Experimental quantum information
processing - the  of the art
Quantum computation workshop, Jan. 2015
Nadav Katz
A biased progress report
• What is a quantum information and why do we want to
process it?
• Different models – gates, cluster, adiabatic, topological.
• Different realizations – photons, atoms, ions, semiconductors and superconductors.
•Outlook and future directions
Contact:
katzn@phys.huji.ac.il 02-6584133
Motivation
&
Wait for
one half-life
2
Single atom decays – cat dies!
We NEVER see such macroscopic superpositions – why?
Schrödinger:
Aristotle: Nature abhors coherence
a vacuum
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?
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 simulate
In the presence of symmetry and structure, sometimes dramatic
speedup is predicted
Storage of Information: Bits
• Classical bit: definite 0 or 1
+ 5V
Vout
• Quantum bits: superpose 0 or 1
Example:
0 1
H atom
wavefunctions:
Transistor Logic:
0 = 0 volts
1 = 5 volts
0
1
2
Bloch representation
Geometrical picture:
Useful for any two-level
system
Control: resonant (or close to resonant) pulses can be visualized
as a rotation!
Qubit Characterization
1
Rabi
time
Meas.
x
lifetime
T1 ~450ns
time
Ramsey
x/2
x/2
time
Echo
0
1
x/2 y x/2
time
Data from 2007…
0
1
T~100ns
P1
0
1
T2 ~350ns
0
0
100
200
300
400
time [ns]
500
600
Entanglement

Qubit 1

Qubit 2

Qubit 3
Qubit 4
• Require 2N complex numbers to specify a general N-qubit state!
• Many (most actually) such states are not separable = entangled
Classic 2-qubit example: Bell state
Resource for secure communication
(not discussed)
01  10
2
Such (anti-)correlations are normally generated by interactions (gates).
Gate model
Classical Computation:
(DiVincenzo criteria)
Quantum Computation:
• Initialize state
• Initialize state Yi = |000..0>
• Logic
• Logic via series of operations:
not
0 -> 1
1 -> 0
and
00 -> 0
01 -> 0
10 -> 0
11 -> 1
|0> -> |1>
|1> -> |0>
|0> -> (|0>|1>)/21/2
State
Manipulation
(1 qubit)
Controlled not
(2 qubit)
bit
• Output result
|00> -> |00>
|10> -> |10>
|01> -> |11>
|11> -> |01>
}
+ linear
superposition
control
• Final state measurement
Measure qubits of state Yf
• Logic errors:
Error correction possible
• Coherence:
tcoherence / tlogic ~ number logic operations
> 102 for error correction
Need to be clever
When we measure – we want to see something interesting (and not some
random, useless state out of 2N)…
Well-known quantum computing algorithms:
•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)…
IMPORTANT: Error correction can make it work even if gates are not perfect!
(Shor+many others…)
Qubit progress
From Devoret and Schoelkopf, Science (2013)
Remarkable progress of the past 15 years
Already passed the fault tolerant threshold
Alternative computational models
Cluster states
Briegel & Raussendorf (2001)
Generate a massively entangled initial state (c-not gates between
nodes in graph, compute by measuring in a specific order)
Single photons
Knill, Leflamme, Milburn (2001)
Using single photons (if you have them!) and linear optics – Scalable QIP is possible!
Adiabatic
Farhi (2001)
Slowly evolve the Hamiltonian
to remain in the ground state
Topological Kitaev (1997)
D-wave (??)
Exponentially degenerate
ground state (phases) with
large gap. Braiding particles
evolves the state.
All are theoretically equivalent – but experimentally VERY different…
Experimental Quantum Information Processing (QIP)
a perplexing flora and fauna of different systems
Quantum dots
Neutral atoms
??
Quantum optics
Josephson
superconducting qubits
Trapped ions
NMR
Experimental QIP – a guide for the
perplexed
Smaller
Bigger
Easier to isolate
Harder to couple
photons
Ions
Neutral Atoms
NMR
• Excellent single qubit
• coupling hard…
•Sinlge photon/graph states
Easier to couple & construct
Harder to isolate
Semiconductor Spins
Superconducting
Quantum Dots and defects
Circuits
• Dots: LONG T1 and T2
• Coherent Oscillations
• Coupling?
• NMR: 2 to 7 qubits;
scalability?
• Ions: up to 14 qubits + scalable
•Many technical issues still unsolved
Goal - reach the fault tolerant threshold – F  99 %
• Little dissipation
• Reasonable coherence
• Coupling
• 9 qubits demonstrated
Recent results
Photons – 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)
Recent results – cont.
Atoms – Mott insulator + controlled collisons + site addressing (Bloch group)
Semiconductors – even denominator fractional
Hall states demonstrated
A possible model system for
topological QIP.
Heiblum group (2010)
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)
Recent results – cont (2b).
Superconductors –
(2) errors suppressed by logical qubits – for the first time! (Martinis 2014)
Recent results – cont (3).
Superconductors
–
Circuit cavity electrodynamics
Schoelkopf (2010)
Simmonds (2007)
Generation of Fock states up to
N=16, with full state tomography
Martinis (2010-2013), Katz (2013-2014)
Outlook - hybrids
Cavity – qubit interfaces will improve
Yamamoto (2006-2008)
Mechanical – qubit interfaces
Kimbel (2008), Dayan (2014)
Can we make a mechanical S-cat?
Yes we can!
Lehnert (2008-2013)
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…