
Daniel Lidar
From the Special Topic of
Quantum Computers

According to our Special Topics analysis of
quantum computers research over the past decade, the work
of Dr. Daniel Lidar ranks at #4 by total number of papers,
based on 79 papers cited a total of 1,814 times between
January 1, 1999 and December 31, 2009.
In the
Web of Science®, Dr. Lidar
currently has 113 original articles, reviews, and
proceedings papers from 19982010, cited a total of
3,318 times. Six of these papers have been named as
Highly Cited Papers in the field of Physics in
Essential Science Indicators^{SM} from
Thomson
Reuters.


Dr. Lidar is Associate Professor in the Departments of Electrical
Engineering and Chemistry at the University of Southern California in Los
Angeles. He is also the Director and cofounding member of the USC Center
for Quantum Information Science and Technology (CQIST).
In this interview, he talks with ScienceWatch.com
about his highly cited research on quantum computers.
What first drew your interest to the field
of quantum computing?
As I was finishing my Ph.D. research on scattering theory and disordered
systems I realized I wanted a change of subject. A fellow graduate student
told me about Shor's algorithm—the algorithm for efficient factoring
which launched the field of quantum computing—and I was hooked. You
can read about my educational background and research
experiences at the end of this page.
This was in '96, and Shor had published his algorithm two years earlier, so
the field was still relatively embryonic and unpopulated. All the papers
that had been written on the subject literally fit on my desk. I thought it
would be a good idea to move into an exciting young field of study which I
could read everything about, and decided to switch to quantum computing.
Moreover, this field seemed to contain a nice mix of fundamental questions
and practical applications, both of which appealed, and continue to appeal,
to me.
I wrote my first quantum computing paper with my Ph.D. advisor Ofer Biham
several months later. At the time there were very few postdoc positions in
the field, and I was lucky enough to find one at UC Berkeley, in Birgitta
Whaley's group. Several terrific graduate students joined the group, and we
worked well together. It was a very productive and inspiring period, which
solidified my interest in quantum computing.
What is your main focus in the
field?
My main focus is on ensuring that quantum computers can work reliably in
spite of their extreme fragility. Quantum computers are particularly
susceptible to decoherence, which is the result of their inevitable
interactions with their environments. Decoherence can be thought of the
process by which a quantum system becomes classical. For a quantum computer
this means the loss of any computational advantage over classical
computers.
I have worked on a variety of different approaches designed to ensure the
reliable operation of quantum computers in the presence of inevitable
decoherence and other sources of noise and imperfections. These approaches
include "hiding" a quantum computer from its environment (decoherencefree
subspaces), minimizing the interaction between computer and environment
(dynamical decoupling), and correcting errors induced by the environment
and other noise sources (quantum error correcting codes).
"One reason that decoherencefree subspaces are
important is because they offer a way to protect quantum
information 'for free."

Most of my recent work on overcoming decoherence has focused on dynamical
decoupling. The basic idea comes from the spinecho effect in nuclear
magnetic resonance. More than 50 years ago Hahn observed that the rapidly
decaying signal from nuclear magnetic resonance measurement could be
revived, or "refocused," by applying a series of strong and frequent
modulating pulses to the system under investigation.
This idea was picked up in the quantum computing community, starting with
Lorenza Viola and Seth Lloyd in 1998, to overcome decoherence in quantum
computers. In 2005 my former student Kaveh Khodjasteh (now a postdoc at
Dartmouth College) and I proposed a variation on dynamical decoupling we
called "concatenated dynamical decoupling," which involves recursively
constructed pulse sequence and can in principle reduce decoherence to
arbitrarily low levels much faster than other decoupling methods, and is
inherently faulttolerant to some degree.
Very recently we generalized these ideas, together with Lorenza Viola, to
show that arbitrarily accurate quantum logic gates can also be implemented
using concatenated pulses design ("Arbitrarily accurate dynamical control
in open quantum systems," Physical Review Letters 104[9]: art. no.
090501, 5 March 2010). I continue to work on dynamical decoupling with my
students Gregory Quiroz and WanJung Kuo.
Another focus of my work (mostly with my former student Joseph Geraci, now
a scientist at the Ontario Cancer Biomarker Network) has been the design of
algorithms which could run more efficiently on quantum than on classical
computers, especially those pertaining to simulations of classical physics.
I have also been quite interested in developing methods to experimentally
measure and characterize quantum noise channels, technically known as
quantum process tomography. My former student Masoud Mohseni (now a postdoc
at MIT) and I found efficient ways to do this using techniques borrowed
from quantum error correction theory.
Most recently I have been devoting much of my attention, together with my
postdocs Dr. Ali Rezakhani and Alioscia Hamma (now at the Perimeter
Institute) and graduate students WanJung Kuo and Kristen Pudenz, to an
approach to quantum computing called "adiabatic quantum computing," which I
find particularly intriguing and promising.
In the adiabatic approach the idea is to very slowly change the
interactions between the particles in the quantum computer, so that while
the initial interactions correspond to a Hamiltonian with a very simple
ground state, the final interactions correspond to a Hamiltonian with a
complicated ground state that encodes the answer to a hard computational
question.
There are some similarities between this idea and the wellknown simulated
annealing algorithm, but the difference is that in adiabatic quantum
computing the system is supposed to always remain in its ground state, so
that the entire evolution actually takes place very close to zero
temperature. This implies some natural robustness against decoherence, as
well as intriguing connections to quantum phase transitions, and more
widely to condensed matter physics.
As a result adiabatic quantum computing provides a natural bridge between
computer science and physics, which I find particularly appealing. I have
always believed in the fruitfulness of combining ideas and techniques from
a variety of different fields, which is another reason I was initially
drawn to quantum computing.
Your most influential paper in the field wasn't
actually included in our analysis, as it was published a year prior to
our 10year time window, but it's important to address it—your
1998 Physical Review Letters paper, "DecoherenceFree
Subspaces for Quantum Computation," (Lidar DA, et al.,
81[12]: 25947, 21 September 1998). Why is this paper cited so
much?
This paper was among the first to point out that symmetry can be used to
hide quantum information from the detrimental effects of decoherence.
Symmetry has always fascinated physicists, and putting it to use to
overcome some of the initial skepticism directed at quantum computing in
light of decoherence was apparently an idea that was appreciated by the
community.
I should point out that my USC colleague Paolo Zanardi coauthored an
earlier paper on a closely related topic (Zanardi P, Rasetti M, "Noiseless
quantum codes", Physical Review Letters 79[17]: 33069, 27 October
1997) which really provided the inspiration for our 1998 paper.
Many of your papers in our analysis deal with
decoherencefree subspaces. Could you explain what these are and why
they are important?
A decoherencefree subspace is a way to exploit a preexisting symmetry in
order to hide quantum information from the environment that tries to
corrupt this information by measuring the state of the quantum computer.
Here is a classical analogy: You have two coins and want to use them to
store one bit of classical information. "Easy," you say, "since two coins
represent two bits of information." But now imagine that some nasty demon
keeps flipping the coins at random, so that your efforts to store a bit are
frustrated. Fortunately the demon can only flip both coins simultaneously.
Is it still possible to reliably store a classical bit?
"I have worked on a variety of different approaches
designed to ensure the reliable operation of quantum
computers in the presence of inevitable decoherence and
other sources of noise and imperfections."

A moment's reflection reveals that the answer is yes: define the two
subspaces "equal" (even parity) and "opposite" (odd parity). The first is
the subspace comprising the states {heads,heads} and {tails,tails}. The
second subspace is {heads,tails} and {tails,heads}. Now call "equal" 0 and
call "opposite" 1. Since the demon can only flip both coins together, these
0 and 1 are protected. Indeed, under the demon's action
{heads,heads}<–>{tails,tails} and
{heads,tails}<–>{tails,heads}, so that the two subspaces never
get mixed.
Thus, instead of encoding a bit into each coin, we should encode a bit into
the parity of the two coins. What is special about parity? It is the fact
that it respects the symmetry induced by the demon's inability to
distinguish between the two coins, a permutation symmetry.
One reason that decoherencefree subspaces are important is because they
offer a way to protect quantum information "for free." Almost all other
methods require active intervention. But perhaps more importantly, it turns
out that the idea of using symmetry to protect quantum information actually
lays at the heart of all other quantum information protection methods as
well. Thus the concept of a decoherencefree subspace provides the starting
point for a unified theory of quantum information protection.
Another important reason is that of all the ideas for quantum information
protection, decoherencefree subspaces have been probably been most
thoroughly experimentally tested. There is now plenty of experimental
evidence, in a variety of different systems (linear optics, trapped ions,
nuclear magnetic resonance, quantum dots), that decoherencefree subspaces
exist and can be used as a first layer of defense in the quest to protect
quantum information.
The Physical Review Letters paper you
wrote with Alireza Shabani last year, "Vanishing Quantum Discord is
Necessary and Sufficient for Completely Positive Maps" (102[10]: art.
no. 100402, 13 March 2009), has been receiving citation attention.
Would you tell us a bit about this paper?
This paper addresses a fairly technical problem, with a foundational
flavor. Almost all of the mathematical work in quantum computing, and more
generally in quantum information theory, takes for granted that quantum
dynamics of open (nonisolated) systems can be described using a relatively
simple type of transformation called a completely positive map, which is in
some sense a generalization of the Schrödinger equation.
My former student Alireza Shabani (now a postdoc at Princeton) and I wanted
to understand the precise conditions under which such transformations
actually apply to open quantum systems. Building on an earlier breakthrough
by Cesar RodriguezRosario et al., we showed that the necessary
and sufficient condition for the validity of the completely positive map
description (given certain standard assumptions) is that the system (e.g.,
a quantum computer) and its environment are purely classical correlated,
i.e., contain no quantum correlations whatsoever.
Technically such correlations can be quantified using a quantity called
quantum discord, and the case of purely classical correlations is when the
discord vanishes. The implication of our result is that the standard tool
of completely positive maps now has a welldefined and wellunderstood
domain of applicability.
More fundamentally, the implication is that any correlations with
nonvanishing quantum discord can be interpreted as not allowing a
consistent separation between system and environment, since when the
transformation describing the evolution of the system is not a completely
positive map, it is well known that in some cases nonphysical predictions
can arise, in particular events with negative probabilities.
Were there any papers not covered in our analysis
that you feel are particularly key to the field? Which papers and
why?
Well, clearly the 1998 Physical Review Letters paper mentioned
above is in this category, but it wasn't covered since it was published
prior to 1999.
Two other papers, which are named as Highly Cited Papers in the field of
Physics by Essential Science Indicators from Thomson Reuters, but
which were left out of the Special Topics analysis are "Concatenating
decoherencefree subspaces with quantum error correcting codes" (with D.
Bacon and K.B. Whaley, Physical Review Letters 82[22]: 45569, 31
May 1999), and "Quantum phase transitions and bipartite entanglement" (with
L.A. Wu and M.S. Sarandy, both former postdocs of mine with faculty
positions in Spain and Brazil, respectively, Physical Review
Letters 93[25]: art. no. 250404, 17 December 2004).
The first of these established that the informationprotection methods of
decoherencefree subspaces and quantum error correcting codes can be
combined to yield a single, more economical and robust method than provided
by either methods used separately. The second paper resolved a problem at
the interface of quantum computing and condensed matter theory: why quantum
phase transitions are often accompanied by drastic changes in quantum
entanglement.
How has the field of quantum computing changed in
the past decade? Where do you hope to see it go in the next?
The field has undergone tremendous progress, from one driven mostly by
theoretical work to a thriving discipline with numerous experimental groups
and steady progress toward the goal of building larger and more robust
quantum informationprocessing devices, and a much clearer theoretical
understanding of the source of the power of quantum computers and of means
of making them robust.
The field has also gained official recognition with a topical group in the
American Physical Society, several dedicated journals, special sections in
established journals, and dedicated federal funding.
In the next decade I would hope to see the first generation of commercially
viable quantum computers, perhaps as dedicated machines capable of
performing specialized simulation tasks (the efforts of the Canadian
startup DWave Systems Inc. are notable in this regard).
I would also hope to see a wave of new faculty positions at US institutions
for quantum computation theoreticians and experimentalists. We now have the
first generation of students and postdocs trained in this field, many of
whom are finding it very difficult to land faculty positions in the US, and
are forced to seek such employment in other countries. This is most
unfortunate, and I hope that US universities will reverse this
trend.
Daniel Lidar, Ph.D.
Departments of Electrical Engineering and Chemistry
University of Southern California
Los Angeles, CA, USA
Additional Information:
Read about the educational background and
research experiences of Dr. Daniel Lidar.
Daniel Lidar's current mostcited paper in Essential Science
Indicators, with 176 cites:
Kempe J, et al., "Theory of decoherencefree faulttolerant
universal quantum computation," Phys. Rev. A 63(4): art. no.
042307, April 2001. Source:
Essential Science Indicators from
Thomson Reuters.
KEYWORDS: QUANTUM COMPUTATION, SHOR'S ALGORITHM, DECOHERENCE, NOISE,
IMPERFECTIONS, DECOHERENCEFREE SUBSPACES, DYNAMICAL DECOUPLING, QUANTUM
ERROR CORRECTING CODES, CONCATENATED DYNAMICAL DECOUPLING, QUANTUM PROCESS
TOMOGRAPHY, ADIABATIC QUANTUM COMPUTING, QUANTUM PHASE TRANSITIONS,
CONDENSED MATTER PHYSICS.