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Experimental quantum information processing - the of the art
Nadav Katz
A biased progress report
Contact: [email protected] 02-6584133
Quantum computation workshop, Jan. 2015
• What is a quantum information and why do we want to
process it?
• Different models – gates, cluster, adiabatic, topological.
• Different realizations – photons, atoms, ions, semi-
conductors and superconductors.
•Outlook and future directions
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Motivation
Single atom decays – cat dies!
2
&
Wait forone half-life
We NEVER see such macroscopic superpositions – why?
Dual/related problem (Feynman): exponential computational overhead for simulating many-body quantum systems
Quantum Information Processing –• Practical advantages over classical info. ($$)• Relates to quantum phase transitions and computation complexity • How big a Schrödinger kitten can we build?
Aristotle: Nature abhors a vacuumcoherenceSchrödinger:
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Some comments about QC
It is mainstream physics to assume it is possible with established error-correction codes (is nature malicious/ingenious?)
Failure actually implies fundamentally new physics regarding decoherence(no evidence for this in known physics)
QC is not magic:General/Generic unitary evolution of a many-body is still
exponentially hard to simulateIn the presence of symmetry and structure, sometimes dramatic
speedup is predicted
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• Classical bit: definite 0 or 1
+ 5V
Vout
Transistor Logic:0 = 0 volts1 = 5 volts
2
10
Storage of Information: Bits
• Quantum bits: superpose 0 or 1 H atomwavefunctions: 0
1Example:
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Bloch representation
Control: resonant (or close to resonant) pulses can be visualized as a rotation!
Geometrical picture:Useful for any two-level system
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Qubit Characterization
T2 ~350ns
Meas.time
T1 ~450ns
0 100 200 300 400 500 600
time [ns]
T~100ns
Rabi
time
x/2
time
x/2
x/2 x/2y
Ramsey
Echo
time
xlifetime
P1
0
1
1
011
01
0
Data from 2007…
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Entanglement
• Require 2N complex numbers to specify a general N-qubit state!
• Many (most actually) such states are not separable = entangled
Qubit 1 Qubit 2 Qubit 3 Qubit 4
Classic 2-qubit example: Bell state
2
1001
Such (anti-)correlations are normally generated by interactions (gates).
Resource for secure communication (not discussed)
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Gate model (DiVincenzo criteria)
Classical Computation:
not
and
Quantum Computation:
• Initialize state Yi = |000..0>
• Logic via series of operations: State Manipulation (1 qubit)
Controlled not (2 qubit)
• Final state measurement Measure qubits of state Yf
• Coherence: tcoherence / tlogic ~ number logic operations > 102 for error correction
} + linearsuperposition
controlbit
• Initialize state
• Logic
• Output result
• Logic errors: Error correction possible
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Need to be clever
When we measure – we want to see something interesting (and not some random, useless state out of 2N)…
•Deutsch-Josza’s algorithm – find the parity of a function (exponentially fast!)
•Shore’s algorithm – find the prime factors of a number (exponentially fast!)
•Grover’s algorithm – check if a database contains an element (poly-faster)
•These are famous, but there are some more (Eigenvalue estimation, random walk, Boson sampling hidden subgroup)…
Well-known quantum computing algorithms:
IMPORTANT: Error correction can make it work even if gates are not perfect!
(Shor+many others…)
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Qubit progress
Remarkable progress of the past 15 yearsAlready passed the fault tolerant threshold
From Devoret and Schoelkopf, Science (2013)
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Alternative computational models
Cluster states
Single photons
Adiabatic
Topological
All are theoretically equivalent – but experimentally VERY different…
Briegel & Raussendorf (2001)
Farhi (2001)
Kitaev (1997)
Exponentially degenerateground state (phases) withlarge gap. Braiding particlesevolves the state.
Generate a massively entangled initial state (c-not gates betweennodes in graph, compute by measuring in a specific order)
Knill, Leflamme, Milburn (2001)
Using single photons (if you have them!) and linear optics – Scalable QIP is possible!
D-wave (??)
Slowly evolve the Hamiltonian to remain in the ground state
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Experimental Quantum Information Processing (QIP)a perplexing flora and fauna of different systems
NMR
Quantum optics
Trapped ions
Neutral atoms
Josephson superconducting qubits
Quantum dots
??
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Experimental QIP – a guide for the perplexed
Smaller
IonsNeutral AtomsNMR
Semiconductor SpinsQuantum Dots and defects
Superconducting Circuits
Easier to isolateHarder to couple
Easier to couple & constructHarder to isolate
Bigger
• NMR: 2 to 7 qubits; scalability?• Ions: up to 14 qubits + scalable•Many technical issues still unsolved
• Dots: LONG T1 and T2
• Coherent Oscillations• Coupling?
• Little dissipation• Reasonable coherence • Coupling• 9 qubits demonstrated
Goal - reach the fault tolerant threshold – F 99 %
photons
• Excellent single qubit• coupling hard…•Sinlge photon/graph states
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Recent resultsPhotons – 8 photon cluster states (2012)
(Jian-Wei Pan group)
Ions –99.93% fidelity of 1-qubit and 2-qubit gate demonstrated (Lucas group 2014):
Coherent 14 and 6 ion states demonstated (Blatt/Wineland)
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Recent results – cont.Atoms – Mott insulator + controlled collisons + site addressing (Bloch group)
Semiconductors – even denominator fractional Hall states demonstrated
Heiblum group (2010)
A possible model system for topological QIP.
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Recent results – cont (2).Superconductors – (1) surface code fault tolerance demonstrated (Martinis, 2013) (2) errors suppressed by logical qubits – for the first time! (Martinis 2014)
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Recent results – cont (2b).Superconductors – (2) errors suppressed by logical qubits – for the first time! (Martinis 2014)
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Recent results – cont (3).Superconductors – Circuit cavity electrodynamics
Schoelkopf (2010)
Martinis (2010-2013), Katz (2013-2014)
Simmonds (2007)
Generation of Fock states up toN=16, with full state tomography
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Outlook - hybridsCavity – qubit interfaces will improve
Mechanical – qubit interfaces
Kimbel (2008), Dayan (2014)
Yamamoto (2006-2008)
Lehnert (2008-2013)
Can we make a mechanical S-cat?Yes we can!
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Summary
Exciting new computational models – better suited for implementation
Experimental control/coherence of quantum systems is steadily growing
Expect very exciting advances in the next decade…