Friday September 13th at 12:30 pm, T-Division Conference Room
Fault tolerant quantum computing
Andrew Steane; Oxford University
Abstract:
I will address the question: Can a quantum computer be made to work?
It is well known that any system allowing sufficiently large entanglement
to be useful for quantum computing is extremely sensitive to noise
(especially decoherence). At first it seemed that this problem would
be essentially insurmountable, but the concept of quantum error
correction has given some hope that such sensitive quantum systems can
be stabilised after all. However, must error correction itself assume
noise-free computing during the correction process, or can it work even
when the corrector is noisy? I will discuss this question and give
some recent results which are very promising in this regard.
Friday November 1st at 12:30 pm, T-Division Conference Room
Introduction to Quantum Error Correction
Raymond Laflamme; T-6
Abstract:
This will be the first of a series of seminars on
error correction for quantum computation/cryptography.
I will give an introduction to the subject and
it should be understandable by most poeple knowing quantum mechanics.
I will give an example of the simplest quantum error correction;
the 3bit code correcting for decoherence.
I will then generalise to the most general 1 bit error
and give example of codes which correct these errors.
Thursday 7th November, 3:45 pm, Physics Auditorium
Putting Weirdness to Work: The Promise of Quantum Computation
John Preskill; Caltech
"Information" is something that can be encoded in the state of a physical
system, and a "computation" is atask that can be performed with a
physically realizable device. Therefore, since the physical world is
fundamentally quantum mechanical, the foundations of information theory and
computer science should be sought in quantum physics. In fact, quantum
information has weird properties that contrast sharply with the familiar
properties of "classical" information. A quantum computer -- a new type of
machine that exploits the quantum properties of information -- could
perform certain types of calculations far more efficiently than any
foreseeable classical computer. To build a functional quantum computer
will be an enormous technical challenge. As a first step, new methods for
"quantum error correction" are being developed that can help to prevent a
quantum computer from crashing.
Friday 8th November, 12:30 pm, T-Division Conference Room
Reliable Quantum Computation
John Preskill; Caltech
John Preskill will talk about how reliable computations can be done
with a quantum computer with imperfect components.
Friday 15th November, 12:30 pm, T-Division Conference Room
Overview of Theoretical Research in Quantum Computation
Jim Anglin, Manny Knill, Raymond Laflamme and Wocjcieh Zurek
Wednesday 20th November, 2:30 pm, New Theory Building Conference Room 524
A general theory of decoherence
R. Omnes, Universite de Paris Sud (Orsay)
Friday 5th December, 12:30 pm, T-Division Conference Room
Capacity of a noisy quantum channel
Chris Adami; Caltech
Abstract: I analyze a quantum channel for information transmission and storage
within quantum information theory. In analogy to classical channels,
I propose to define the quantum channel capacity as the maximum rate
of *mutual entanglement* processed by the channel (for the
transmission and storage of quantum entanglement), which reduces to
the maximum mutual information processed by the channel for the
transmission of classical data. The mutual entanglement and the
capacity are calculated explicitly for the quantum ``depolarizing''
channel.
Friday 13th December, 12:30 pm, T-Division Conference Room
Decoherence and the Physics of Information
Wojciech Zurek, T6
Wednesday 8th January, 11:00 am, T-Division Conference Room
Quantum Control Theory
Seth Lloyd; MIT
Friday 10th January, 12:30 pm, T-Division Conference Room
Estimate on the threshold for the quantum-gate
precision for being able to carry out arbitrarily
large quantum computations
Chris Zalka; T6
Abstract: I will discuss:
1)fault tolerant quantum error correction a la Shor (quant-ph/9605011)
2)iterated encoding (concatenated codes) to achieve arbitrary precision
(quant-ph/9610011)
3)general error patterns and justification for simplyfied error models
Friday 31st January, 12:30 pm, T-Division Conference Room
MacWilliams Identities for Quantum Error Correcting Codes
Raymond Laflamme; T6
I will describe recent work I have done with Peter Shor on the
relationship between two different notions of fidelity
(entanglement fidelity and average fidelity)
for a completely depolarizing quantum channel.
This relationship gives rise to a quantum analog of the MacWilliams
identities in classical coding theory. These identities
relate the weight enumerator of a code to the one of its dual
and, with linear programming techniques, provided a powerful tool
to investigate the possible existence of codes.
The same techniques can be adapted
to the quantum case. I will give a simple example of their power
by showing that no degenerate 5-bit quantum code exists.
Friday 14th of February, 12:30 pm, T-Division Conference Room
Quantum Error Correction and Orthogonal Geometry
Robert Calderbank, AT&T
A group theoretic framework is introduced that simplifies the
description of known quantum error-correcting codes and greatly
facilitates the construction of new examples.
The problem of finding quantum-error-correcting codes
is transformed into the problem of finding additive codes over the field
$GF(4)$ which are self-orthogonal with respect to a certain trace inner product.
Many new codes and new bounds are presented, as well as
a table of upper and lower bounds on
such codes of length up to 30 qubits.
Friday 21st of February, 12:30 pm, T-Division Conference Room
Upper bounds on quantum codes: quantum weight enumerators
Eric Rains AT&T
One of the fundamental problems in the theory of quantum error
correcting codes is that of finding good upper bounds on the minimum
distance of a code of specified length and dimension.
In classical coding theory, one of the most powerful tools for producing
bounds is the linear-programming method, which uses linear relations between
the weight enumerator of a code and a dual to find a contradiction.
Thus, to adapt this method to quantum codes, we need analogues of
these weight enumerators; such analogues are given by the quantum weight
enumerators of Shor and Laflamme. I will explain these enumerators, as
well as the "quantum shadow enumerator", and show how one can use them
to produce bounds.
Friday 28th of February, 12:30 pm, T-Division Conference Room
Quantum Computation with an ion trap
Rainer Blatt, Innsbruck
Friday March 14th, 12:30 pm, T-Division Conference Room
Error Correction and Fault-Tolerance in Quantum Computation
Daniel Gottesman; Caltech
I will describe the class of stabilizer codes,
a subclass of quantum error-correcting codes with
a straightforward group-theoretic structure. This
structure enables us to understand fault-tolerant operations
on such codes as symmetries of the stabilizer. I will discuss how
this allows us to preform universal quantum computation with any
stabilizer code.
Friday March 21th, 12:30 pm, T-Division Conference Room
Quantum information transmission through noisy channels
Michael Nielsen; University of New Mexico
What is the greatest rate at which information can be sent through a
noisy quantum channel? This is a problem whose solution is only partially
understood. I will outline what is known, including several upper bounds
on the rate of information transmsission, and some of the peculiarly
"quantum" features of the noisy channel problem.
Thursday March 27th, 1:30 pm, T-Division Conference Room
Quantum information transmission through noisy channels; Part 2
Howard Barnum; University of New Mexico
What is the greatest rate at which information can be sent through a
noisy quantum channel? This is a problem whose solution is only partially
understood. I will outline what is known, including several upper bounds
on the rate of information transmsission, and some of the peculiarly
"quantum" features of the noisy channel problem.
Friday March 28th, 12:30 pm, T-Division Conference Room
Efficient simulation of quantum systems by quantum computers.
Chris Zalka; University of New Mexico
The (possibly discretized) wavefunction of a quantum system can be "stored" on
a quantum computer by the QC's amplitudes (e.g. amplitudes of the "classical"
basis states). Discretization can be made very fine as the number of
amplitudes of a QC grows exponentially with the number of qubits. Clearly the
necessary size of the QC is only proportional to the number of simulated
quantum mechanical particles. Quantum fields would have to be spatially
discretized like in lattice QCD. I have figured out a way to time-evolve the
"stored" state vector on the QC using the Fast Fourier Transformation (FFT).
The readout problem: Of course we cannot read out individual QC amplitudes,
rather we are restricted to QT-type measurements, analogous to dealing with
the original physical system. However in the QC simulation we are in a better
position, as we can do all kinds of (possibly unphysical) unitary
manipulations before observing the QC. This e.g. allows us to "measure"
observables (hermitian operators) which we couldn't observe "in vivo".
papers: my newest version is available at:
http://qso.lanl.gov/~zalka/ (3. item)
Stephen Wiesners paper is short and quite readable: quant-ph/9603028
Monday April 7th, 3:30 pm, CNLS Conference Room
What is needed to build a quantum computer?
David DiVincenzo, IBM
I have boiled down the requirements for physical realization
of a quantum computer to five items: 1) Hilbert space control; 2)
quantum state cooling; 3) isolation from environment; 4) controlled
time evolution; 5) strong quantum measurement. I will explain what
each of these items means with some concrete examples from solid state
and atomic physics, along with giving a very quick refresher course on
what a quantum computer is and why we want one.
Friday, April 25th, 12.30 pm, T-Division Conference Room
Fault-tolerant quantum computation by anyons.
A. Kitaev, Landau Institute
I propose a class of stabilizer quantum codes associated with lattices on
the torus and other 2-D surfaces. Qubits live on the edges of the lattice
whereas the stabilizer operators correspond to the vertices and the faces.
These operators can be put together to make up a Hamiltonian with local
interaction. (This is a kind of penalty function; violating each
stabilizer condition costs energy). The ground state of this Hamiltonian
coincides with the protected space of the code. It is $4^g$-degenerate,
where $g$ is the genus of the surface. The degeneracy is persistant to local
perturbation. Under small enough perturbation, the splitting of the ground
state is estimated as $\exp(-aL)$, where $L$ is the smallest dimension of the
lattice. This model may be considered as a quantum memory, where
stability is attained at the physical level rather than by an explicit
error correction procedure.
Excitations in this model are anyons, meaning that the global wavefunction
acquires some phase factor when one excitation moves around the other. One
can operate on the ground state space by creating an exitation pair, moving
one of the exitations around the torus, and annihilating with the second one.
Unfortunately, such operations do not form a complete basis. It seems this
problem can be removed in a more general model (or models) where the Hilbert
space of a qubit have dimensionality $>2$. This model is related to Hopf
algebras.
In the new model, we don't need torus to have degeneracy. An $n$-particle
excited state on the plane is already degenerate, unless the particles
(excitations) come close to each other. These particles are nonabelian anyons,
i.e. the degenerate state undergoes a nontrivial unitary transformation when
one particle moves around the other. Such motion ("briading") can be considered
as fault-tolerant quantum computation. A measurement of the final state can
be performed by joining the particles in pairs and observing the result of
fusion.
Friday, May 2nd, 12:30 pm, T-Division Conference Room
Quantum Trajectory Simulations of Error Correction.
Todd Brun; ITP, UCSB
Quantum trajectory techniques enable one to replace a Markovian master
equation with a stochastic differential equation for a single quantum
state in Hilbert space; as such, they are useful as quantum Monte Carlo
techniques. The advantages and disadvantages of quantum trajectory
simulations for quantum error correction are discussed, along with the
results of simulations for simple and fault-tolerant correction algorithms,
and the object-oriented code used to generate the results.
Friday, May 9th, 12:30 pm, T-Division Conference Room
NMR Quantum Computing at Los Alamos: Theory and Experiment.
Manny Knill (CIC-3)
The fundamental ideas for using Nuclear Magnetic Resonance in bulk
quantum computation will be introduced. The main difference between
bulk quantum computation and the usual paradigm is that it uses an
incoherent sum of quantum computers which cannot be accessed
individually, both in the state preparation and in the readout
process. For the purposes of solving computational problems, bulk
quantum computation is as powerful as the traditional model. An
important step in establishing this fact involves transforming a mixed
input state into an effective pure state suitable for manipulation by
a traditional quantum algorithm. I will describe a simple
randomization method based on certain permutations to isolate the
desired pure states components of the initial mixed state.
Recent experimental results obtained here in Los Alamos will also be
discussed. A small quantum circuit to produce a quantum entanglement was
implemented in chloroform (CHCl_3) to demonstrate the non-classical
behavior of NMR. An overview of future plans will be given.
Friday, May 16th, 12:30 pm, T-Division Conference Room
Quantum Computation.
Richard Feynman
Video recording of a seminar that Richard Feynman gave at AT&T in 1985
on quantum computation.
Friday, May 23th, 12:30 pm, T-Division Conference Room
Ion Trap Quantum Computers: what are the prospects
for scaling them up to do "large" calculations?
Daniel James (T-4)
I will discuss the latest ideas about doing
quantum computing with trapped ions, and
discuss what are the ultimate fundamental
limitations on the technology.
Friday, May 30th, 12:30 pm, T-Division Conference Room
Nuclear Magnetic Resonance Spectroscopy: An Experimentally
Accessible Paradigm for Quantum Computing
Timothy F. Havel (Harvard)
We describe a new physical mechanism that is capable of
computation, along with experimental results which demonstrate
its potential. The mechanism is Nuclear Magnetic Resonance
Spectroscopy, or NMR. This approach is based on the fact that
the spin 1/2 nuclei of each molecule in a liquid sample are
largely isolated from the spins in all the other molecules. This
makes it possible to describe the state of the sample by a
reduced density matrix of size 2^n, where n is the number of
spins in one molecule, rather than 2^N where N ~ 10^23 is the
total number of spins in the sample. It also effectively makes
each molecule into an independent quantum computer, with a
decoherence time on the order of seconds. We call a computer
based on these principles an Ensemble Quantum Computer, or EQC.
In this talk we present experimental results which show how
this approach enables us to easily implement the usual
controlled-NOT or quantum XOR gate on single states as well as on
"coherent superpositions". We also show how standard techniques
in experimental NMR spectroscopy enable us to implement the
universal Toffoli gate. Scaling these experiments to molecules
with as many as ten inequivalent spins in them is
straightforward. A variety of experimental difficulties, in
particular the limited signal-to-noise of the receivers used to
collect NMR spectra, make scaling much past ten spins
challenging. Nevertheless, the availability of this exper-
imentally accessible paradigm for quantum computing should be of
considerable utility in further developing the theory and algor-
ithms that will be needed to solve significant problems by either
quantum computing, or by ensemble quantum computing.
List of Conferences and Seminars