3,344 research outputs found
The Equivalence of Sampling and Searching
In a sampling problem, we are given an input x, and asked to sample
approximately from a probability distribution D_x. In a search problem, we are
given an input x, and asked to find a member of a nonempty set A_x with high
probability. (An example is finding a Nash equilibrium.) In this paper, we use
tools from Kolmogorov complexity and algorithmic information theory to show
that sampling and search problems are essentially equivalent. More precisely,
for any sampling problem S, there exists a search problem R_S such that, if C
is any "reasonable" complexity class, then R_S is in the search version of C if
and only if S is in the sampling version. As one application, we show that
SampP=SampBQP if and only if FBPP=FBQP: in other words, classical computers can
efficiently sample the output distribution of every quantum circuit, if and
only if they can efficiently solve every search problem that quantum computers
can solve. A second application is that, assuming a plausible conjecture, there
exists a search problem R that can be solved using a simple linear-optics
experiment, but that cannot be solved efficiently by a classical computer
unless the polynomial hierarchy collapses. That application will be described
in a forthcoming paper with Alex Arkhipov on the computational complexity of
linear optics.Comment: 16 page
Integrated software package STAMP for minor planets
The integrated software package STAMP allowed for rapid and exact reproduction of the tables of the year-book 'Ephemerides of Minor Planets.' Additionally, STAMP solved the typical problems connected with the use of the year-book. STAMP is described. The year-book 'Ephemerides of Minor Planets' (EMP) is a publication used in many astronomical institutions around the world. It contains all the necessary information on the orbits of the numbered minor planets. Also, the astronomical coordinates are provided for each planet during its suitable observation period
Qubit Entanglement Breaking Channels
This paper continues the study of stochastic maps, or channels, which break
entanglement. We give a detailed description of entanglement-breaking qubit
channels, and show that such maps are precisely the convex hull of those known
as classical-quantum channels. We also review the complete positivity
conditions in a canonical parameterization and show how they lead to
entanglement-breaking conditions.Comment: Contains main results from section 2 of quant-ph/0207100 Version 2
corrects minor typos. Final version to appear in Rev. Math. Phy
An Universal Quantum Network - Quantum CPU
An universal quantum network which can implement a general quantum computing
is proposed. In this sense, it can be called the quantum central processing
unit (QCPU). For a given quantum computing, its realization of QCPU is just its
quantum network. QCPU is standard and easy-assemble because it only has two
kinds of basic elements and two auxiliary elements. QCPU and its realizations
are scalable, that is, they can be connected together, and so they can
construct the whole quantum network to implement the general quantum algorithm
and quantum simulating procedure.Comment: 8 pages, Revised versio
Optimizing local protocols implementing nonlocal quantum gates
We present a method of optimizing recently designed protocols for
implementing an arbitrary nonlocal unitary gate acting on a bipartite system.
These protocols use only local operations and classical communication with the
assistance of entanglement, and are deterministic while also being "one-shot",
in that they use only one copy of an entangled resource state. The optimization
is in the sense of minimizing the amount of entanglement used, and it is often
the case that less entanglement is needed than with an alternative protocol
using two-way teleportation.Comment: 11 pages, 1 figure. This is a companion paper to arXiv:1001.546
Optimum Quantum Error Recovery using Semidefinite Programming
Quantum error correction (QEC) is an essential element of physical quantum
information processing systems. Most QEC efforts focus on extending classical
error correction schemes to the quantum regime. The input to a noisy system is
embedded in a coded subspace, and error recovery is performed via an operation
designed to perfectly correct for a set of errors, presumably a large subset of
the physical noise process. In this paper, we examine the choice of recovery
operation. Rather than seeking perfect correction on a subset of errors, we
seek a recovery operation to maximize the entanglement fidelity for a given
input state and noise model. In this way, the recovery operation is optimum for
the given encoding and noise process. This optimization is shown to be
calculable via a semidefinite program (SDP), a well-established form of convex
optimization with efficient algorithms for its solution. The error recovery
operation may also be interpreted as a combining operation following a quantum
spreading channel, thus providing a quantum analogy to the classical diversity
combining operation.Comment: 7 pages, 3 figure
Entropy Bound for the Classical Capacity of a Quantum Channel Assisted by Classical Feedback
We prove that the classical capacity of an arbitrary quantum channel assisted
by a free classical feedback channel is bounded from above by the maximum
average output entropy of the quantum channel. As a consequence of this bound,
we conclude that a classical feedback channel does not improve the classical
capacity of a quantum erasure channel, and by taking into account energy
constraints, we conclude the same for a pure-loss bosonic channel. The method
for establishing the aforementioned entropy bound involves identifying an
information measure having two key properties: 1) it does not increase under a
one-way local operations and classical communication channel from the receiver
to the sender and 2) a quantum channel from sender to receiver cannot increase
the information measure by more than the maximum output entropy of the channel.
This information measure can be understood as the sum of two terms, with one
corresponding to classical correlation and the other to entanglement.Comment: v2: 6 pages, 1 figure, final version published in conference
proceeding
Magnetic qubits as hardware for quantum computers
We propose two potential realisations for quantum bits based on nanometre
scale magnetic particles of large spin S and high anisotropy molecular
clusters. In case (1) the bit-value basis states |0> and |1> are the ground and
first excited spin states Sz = S and S-1, separated by an energy gap given by
the ferromagnetic resonance (FMR) frequency. In case (2), when there is
significant tunnelling through the anisotropy barrier, the qubit states
correspond to the symmetric, |0>, and antisymmetric, |1>, combinations of the
two-fold degenerate ground state Sz = +- S. In each case the temperature of
operation must be low compared to the energy gap, \Delta, between the states
|0> and |1>. The gap \Delta in case (2) can be controlled with an external
magnetic field perpendicular to the easy axis of the molecular cluster. The
states of different molecular clusters and magnetic particles may be entangled
by connecting them by superconducting lines with Josephson switches, leading to
the potential for quantum computing hardware.Comment: 17 pages, 3 figure
Engineered Microbial Habitats for Health, Fuel, and Food
Microorganisms are of vital importance in medicine, in industry, and in the natural environment. In agricultural systems, bacteria fix nitrogen, protect crop roots from pathogens, and promote water retention in soils. In the biotech industry, microbes are harnessed to produce food, pharmaceuticals and biofuels. Microbes are essential for health, yet microbial pathogens continue to cause more human deaths worldwide than all forms of cancer combined. In each case, whether microbes are found in soil, in industry, or in vivo, micron-scale habitat conditions critically impact the structure and function of microbial communities. In our work, we design and build artificial microbial habitats that emulate selected micron-scale features of real microbial habitats. In this talk I will survey ongoing research projects including (i) a microfluidic biofilm array for screening antimicrobial combinations and measuring the effect of antimicrobial delivery rate on biofilm inhibition; (ii) a growth chamber with appropriately-scaled oxygen gradients for sustaining the complex hindgut microbiome of cellulose-degrading termites; and (iii) a testing device for seed coating technology aimed at enhancing crop yields in the developing world
- …