## Guifre Vidal Disentangles Quantum Entanglement

#### Interview for the Special Topic of Quantum Computers, July 2010

*According to our Special Topics analysis of
quantum computers research over the past decade, the work of
Professor Guifre Vidal ranks at #8 by total cites, with 27 papers
cited 2,751 times.*

*His record in*
Essential Science Indicators^{SM} *from Clarivate Analytics
includes 47 papers cited a total of 3,888 times between January 1, 2000
and February 28, 2010 in the field of Physics. In the*
*
Web of Science ^{®}*

*, Vidal's record includes 67 papers cited a total of 4,490 times between January 1, 2000 and June 3, 2010.*

*Vidal is an Australian Research Council Federation Fellow in the
School of Mathematics and Physics at the University of Queensland in
Brisbane, Australia, as well as a Distinguished Research Chair at the
Perimeter Institute for Theoretical Physics in Waterloo, Canada.*

**Would you tell us a bit about your educational
background and research experiences?**

I grew up in Barcelona, where in 1999 I obtained a Ph.D. in Physics from the University of Barcelona under the supervision of Prof. Rolf Tarrach.

Then I worked for two years in Prof. Ignacio Cirac's group at the University of Innsbruck, Austria, with a Marie Curie Postdoctoral Fellowship from the European Community. In 2002 I moved to the United States to work in Prof. John Preskill's Institute for Quantum Information at the California Institute of Technology with a Sherman Fairchild Postdoctoral Fellowship.

Since 2005 I have been a Professor in the School of Mathematics and Physics at the University of Queensland, in Brisbane, Australia, where I have built a research group in quantum information, computational physics, and condensed matter.

**What do you consider the main focus of your
research within the area of quantum computing?**

A long-term goal of my research has been to better understand quantum entanglement. Entanglement is a natural consequence of the superposition principle of quantum mechanics when applied to composite systems. It turns out that correlations between entangled quantum systems can be stronger than correlations between classical systems.

I was first attracted to this fascinating subject in the context of quantum computing, where entanglement is used as a resource for quantum information processing. However, nowadays entanglement is also intensively studied in the broader context of quantum many-body physics and has found important applications both as a natural theoretical framework to study quantum phases of matter (e.g. in condensed matter physics) and as the key to the development of new computational tools for strongly correlated systems.

**Two of your most-cited papers are the 2000
Physical Review A paper, "Three qubits can be entangled in two
inequivalent ways" (Dur W, Vidal G, Cirac JI, 62[6]: art. no. 062314,
December 2000) and the 2002 Physical Review A paper,
"Computable measure of entanglement" (Vidal G, Werner RF, 65[3]: art.
no. 032314, March 2002). Would you tell us about these papers and why
you think they are so highly cited?**

"...while it may still be unclear whether and when it will be possible to build a quantum computer, it is important to notice that the areas of quantum information processing and quantum computing have already produced a lot of useful outcomes."

During my Ph.D. and first years as a postdoctoral researcher, I joined an ongoing effort devoted to characterizing entanglement in systems made of a small number of parts, typically just two or three parts. Back then, entanglement had been identified as a resource for quantum information processing, including quantum teleportation and quantum cryptography, and developing a theory of entanglement became a priority.

The aim was to understand how entanglement, as a physical resource, could be created, transformed, and used in an optimal way. Several notions and measures of bipartite and tripartite entanglement, as well as pure-state and mixed-state entanglement, were proposed during this period.

These two papers contributed to that ongoing effort by, respectively, classifying the possible types of entanglement in a system made of three quantum bits (or qubits), and by proposing a measure of entanglement for mixed states that can be easily computed. These results turned out to be useful milestones in the development of a theory of entanglement.

**Another highly cited paper is your 2003
Physical Review Letters paper, "Entanglement in quantum
critical phenomena" (Vidal G, et al., 90[22]: art. no. 227902,
6 June 2003). What does entanglement have to do with critical phenomena
and why is this paper significant?**

As I mentioned earlier, the study of entanglement is of relevance well beyond the context of quantum computing. This paper investigated entanglement in the ground state of quantum spin chains. The goal was to establish whether the entanglement between different parts of a many-body system was enhanced near a quantum phase transition.

We found that, at criticality, entanglement scales in a very simple way that reveals the universality class to which the quantum phase transition belongs. These results pioneered the use of entanglement measures to characterize quantum many-body phenomena and illustrated how tools developed in the context of quantum computing could be useful in other areas of research.

It also unveiled connections between the recently developed theory of entanglement, important computational tools such as Prof. Steven White's density matrix renormalization group, and previous calculations in conformal field theory. In other words, it was a good mixture, with the potential of attracting the interest of researchers with different backgrounds and skills.

Since then, the study of entanglement in many-body systems, especially in connection to quantum criticality and topological order, remains very active.

**The 2003 and 2004 Physical Review Letters
papers "Efficient classical simulation of slightly entangled quantum
computations" (Vidal G, 91[14]: art. no. 147902, 3 October 2003) and
"Efficient simulation of one-dimensional quantum many-body systems"
(Vidal G, 93[4]: art. no. 040502, 23 July 2004) are concerned with the
numerical simulation of quantum systems and represent a radical
departure from your previous work. Did you grow tired of quantum
computing**?

Oh, no, I did not get tired of quantum computing. At that time it became clear, however, that new insights acquired in the context of quantum computing would also lead to significant progress in our ability to numerically simulate many-body systems. With a few colleagues, including Prof. Frank Verstraete and Prof. Ignacio Cirac, we started to explore these possibilities.

"...the study of entanglement is of relevance well beyond the context of quantum computing."

By using concepts such as quantum circuits and entanglement, we were able to propose new variational wave functions to efficiently represent the ground state of many-body systems, or came up with algorithms to simulate time evolution. These developments were significant because they opened up a new route to simulating strongly correlated systems.

We must keep in mind that a large number of models proposed to describe condensed matter systems, including very simple lattice models of frustrated antiferromagnets and of interacting fermions, remain unsolved due to the lack of proper computational tools to address them. For instance, the phase diagram of the Hubbard model for interacting electrons in two dimensions, which was first proposed in the 1960s and is used to investigate the metal to insulator transition and cuprate high-temperature superconductors, still remains highly controversial.

For decades, this lack of numerical tools has slowed progress in several areas dealing with strongly correlated systems. Our hope is that the new computational approaches, known as tensor network algorithms, will finally allow us to answer a number of long-standing open questions, including perhaps the mechanisms of high-temperature superconductivity.

We have good reasons to remain optimistic, especially after last year's irruption of fermionic tensor network algorithms for interacting fermions. It is also encouraging to see that prestigious condensed matter physicists such as Prof. Xiao-Gang Wen have joined this effort with their own important contributions.

**How has the field of quantum computing changed in
the past decade? Where do you hope to see it go in the next?**

Perhaps the original euphoria concerning the feasibility of quantum computing has been replaced with a more realistic understanding of the long way ahead of us. Now that the theoretical foundations are largely in place, we have to wait for further experimental and technological progress.

However, while it may still be unclear whether and when it will be possible to build a quantum computer, it is important to notice that the areas of quantum information processing and quantum computing have already produced a lot of useful outcomes.

Apart from enormously stimulating experimental research, which has led to impressive progress in our ability to control quantum systems, thinking about quantum computers has given birth to a new way of looking at quantum mechanical problems, including a new framework and new tools to address strongly correlated quantum many-body systems.

**Guifre Vidal, Ph.D.
School of Mathematics and Physics
University of Queensland
Brisbane, Queensland, Australia**

GUIFRE VIDAL'S MOST CURRENT MOST-CITED PAPER IN ESSENTIAL SCIENCE INDICATORS:

Dur W, Vidal G, Cirac JI, "Three qubits can be entangled in two
inequivalent ways," *Phys. Rev. A* 62(6): art. no. 062314, December
2000 with 731 cites. Source:
*Essential Science Indicators* from
*Thomson
Reuters* .

KEYWORDS: QUANTUM COMPUTATION, QUANTUM INFORMATION, QUANTUM MANY-BODY PHYSICS, ENTANGLEMENT, BIPARTITE AND MULTIPARTITE QUANTUM STATES, QUANTUM PHASE TRANSITIONS, TOPOLOGICAL ORDER, QUANTUM CRITICAL PHENOMENA, SIMILATION ALGORITHMS.

Citing URL: http://sciencewatch.com/ana/st/quantum/10julSTVida/