227 research outputs found
Quantum Computing with Very Noisy Devices
In theory, quantum computers can efficiently simulate quantum physics, factor
large numbers and estimate integrals, thus solving otherwise intractable
computational problems. In practice, quantum computers must operate with noisy
devices called ``gates'' that tend to destroy the fragile quantum states needed
for computation. The goal of fault-tolerant quantum computing is to compute
accurately even when gates have a high probability of error each time they are
used. Here we give evidence that accurate quantum computing is possible with
error probabilities above 3% per gate, which is significantly higher than what
was previously thought possible. However, the resources required for computing
at such high error probabilities are excessive. Fortunately, they decrease
rapidly with decreasing error probabilities. If we had quantum resources
comparable to the considerable resources available in today's digital
computers, we could implement non-trivial quantum computations at error
probabilities as high as 1% per gate.Comment: 47 page
Universal Quantum Computation with the Exchange Interaction
Experimental implementations of quantum computer architectures are now being
investigated in many different physical settings. The full set of requirements
that must be met to make quantum computing a reality in the laboratory [1] is
daunting, involving capabilities well beyond the present state of the art. In
this report we develop a significant simplification of these requirements that
can be applied in many recent solid-state approaches, using quantum dots [2],
and using donor-atom nuclear spins [3] or electron spins [4]. In these
approaches, the basic two-qubit quantum gate is generated by a tunable
Heisenberg interaction (the Hamiltonian is between spins and ), while the one-qubit gates require the control
of a local Zeeman field. Compared to the Heisenberg operation, the one-qubit
operations are significantly slower and require substantially greater materials
and device complexity, which may also contribute to increasing the decoherence
rate. Here we introduce an explicit scheme in which the Heisenberg interaction
alone suffices to exactly implement any quantum computer circuit, at a price of
a factor of three in additional qubits and about a factor of ten in additional
two-qubit operations. Even at this cost, the ability to eliminate the
complexity of one-qubit operations should accelerate progress towards these
solid-state implementations of quantum computation.Comment: revtex, 2 figures, this version appeared in Natur
Topics in Quantum Computers
I provide an introduction to quantum computers, describing how they might be
realized using language accessible to a solid state physicist. A listing of the
minimal requirements for creating a quantum computer is given. I also discuss
several recent developments in the area of quantum error correction, a subject
of importance not only to quantum computation, but also to some aspects of the
foundations of quantum theory.Comment: 22 pages, Latex, 1 eps figure, Paper to be published in "Mesoscopic
Electron Transport", edited by L. Kowenhoven, G. Schoen and L. Sohn, NATO ASI
Series E, Kluwer Ac. Publ., Dordrecht. v2: typos in refrences fixe
Unforgeable Quantum Encryption
We study the problem of encrypting and authenticating quantum data in the
presence of adversaries making adaptive chosen plaintext and chosen ciphertext
queries. Classically, security games use string copying and comparison to
detect adversarial cheating in such scenarios. Quantumly, this approach would
violate no-cloning. We develop new techniques to overcome this problem: we use
entanglement to detect cheating, and rely on recent results for characterizing
quantum encryption schemes. We give definitions for (i.) ciphertext
unforgeability , (ii.) indistinguishability under adaptive chosen-ciphertext
attack, and (iii.) authenticated encryption. The restriction of each definition
to the classical setting is at least as strong as the corresponding classical
notion: (i) implies INT-CTXT, (ii) implies IND-CCA2, and (iii) implies AE. All
of our new notions also imply QIND-CPA privacy. Combining one-time
authentication and classical pseudorandomness, we construct schemes for each of
these new quantum security notions, and provide several separation examples.
Along the way, we also give a new definition of one-time quantum authentication
which, unlike all previous approaches, authenticates ciphertexts rather than
plaintexts.Comment: 22+2 pages, 1 figure. v3: error in the definition of QIND-CCA2 fixed,
some proofs related to QIND-CCA2 clarifie
Quantum information can be negative
Given an unknown quantum state distributed over two systems, we determine how
much quantum communication is needed to transfer the full state to one system.
This communication measures the "partial information" one system needs
conditioned on it's prior information. It turns out to be given by an extremely
simple formula, the conditional entropy. In the classical case, partial
information must always be positive, but we find that in the quantum world this
physical quantity can be negative. If the partial information is positive, its
sender needs to communicate this number of quantum bits to the receiver; if it
is negative, the sender and receiver instead gain the corresponding potential
for future quantum communication. We introduce a primitive "quantum state
merging" which optimally transfers partial information. We show how it enables
a systematic understanding of quantum network theory, and discuss several
important applications including distributed compression, multiple access
channels and multipartite assisted entanglement distillation (localizable
entanglement). Negative channel capacities also receive a natural
interpretation
An area law for entanglement from exponential decay of correlations
Area laws for entanglement in quantum many-body systems give useful
information about their low-temperature behaviour and are tightly connected to
the possibility of good numerical simulations. An intuition from quantum
many-body physics suggests that an area law should hold whenever there is
exponential decay of correlations in the system, a property found, for
instance, in non-critical phases of matter. However, the existence of quantum
data-hiding state--that is, states having very small correlations, yet a volume
scaling of entanglement--was believed to be a serious obstruction to such an
implication. Here we prove that notwithstanding the phenomenon of data hiding,
one-dimensional quantum many-body states satisfying exponential decay of
correlations always fulfil an area law. To obtain this result we combine
several recent advances in quantum information theory, thus showing the
usefulness of the field for addressing problems in other areas of physics.Comment: 8 pages, 3 figures. Short version of arXiv:1206.2947 Nature Physics
(2013
Observation of Faraday rotation from a single confined spin
Ability to read-out the state of a single confined spin lies at the heart of
solid-state quantum information processing. While all-optical spin measurements
using Faraday rotation has been successfully implemented in ensembles of
semiconductor spins, read-out of a single semiconductor spin has only been
achieved using transport measurements based on spin-charge conversion. Here, we
demonstrate an all-optical dispersive measurement of the spin-state of a single
electron trapped in a semiconductor quantum dot. We obtain information on the
spin state through conditional Faraday rotation of a spectrally detuned optical
field, induced by the polarization- and spin-selective trion (charged quantum
dot) transitions. To assess the sensitivity of the technique, we use an
independent resonant laser for spin-state preparation. An all-optical
dispersive measurement on single spins has the important advantage of
channeling the measurement back-action onto a conjugate observable, thereby
allowing for repetitive or continuous quantum nondemolition (QND) read-out of
the spin-state. We infer from our results that there are of order unity
back-action induced spin-flip Raman scattering events within our measurement
timescale. Therefore, straightforward improvements such as the use of a
solid-immersion lens and higher efficiency detectors would allow for
back-action evading spin measurements, without the need for a cavity
Single valley Dirac fermions in zero-gap HgTe quantum wells
Dirac fermions have been studied intensively in condensed matter physics in
recent years. Many theoretical predictions critically depend on the number of
valleys where the Dirac fermions are realized. In this work, we report the
discovery of a two dimensional system with a single valley Dirac cone. We study
the transport properties of HgTe quantum wells grown at the critical thickness
separating between the topologically trivial and the quantum spin Hall phases.
At high magnetic fields, the quantized Hall plateaus demonstrate the presence
of a single valley Dirac point in this system. In addition, we clearly observe
the linear dispersion of the zero mode spin levels. Also the conductivity at
the Dirac point and its temperature dependence can be understood from single
valley Dirac fermion physics.Comment: version 2: supplementary material adde
The Uncertainty Principle in the Presence of Quantum Memory
The uncertainty principle, originally formulated by Heisenberg, dramatically
illustrates the difference between classical and quantum mechanics. The
principle bounds the uncertainties about the outcomes of two incompatible
measurements, such as position and momentum, on a particle. It implies that one
cannot predict the outcomes for both possible choices of measurement to
arbitrary precision, even if information about the preparation of the particle
is available in a classical memory. However, if the particle is prepared
entangled with a quantum memory, a device which is likely to soon be available,
it is possible to predict the outcomes for both measurement choices precisely.
In this work we strengthen the uncertainty principle to incorporate this case,
providing a lower bound on the uncertainties which depends on the amount of
entanglement between the particle and the quantum memory. We detail the
application of our result to witnessing entanglement and to quantum key
distribution.Comment: 5 pages plus 12 of supplementary information. Updated to match the
journal versio
All Optical Implementation of Multi-Spin Entanglement in a Semiconductor Quantum Well
We use ultrafast optical pulses and coherent techniques to create spin
entangled states of non-interacting electrons bound to donors (at least three)
and at least two Mn2+ ions in a CdTe quantum well. Our method, relying on the
exchange interaction between localized excitons and paramagnetic impurities,
can in principle be applied to entangle a large number of spins.Comment: 17 pages, 3 figure
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