950 research outputs found
Introduction to Quantum Error Correction
In this introduction we motivate and explain the ``decoding'' and
``subsystems'' view of quantum error correction. We explain how quantum noise
in QIP can be described and classified, and summarize the requirements that
need to be satisfied for fault tolerance. Considering the capabilities of
currently available quantum technology, the requirements appear daunting. But
the idea of ``subsystems'' shows that these requirements can be met in many
different, and often unexpected ways.Comment: 44 pages, to appear in LA Science. Hyperlinked PDF at
http://www.c3.lanl.gov/~knill/qip/ecprhtml/ecprpdf.pdf, HTML at
http://www.c3.lanl.gov/~knill/qip/ecprhtm
Multiqubit Spin
It is proposed that the state space of a quantum object with a complicated
discrete spectrum can be used as a basis for multiqubit recording and
processing of information in a quantum computer. As an example, nuclear spin
3/2 is considered. The possibilities of writing and reading two quantum bits of
information, preparation of the initial state, implementation of the "rotation"
and "controlled negation" operations, which are sufficient for constructing any
algorithms, are demonstrated.Comment: 7 pages, PostScript, no figures; translation of Pis'ma Zh. Eksp.
Teor. Fiz. 70, No. 1, pp. 59-63, 10 July 1999; (Submitted 29 April 1999;
resubmitted 2 June 1999
Using error correction to determine the noise model
Quantum error correcting codes have been shown to have the ability of making
quantum information resilient against noise. Here we show that we can use
quantum error correcting codes as diagnostics to characterise noise. The
experiment is based on a three-bit quantum error correcting code carried out on
a three-qubit nuclear magnetic resonance (NMR) quantum information processor.
Utilizing both engineered and natural noise, the degree of correlations present
in the noise affecting a two-qubit subsystem was determined. We measured a
correlation factor of c=0.5+/-0.2 using the error correction protocol, and
c=0.3+/-0.2 using a standard NMR technique based on coherence pathway
selection. Although the error correction method demands precise control, the
results demonstrate that the required precision is achievable in the
liquid-state NMR setting.Comment: 10 pages, 3 figures. Added discussion section, improved figure
Bounds on the entanglability of thermal states in liquid-state nuclear magnetic resonance
The role of mixed state entanglement in liquid-state nuclear magnetic
resonance (NMR) quantum computation is not yet well-understood. In particular,
despite the success of quantum information processing with NMR, recent work has
shown that quantum states used in most of those experiments were not entangled.
This is because these states, derived by unitary transforms from the thermal
equilibrium state, were too close to the maximally mixed state. We are thus
motivated to determine whether a given NMR state is entanglable - that is, does
there exist a unitary transform that entangles the state? The boundary between
entanglable and nonentanglable thermal states is a function of the spin system
size and its temperature . We provide new bounds on the location of this
boundary using analytical and numerical methods; our tightest bound scales as
, giving a lower bound requiring at least proton
spins to realize an entanglable thermal state at typical laboratory NMR
magnetic fields. These bounds are tighter than known bounds on the
entanglability of effective pure states.Comment: REVTeX4, 15 pages, 4 figures (one large figure: 414 K
Compiling gate networks on an Ising quantum computer
Here we describe a simple mechanical procedure for compiling a quantum gate
network into the natural gates (pulses and delays) for an Ising quantum
computer. The aim is not necessarily to generate the most efficient pulse
sequence, but rather to develop an efficient compilation algorithm that can be
easily implemented in large spin systems. The key observation is that it is not
always necessary to refocus all the undesired couplings in a spin system.
Instead the coupling evolution can simply be tracked and then corrected at some
later time. Although described within the language of NMR the algorithm is
applicable to any design of quantum computer based on Ising couplings.Comment: 5 pages RevTeX4 including 4 figures. Will submit to PR
Introduction to Quantum Information Processing
As a result of the capabilities of quantum information, the science of
quantum information processing is now a prospering, interdisciplinary field
focused on better understanding the possibilities and limitations of the
underlying theory, on developing new applications of quantum information and on
physically realizing controllable quantum devices. The purpose of this primer
is to provide an elementary introduction to quantum information processing, and
then to briefly explain how we hope to exploit the advantages of quantum
information. These two sections can be read independently. For reference, we
have included a glossary of the main terms of quantum information.Comment: 48 pages, to appear in LA Science. Hyperlinked PDF at
http://www.c3.lanl.gov/~knill/qip/prhtml/prpdf.pdf, HTML at
http://www.c3.lanl.gov/~knill/qip/prhtm
Implementation of the Five Qubit Error Correction Benchmark
The smallest quantum code that can correct all one-qubit errors is based on
five qubits. We experimentally implemented the encoding, decoding and
error-correction quantum networks using nuclear magnetic resonance on a five
spin subsystem of labeled crotonic acid. The ability to correct each error was
verified by tomography of the process. The use of error-correction for
benchmarking quantum networks is discussed, and we infer that the fidelity
achieved in our experiment is sufficient for preserving entanglement.Comment: 6 pages with figure
Efficient solvability of Hamiltonians and limits on the power of some quantum computational models
We consider quantum computational models defined via a Lie-algebraic theory.
In these models, specified initial states are acted on by Lie-algebraic quantum
gates and the expectation values of Lie algebra elements are measured at the
end. We show that these models can be efficiently simulated on a classical
computer in time polynomial in the dimension of the algebra, regardless of the
dimension of the Hilbert space where the algebra acts. Similar results hold for
the computation of the expectation value of operators implemented by a
gate-sequence. We introduce a Lie-algebraic notion of generalized mean-field
Hamiltonians and show that they are efficiently ("exactly") solvable by means
of a Jacobi-like diagonalization method. Our results generalize earlier ones on
fermionic linear optics computation and provide insight into the source of the
power of the conventional model of quantum computation.Comment: 6 pages; no figure
Classicality of quantum information processing
The ultimate goal of the classicality programme is to quantify the amount of
quantumness of certain processes. Here, classicality is studied for a
restricted type of process: quantum information processing (QIP). Under special
conditions, one can force some qubits of a quantum computer into a classical
state without affecting the outcome of the computation. The minimal set of
conditions is described and its structure is studied. Some implications of this
formalism are the increase of noise robustness, a proof of the quantumness of
mixed state quantum computing and a step forward in understanding the very
foundation of QIP.Comment: Minor changes, published in Phys. Rev. A 65, 42319 (2002
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