Quantum Information Science Atomic-Molecular Optical Physics Condensed Matter Physics Exotic Quantum States of Matter! J. Preskill 3 Dec. 2008

Quantum Information Science Planck 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. Turing Shannon

Information is encoded in the state of a physical system.

Information is encoded in the state of a quantum 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 6440590556627 8102516769401 3491701270214 5005666254024 4048387341127 5908123033717 8188796656318 2013214880557 = ? ? ´ 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 6440590556627 8102516769401 3491701270214 5005666254024 4048387341127 5908123033717 8188796656318 2013214880557 3968599945959 7454290161126 1628837860675 7644911281006 4832555157243 4553449864673 5972188403686 8972744088643 5630126320506 9600999044599 ´ = 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.

John Preskill Physics Jeff Kimble Physics Alexei Kitaev Physics and Computer Science Gil Refael Physics Leonard Schulman Computer Science CENTER FOR THE PHYSICS OF INFORMATION

Former IQI Postdocs now in faculty positions elsewhere Hallgren Shi Doherty Nayak Geremia Childs Bacon Duan Hayden Terhal Vidal Raussendorf Bose Leung Bravyi Verstraete Wocjan Ardonne

Former IQI Postdocs now in faculty positions elsewhere Penn State Waterloo Michigan Queensland UNM Waterloo Washington Michigan McGill IBM Queensland UBC London Waterloo IBM Vienna U. Cental Fla. Nordita

Some former IQI Students Bob Gingrich (2001) – PIMCO Andrew Landahl (2002) – University of New Mexico Federico Spedalieri (2003) – UCLA Sumit Daftuar (2003) – Goldman Sachs John Cortese (2003) – LIGO (Caltech) Charlene Ahn (2004) – Toyon Research Corporation Dave Beckman (2004) – Toyon Research Corporation Jim Harrington (2004) – Los Alamos National Laboratory Carlos Mochon (2005) – Perimeter Institute Anura Abeyesinghe (2006) – Univ. Central Florida Graeme Smith (2006) – IBM Ben Toner (2006) – CWI, Amsterdam Panos Aliferis (2007) – IBM Parsa Bonderson (2007) -- Microsoft Research Mike Zwolak (2007) – Los Alamos National Laboratory Bonderson Zwolak Gingrich Landahl Spedalieri Daftuar Ahn Cortese Harrington Mochon Abeyesinghe Smith Toner Aliferis

Quantum Information Challenges Cryptography Privacy from physical principles Algorithms What can quantum computers do? Quantum Computer Error correction Reliable quantum computers Hardware Toward scalable devices Noise And …what are the implications of these ideas for basic physics?

Condensed matter physics In a nutshell: whole >  (parts) 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. Fractional quantum Hall state High temp. superconductor Crystalline material

Emergence: the fractional quantum Hall effect 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). 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?

Topology Quantum Computer Noise! Quantum Computer

F

F

F Aharonov-Bohm Phase exp(ieF)

F Aharonov-Bohm Phase exp(ieF)

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).

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).

Topological quantum computation annihilate pairs? Kitaev braid braid braid time create pairs

Topological quantum computation create pairs braid annihilate pairs? Kitaev time

Topological quantum computation 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! time

Topological quantum computation Physical fault tolerance with nonabelian anyons Kitaev Eisenstein

“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).

Condensed matter meets atomic physics 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.

Crossover in fermion pair condensates C. 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. 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.

Many-body physics with polar molecules P. Zoller et al. (2006) J. Ye et al. (2008) 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).

How fast does information escape from a black hole? Hayden, Preskill How fast does information escape from a black hole? Alice black hole Bob strongly mixing unitary maximal entanglement Alice’s qubits Bob decodes black hole radiation 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-Molecular Optical Physics Condensed Matter Physics Exotic Quantum States of Matter!

Exotic Quantum States of Matter! Preskill Kitaev Schulman Kimble Painter Vahala Eisenstein Roukes Refael Motrunich Exotic Quantum States of Matter! All-Star All-Star