Quantum Information Science

Atomic-MolecularOptical Physics

CondensedMatter Physics

Exotic QuantumStates of Matter!

J. Preskill 3 Dec. 2008

Turing

Planck

Shannon

Quantum Information Science

Quantum physics, information theory, and computer science are among the crowning intellectual achievements of the 20th century.

Quantum information science is an emerging synthesis of these themes, which is providing important insights into fundamental issues at the interface of computation and physical science, and may guide the way to revolutionary technological advances.

Information

is encoded in the state of a physical system.

quantum

Information

is encoded in the state of a system.

Put

to work!

Quantum Entanglement

classically correlated socks quantumly correlated photons

• There is just one way to look at a classical bit (like the color of my sock), but there are complementary ways to observe a quantum bit (like the polarization of a single photon). Thus correlations among qubits are richer and much more interesting than correlations among classical bits.

• A quantum system with two parts is entangled when its joint state is more definite and less random than the state of each part by itself. Looking at the parts one at a time, you can learn everything about a pair of socks, but not about a pair of qubits!

The quantum correlations of many entangled qubits cannot be easily described in terms of ordinary classical information. To give a complete classical description of one typical state of just a few hundred qubits would require more bits than the number of atoms in the visible universe!

It will never be possible, even in principle to write down such a description.

We can’t even hope to describe the state of a few hundred qubits in terms of classical bits.

As Feynman first suggested in 1981, a computer that operates on qubits rather than bits (a quantum computer) can perform tasks that are beyond the capability of any conceivable digital computer!

Finding Prime Factors

1807082088687 4048059516561 64405905566278102516769401349170127021450056662540244048387341127590812303371781887966563182013214880557

? ?

An example of a problem that is hard for today’s supercomputers: finding the factors of a large composite number. Factoring e.g. 500 digit numbers will be intractable for classical computers even far into the future.

Finding Prime Factors

1807082088687 4048059516561 64405905566278102516769401349170127021450056662540244048387341127590812303371781887966563182013214880557

39685999459597454290161126162883786067576449112810064832555157243

45534498646735972188403686897274408864356301263205069600999044599

But for a quantum computer, factoring is not much harder than multiplication! The boundary between the problems that are “hard” and the problems that are “easy” is different in a quantum world than a classical world.

Jeff KimblePhysics

Alexei KitaevPhysics and Computer Science

Leonard SchulmanComputer Science

John PreskillPhysics

CENTER FOR THE PHYSICS OF INFORMATION

Gil RefaelPhysics

Hallgren

TerhalBacon Duan

DohertyNayak

VidalHayden

Leung

Shi Geremia

Bose Bravyi Verstraete Wocjan

Former IQI Postdocs now in faculty positions elsewhere

Childs

Raussendorf

Ardonne

Penn State

IBMWashington Michigan

QueenslandWaterloo

QueenslandMcGill

Waterloo

Michigan UNM

London IBM Vienna U. Cental Fla.

Former IQI Postdocs now in faculty positions elsewhere

Waterloo

UBC

Nordita

Some former IQI StudentsBob Gingrich (2001) – PIMCOAndrew Landahl (2002) – University of New Mexico Federico Spedalieri (2003) – UCLASumit Daftuar (2003) – Goldman SachsJohn Cortese (2003) – LIGO (Caltech)Charlene Ahn (2004) – Toyon Research CorporationDave Beckman (2004) – Toyon Research Corporation Jim Harrington (2004) – Los Alamos National LaboratoryCarlos Mochon (2005) – Perimeter InstituteAnura Abeyesinghe (2006) – Univ. Central FloridaGraeme Smith (2006) – IBMBen Toner (2006) – CWI, AmsterdamPanos Aliferis (2007) – IBMParsa Bonderson (2007) -- Microsoft ResearchMike Zwolak (2007) – Los Alamos National Laboratory Daftuar

Aliferis

Spedalieri

CorteseAhn Harrington Mochon Abeyesinghe Smith Toner

LandahlGingrich

ZwolakBonderson

Quantum Information Challenges

And …what are the implications of these ideas for basic physics?

Cryptography

Privacy from physical principles

Hardware

Toward scalable devices

QuantumComputer

Error correction

Reliable quantum computers

Noise

Algorithms

What can quantum computers do?

| | ( )x G

x f x

whole > (parts)

Condensed matter physics

Emergent phenomena: the collective behavior of many particles cannot be easily guessed, even if we have complete knowledge of how the particles interact with one another.

Entangled quantum many-particle systems have an enormous capacity to surprise and delight us.

In a nutshell:

Fractional quantum Hall state High temp. superconductor Crystalline material

Emergence: the fractional quantum Hall effect

The local excitations (“quasi-particles”) of this system are profoundly different than electrons. In fact, a single quasi-particle carries an electric charge that is a fraction (for example, 1/3) of the charge of an electron.

Is this the tip of an enormous iceberg?

Are such phenomena useful?

Fractional quantum Hall state

Highly mobile electrons, confined to a two-dimensional interface between semiconductors, and exposed to a strong magnetic field, find a very exotic highly-entangled quantum state (which can be observed at sufficiently low temperature).

Topology

QuantumComputer

Noise!

QuantumComputer

Aharonov-BohmPhase

exp(ie)

Aharonov-BohmPhase

exp(ie)

Anyons

Quantum information can be stored in the collective state of exotic particles in two dimensions (“anyons”).

The information can be processed by exchanging the positions of the anyons (even though the anyons never come close to one another).

Quantum information can be stored in the collective state of exotic particles in two dimensions (“anyons”).

The information can be processed by exchanging the positions of the anyons (even though the anyons never come close to one another).

Anyons

timecreate pairs

braid

braid

braid

annihilate pairs?

Topological quantum computation

Kitaev

timecreate pairs

braid

braid

braid

annihilate pairs?

Topological quantum computation

Kitaev

time

The computation is intrinsically resistant to noise.

If the paths followed by the particles in spacetime execute the right braid, then the quantum computation is guaranteed to give the right answer!

Topological quantum computation

Kitaev

Topological quantum

computation

Eisenstein

Physical fault tolerance with nonabelian anyons

“The rule of simulation that I would like to have is that the number of computer elements required to simulate a large physical system is only proportional to the space-time volume of the physical system”

R. P. Feynman, “Simulating Physics with Computers” (1981).

Quantum simulators: Condensed matter meets atomic physics

In general, we can’t simulate a many-particle quantum system with a classical computer.

But we can simulate one quantum system with another one!

The atomic physicists have developed remarkable tools for cooling and controlling atoms. Exploiting these tools, we can study (and discover) quantum many-particle phenomena that up until now have been experimentally inaccessible.

Because a superfluid flows without resistance, a rotating superfluid organizes into vortices, each carrying a tiny fraction of the angular momentum, and because the vortices repel one another, they crystalize into a regular lattice. The strength of the interactions between fermionic atoms can be modulated by varying a magnetic field, so that the crossover from (b) to (c) can be studied experimentally.

Crossover in fermion pair condensatesC. Regal et al. (2004) , M. Zwierlein et al. (2005)

Superfluidity persists through the crossover from a molecular condensate of tightly bound pairs of fermionic (potassium or lithium) atoms (BEC) to a condensate of loosely bound Cooper pairs (BCS) analogous to a superconducting state of a system of electrons.

P. Zoller et al. (2006)J. Ye et al. (2008)

Many-body physics with polar molecules

Polar molecules, trapped in an optical lattice, have dipole moments, which provide a useful handle for manipulating the interactions among the molecules and realizing exotic quantum many-body states (for example, the ground state of the Kitaev model, which supports nonabelian anyons).

strongly mixing unitary

maximalentanglement

Alice’s qubits

Bob decodes

blackhole

blackhole

radi

atio

n

radiation

How fast does information escape from a black hole? Hayden,Preskill

Alice

black holeBob

Black holes are (we believe) efficient quantum information processors. How long do we have to wait for information absorbed by a black hole to be revealed in its emitted Hawking radiation? We have recently reconsidered this question using new tools from quantum information theory.

Our (tentative) conclusion is that the retention time can be surprisingly short. The analysis uses the theory of quantum error-correcting codes and quantum circuits.

Quantum Information Science

Atomic-MolecularOptical Physics

CondensedMatter Physics

Exotic QuantumStates of Matter!

Exotic QuantumStates of Matter!

Eisenstein Roukes Refael Motrunich

Preskill Kitaev Schulman

Kimble Painter Vahala

All-Star All-Star