Qubitsareinitializedinasuperpositionstate
§ Applicationoftheoracle
§ Amplitudeamplificationbyinversionusingthediffusionoperator
§ Readout
Grover’sAlgorithm- Steps
Grover,L.K.(1996),28th AnnualACMSymposiumontheTheoryofComputing(212)
|| 4/7/17QIP II : Quantum algorithms with SC qubits 9
|| 4/7/17QIP II : Quantum algorithms with SC qubits 10
Detuned qubits:interactionsuppressedQubits resonant:virtual photonmediated interaction
ExperimentalImplementation
[6]L.DiCarlo etal.,Nature460,08121(2009);A.Blaisetal.,Phys.Rev.A75,032329(2007)
|| 4/7/17QIP II : Quantum algorithms with SC qubits 11
Criteriaforimplementingaquantumcomputer:#1.Ascalablephysicalsystemwithwell-characterizedqubits#2.Theabilitytoinitializethestateofthequbits#3.Long(relative)decoherence times,muchlongerthanthegate-operationtime#4.Auniversalsetofquantumgates#5.Aqubit-specificmeasurementcapability
Plustwocriteriarequiringthepossibilitytotransmitinformation:#6.Theabilitytointerconvertstationaryandmobile(orflying)qubits#7.Theabilitytofaithfullytransmitmobilequbitsbetweenspecifiedlocations
[6]DiVincenzo,D.P.(2000),ThePhysical Implementationof QuantumComputation,arXiv:quant-ph/000207
TheDiVincenzo criteria[6]
|| 4/7/17QIP II : Quantum algorithms with SC qubits 12
Single-qubit-Gates Two-qubit-Gates
𝑅,(𝜃) =cos(34) −sin(34)
sin(34) cos(34)
𝑅8(𝜃) = 𝑒:;<= 00 𝑒;
<=
U=
1 0 0 00 1 0 00 0 1 00 0 0 −1
PhaseGates
L.DiCarlo etal.,Nature460,08121(2009);A.Blaisetal.,Phys.Rev.A75,032329(2007)
|| 4/7/17QIP II : Quantum algorithms with SC qubits 13
Phaseshift (by changing 𝐕𝐫)
𝜙BC = 2𝜋F 𝛿𝑓BC 𝑡 𝑑𝑡K
KL
L.DiCarlo etal.,Nature460,08121(2009);A.Blaisetal.,Phys.Rev.A75,032329(2007)
|| 4/7/17QIP II : Quantum algorithms with SC qubits 14
Phaseshift (by changing 𝐕𝐫)
𝜙BC = 2𝜋F 𝛿𝑓BC 𝑡 𝑑𝑡K
KL
𝜙MM = 2𝜋F 𝛿𝑓MM 𝑡 𝑑𝑡K
KL
𝜙MN = 2𝜋F 𝛿𝑓MN 𝑡 𝑑𝑡K
KL
𝜙NM = 2𝜋F 𝛿𝑓NM 𝑡 𝑑𝑡K
KL
𝜙NN = 2𝜋F 𝛿𝑓NN 𝑡 𝑑𝑡K
KL
= 𝒏𝟏 ∗ 𝟐𝝅
= 𝒏𝟐 ∗ 𝟐𝝅
= 𝒏𝟑 ∗ 𝟐𝝅
= (𝟐𝒏𝟒 + 𝟏) ∗ 𝝅U=
1 0 0 00 1 0 00 0 1 00 0 0 −1
U=
𝑒;WLL 0 0 00 𝑒;WLX 0 00 0 𝑒;WXL 00 0 0 𝑒;WXX
1
DiCarlo etal.(2009),Nature460,08121;Blaisetal.(2007),Phys.Rev.A75,032329
|| 4/7/17QIP II : Quantum algorithms with SC qubits 15
Two – qubit Gates
𝜙BC = 2𝜋F 𝛿𝑓BC 𝑡 𝑑𝑡K
KL
𝑉Z𝑉
DiCarlo etal.(2009),Nature460,08121
|| 4/7/17QIP II : Quantum algorithms with SC qubits 16
Two – qubit Gates
DiCarlo,L.etal.(2009),Nature460,08121
𝑉Z𝑉
𝜙NN = 𝜙MN + 𝜙NM −F 𝜁 𝑡 𝑑𝑡K
KL
∫ 𝜁 𝑡 𝑑𝑡KKL
= 𝜋
|| 4/7/17QIP II : Quantum algorithms with SC qubits 17
𝜙NN = 𝜙MN + 𝜙NM −F 𝜁 𝑡 𝑑𝑡K
KL
∫ 𝜁 𝑡 𝑑𝑡KKL
= 𝜋
U =
1 0 0 00 𝑒;WLX 0 00 0 𝑒;WXL 00 0 0 𝑒;(WLX]WXL]^)
U =
1 0 0 00 1 0 00 0 1 00 0 0 −1
DiCarlo,L.etal.(2009),Nature460,08121
Two – qubit Gates
|| 4/7/17QIP II : Quantum algorithms with SC qubits 18
Parameter 2009 2017
# qubits available 2 5
Coherence time 𝜇 ~ 1 µs ~ 50 µs
Gate error rate ~ 1% ~ 0,3%
Readout error rate ~ 10% ~ 5%
Cloud connected ;) No Yes
From2007inYaletotoday’scloudresourceavailability!
|| 4/7/17QIP II : Quantum algorithms with SC qubits 19
Ø BQP (bounded-error quantum polynomial time) problems
Quantum Algorithm Zoo* : http://math.nist.gov/quantum/zoo/
Current Research for Algorithms for Quantum Computation
*USA National Institute of Standards and Technology
|| 4/7/17QIP II : Quantum algorithms with SC qubits 20
• Hybrid Quantum – Classic approach algorithm
• Used for Quantum Simulation Problems
• Calculation on a quantum computer
• Optimization on a classic CPU
Nature Communications 5,4213 (2014) , doi:10.1038/ncomms5213
Variational Quantum Eigensolver (VQE) Algorithm
|| 4/7/17QIP II : Quantum algorithms with SC qubits 21
VQE Example – Hydrogen Molecule
O’Malley,P.J.J.etal.(2016),PRX6,031007
𝐻 = 𝑔M + 𝑔N𝑍M + 𝑔4𝑍N + 𝑔c𝑍M𝑍N + 𝑔d𝑌M𝑌N + 𝑔f𝑋M𝑋N
|| 4/7/17QIP II : Quantum algorithms with SC qubits 22
IBMQuantumExperience
program 5 qubits
from yoursmartphone
Implementing a Quantum Algorithm in the cloud
https://quantumexperience.ng.bluemix.net/
|| 4/7/17QIP II : Quantum algorithms with SC qubits 23
• Eachqubitcanbereadoutindividually
Physical Layout of the QX chip
|| 4/7/17QIP II : Quantum algorithms with SC qubits 24
Physical Layout of the QX chip – Properties
|| 4/7/17QIP II : Quantum algorithms with SC qubits 25
Id0
1
Quantum Experience set of gates
and
Corresponding measurements
O’Malley,P.J.J.etal.(2016),PRX6,031007
Hydrogen Molecule - VQE Implementation
|| 4/7/17QIP II : Quantum algorithms with SC qubits 26
HamiltonianofthemolecularHydrogen
Simulation and Realistic Results
|| 4/7/17QIP II : Quantum algorithms with SC qubits 27https://quantumexperience.ng.bluemix.net/qstage/#/community/question?questionId=ab63d741626debb659994ebedd3f6e80
The first game in a quantum computer…
Decodoku Project : Gaming for science!
||
10 mK
100mK
700mK
4 K
50 K
Arbitrary WaveformGenerators
Inside a QC fridge!
||
Inside a QC fridge!
||
Inside a QC fridge!
||
Andreas Woitzik
Khandelwal Shishir
Panagiotis Barkoutsos
Thanks for your attention!