774 research outputs found
Quantum Algorithm for Triangle Finding in Sparse Graphs
This paper presents a quantum algorithm for triangle finding over sparse
graphs that improves over the previous best quantum algorithm for this task by
Buhrman et al. [SIAM Journal on Computing, 2005]. Our algorithm is based on the
recent -query algorithm given by Le Gall [FOCS 2014] for
triangle finding over dense graphs (here denotes the number of vertices in
the graph). We show in particular that triangle finding can be solved with
queries for some constant whenever the graph
has at most edges for some constant .Comment: 13 page
Quantum walks can find a marked element on any graph
We solve an open problem by constructing quantum walks that not only detect
but also find marked vertices in a graph. In the case when the marked set
consists of a single vertex, the number of steps of the quantum walk is
quadratically smaller than the classical hitting time of any
reversible random walk on the graph. In the case of multiple marked
elements, the number of steps is given in terms of a related quantity
which we call extended hitting time.
Our approach is new, simpler and more general than previous ones. We
introduce a notion of interpolation between the random walk and the
absorbing walk , whose marked states are absorbing. Then our quantum walk
is simply the quantum analogue of this interpolation. Contrary to previous
approaches, our results remain valid when the random walk is not
state-transitive. We also provide algorithms in the cases when only
approximations or bounds on parameters (the probability of picking a
marked vertex from the stationary distribution) and are
known.Comment: 50 page
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
Genetic steps to organ laterality in zebrafish.
All internal organs are asymmetric along the left-right axis. Here we report a genetic screen to discover mutations which perturb organ laterality. Our particular focus is upon whether, and how, organs are linked to each other as they achieve their laterally asymmetric positions. We generated mutations by ENU mutagenesis and examined F3 progeny using a cocktail of probes that reveal early primordia of heart, gut, liver and pancreas. From the 750 genomes examined, we isolated seven recessive mutations which affect the earliest left-right positioning of one or all of the organs. None of these mutations caused discernable defects elsewhere in the embryo at the stages examined. This is in contrast to those mutations we reported previously (Chen et al., 1997) which, along with left-right abnormalities, cause marked perturbation in gastrulation, body form or midline structures. We find that the mutations can be classified on the basis of whether they perturb relationships among organ laterality. In Class 1 mutations, none of the organs manifest any left-right asymmetry. The heart does not jog to the left and normally leftpredominant BMP4 in the early heart tube remains symmetric. The gut tends to remain midline. There frequently is a remarkable bilateral duplication of liver and pancreas. Embryos with Class 2 mutations have organotypic asymmetry but, in any given embryo, organ positions can be normal, reversed or randomized. Class 3 reveals a hitherto unsuspected gene that selectively affects laterality of heart. We find that visceral organ positions are predicted by the direction of the preceding cardiac jog. We interpret this as suggesting that normally there is linkage between cardiac and visceral organ laterality. Class 1 mutations, we suggest, effectively remove the global laterality signals, with the consequence that organ positions are effectively symmetrical. Embryos with Class 2 mutations do manifest linkage among organs, but it may be reversed, suggesting that the global signals may be present but incorrectly orientated in some of the embryos. That laterality decisions of organs may be independently perturbed, as in the Class 3 mutation, indicates that there are distinctive pathways for reception and organotypic interpretation of the global signals
LGP2 plays a critical role in sensitizing mda-5 to activation by double-stranded RNA.
The DExD/H box RNA helicases retinoic acid-inducible gene-I (RIG-I) and melanoma differentiation associated gene-5 (mda-5) sense viral RNA in the cytoplasm of infected cells and activate signal transduction pathways that trigger the production of type I interferons (IFNs). Laboratory of genetics and physiology 2 (LGP2) is thought to influence IFN production by regulating the activity of RIG-I and mda-5, although its mechanism of action is not known and its function is controversial. Here we show that expression of LGP2 potentiates IFN induction by polyinosinic-polycytidylic acid [poly(I:C)], commonly used as a synthetic mimic of viral dsRNA, and that this is particularly significant at limited levels of the inducer. The observed enhancement is mediated through co-operation with mda-5, which depends upon LGP2 for maximal activation in response to poly(I:C). This co-operation is dependent upon dsRNA binding by LGP2, and the presence of helicase domain IV, both of which are required for LGP2 to interact with mda-5. In contrast, although RIG-I can also be activated by poly(I:C), LGP2 does not have the ability to enhance IFN induction by RIG-I, and instead acts as an inhibitor of RIG-I-dependent poly(I:C) signaling. Thus the level of LGP2 expression is a critical factor in determining the cellular sensitivity to induction by dsRNA, and this may be important for rapid activation of the IFN response at early times post-infection when the levels of inducer are low
Delegating Quantum Computation in the Quantum Random Oracle Model
A delegation scheme allows a computationally weak client to use a server's
resources to help it evaluate a complex circuit without leaking any information
about the input (other than its length) to the server. In this paper, we
consider delegation schemes for quantum circuits, where we try to minimize the
quantum operations needed by the client. We construct a new scheme for
delegating a large circuit family, which we call "C+P circuits". "C+P" circuits
are the circuits composed of Toffoli gates and diagonal gates. Our scheme is
non-interactive, requires very little quantum computation from the client
(proportional to input length but independent of the circuit size), and can be
proved secure in the quantum random oracle model, without relying on additional
assumptions, such as the existence of fully homomorphic encryption. In practice
the random oracle can be replaced by an appropriate hash function or block
cipher, for example, SHA-3, AES.
This protocol allows a client to delegate the most expensive part of some
quantum algorithms, for example, Shor's algorithm. The previous protocols that
are powerful enough to delegate Shor's algorithm require either many rounds of
interactions or the existence of FHE. The protocol requires asymptotically
fewer quantum gates on the client side compared to running Shor's algorithm
locally.
To hide the inputs, our scheme uses an encoding that maps one input qubit to
multiple qubits. We then provide a novel generalization of classical garbled
circuits ("reversible garbled circuits") to allow the computation of Toffoli
circuits on this encoding. We also give a technique that can support the
computation of phase gates on this encoding.
To prove the security of this protocol, we study key dependent message(KDM)
security in the quantum random oracle model. KDM security was not previously
studied in quantum settings.Comment: 41 pages, 1 figures. Update to be consistent with the proceeding
versio
Decision problems with quantum black boxes
We examine how to distinguish between unitary operators, when the exact form
of the possible operators is not known. Instead we are supplied with "programs"
in the form of unitary transforms, which can be used as references for
identifying the unknown unitary transform. All unitary transforms should be
used as few times as possible. This situation is analoguous to programmable
state discrimination. One difference, however, is that the quantum state to
which we apply the unitary transforms may be entangled, leading to a richer
variety of possible strategies. By suitable selection of an input state and
generalized measurement of the output state, both unambiguous and minimum-error
discrimination can be achieved. Pairwise comparison of operators, comparing
each transform to be identified with a program transform, is often a useful
strategy. There are, however, situations in which more complicated strategies
perform better. This is the case especially when the number of allowed
applications of program operations is different from the number of the
transforms to be identified
Quantum Algorithm for Dynamic Programming Approach for DAGs. Applications for Zhegalkin Polynomial Evaluation and Some Problems on DAGs
In this paper, we present a quantum algorithm for dynamic programming
approach for problems on directed acyclic graphs (DAGs). The running time of
the algorithm is , and the running time of the
best known deterministic algorithm is , where is the number of
vertices, is the number of vertices with at least one outgoing edge;
is the number of edges. We show that we can solve problems that use OR,
AND, NAND, MAX and MIN functions as the main transition steps. The approach is
useful for a couple of problems. One of them is computing a Boolean formula
that is represented by Zhegalkin polynomial, a Boolean circuit with shared
input and non-constant depth evaluating. Another two are the single source
longest paths search for weighted DAGs and the diameter search problem for
unweighted DAGs.Comment: UCNC2019 Conference pape
Decoherence induced deformation of the ground state in adiabatic quantum computation
Despite more than a decade of research on adiabatic quantum computation
(AQC), its decoherence properties are still poorly understood. Many theoretical
works have suggested that AQC is more robust against decoherence, but a
quantitative relation between its performance and the qubits' coherence
properties, such as decoherence time, is still lacking. While the thermal
excitations are known to be important sources of errors, they are predominantly
dependent on temperature but rather insensitive to the qubits' coherence. Less
understood is the role of virtual excitations, which can also reduce the ground
state probability even at zero temperature. Here, we introduce normalized
ground state fidelity as a measure of the decoherence-induced deformation of
the ground state due to virtual transitions. We calculate the normalized
fidelity perturbatively at finite temperatures and discuss its relation to the
qubits' relaxation and dephasing times, as well as its projected scaling
properties.Comment: 10 pages, 3 figure
Operational approach to open dynamics and quantifying initial correlations
A central aim of physics is to describe the dynamics of physical systems.
Schrodinger's equation does this for isolated quantum systems. Describing the
time evolution of a quantum system that interacts with its environment, in its
most general form, has proved to be difficult because the dynamics is dependent
on the state of the environment and the correlations with it. For discrete
processes, such as quantum gates or chemical reactions, quantum process
tomography provides the complete description of the dynamics, provided that the
initial states of the system and the environment are independent of each other.
However, many physical systems are correlated with the environment at the
beginning of the experiment. Here, we give a prescription of quantum process
tomography that yields the complete description of the dynamics of the system
even when the initial correlations are present. Surprisingly, our method also
gives quantitative expressions for the initial correlation.Comment: Completely re-written for clarity of presentation. 15 pages and 2
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