Experimental quantum information processing - the  of the art

Nadav Katz

A biased progress report

Contact: katzn@phys.huji.ac.il 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

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:

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

• 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:

Bloch representation

Control: resonant (or close to resonant) pulses can be visualized as a rotation!

Geometrical picture:Useful for any two-level system

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…

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)

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

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…)

Qubit progress

Remarkable progress of the past 15 yearsAlready passed the fault tolerant threshold

From Devoret and Schoelkopf, Science (2013)

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

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

??

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

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)

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.

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)

Martinis (2010-2013), Katz (2013-2014)

Simmonds (2007)

Generation of Fock states up toN=16, with full state tomography

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!

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…