218 research outputs found
Robust and parsimonious realisations of unitaries in the one-way model
We present a new set of generators for unitary maps over \otimes^n(C^2) which
differs from the traditional rotation-based generating set in that it uses a
single-parameter family of 1-qubit unitaries J(a), together with a single
2-qubit unitary controlled-Z.
Each generator is implementable in the one-way model using only two qubits,
and this leads to both parsimonious and robust implementations of general
unitaries. As an illustration, we give an implementation of the controlled-U
family which uses only 14 qubits, and has a 2-colourable underlying
entanglement graph (known to yield robust entangled states).Comment: 8 pages, 2 figures, keywords: unitary transformations,
measurement-based quantum computin
Diffusion Controlled Reactions, Fluctuation Dominated Kinetics, and Living Cell Biochemistry
In recent years considerable portion of the computer science community has
focused its attention on understanding living cell biochemistry and efforts to
understand such complication reaction environment have spread over wide front,
ranging from systems biology approaches, through network analysis (motif
identification) towards developing language and simulators for low level
biochemical processes. Apart from simulation work, much of the efforts are
directed to using mean field equations (equivalent to the equations of
classical chemical kinetics) to address various problems (stability,
robustness, sensitivity analysis, etc.). Rarely is the use of mean field
equations questioned. This review will provide a brief overview of the
situations when mean field equations fail and should not be used. These
equations can be derived from the theory of diffusion controlled reactions, and
emerge when assumption of perfect mixing is used
Rule-based Modelling and Tunable Resolution
We investigate the use of an extension of rule-based modelling for cellular
signalling to create a structured space of model variants. This enables the
incremental development of rule sets that start from simple mechanisms and
which, by a gradual increase in agent and rule resolution, evolve into more
detailed descriptions
Distributed measurement-based quantum computation
We develop a formal model for distributed measurement-based quantum
computations, adopting an agent-based view, such that computations are
described locally where possible. Because the network quantum state is in
general entangled, we need to model it as a global structure, reminiscent of
global memory in classical agent systems. Local quantum computations are
described as measurement patterns. Since measurement-based quantum computation
is inherently distributed, this allows us to extend naturally several concepts
of the measurement calculus, a formal model for such computations. Our goal is
to define an assembly language, i.e. we assume that computations are
well-defined and we do not concern ourselves with verification techniques. The
operational semantics for systems of agents is given by a probabilistic
transition system, and we define operational equivalence in a way that it
corresponds to the notion of bisimilarity. With this in place, we prove that
teleportation is bisimilar to a direct quantum channel, and this also within
the context of larger networks.Comment: 17 page
Quadratic Form Expansions for Unitaries
We introduce techniques to analyze unitary operations in terms of quadratic
form expansions, a form similar to a sum over paths in the computational basis
when the phase contributed by each path is described by a quadratic form over
. We show how to relate such a form to an entangled resource akin to
that of the one-way measurement model of quantum computing. Using this, we
describe various conditions under which it is possible to efficiently implement
a unitary operation U, either when provided a quadratic form expansion for U as
input, or by finding a quadratic form expansion for U from other input data.Comment: 20 pages, 3 figures; (extended version of) accepted submission to TQC
200
Commitment Against Front Running Attacks
We provide a game-theoretic analysis of the problem of front-running attacks.
We use it to distinguish attacks from legitimate competition among honest users
for having their transactions included earlier in the block. We also use it to
introduce an intuitive notion of the severity of front-running attacks. We then
study a simple commit-reveal protocol and discuss its properties. This protocol
has costs because it requires two messages and imposes a delay. However, we
show that it prevents the most severe front-running attacks while preserving
legitimate competition between users, guaranteeing that the earliest
transaction in a block belongs to the honest user who values it the most.
Furthermore, it reduces competition among attackers, which also benefits honest
users
Determinism in the one-way model
We introduce a flow condition on open graph states (graph states with inputs
and outputs) which guarantees globally deterministic behavior of a class of
measurement patterns defined over them. Dependent Pauli corrections are derived
for all such patterns, which equalize all computation branches, and only depend
on the underlying entanglement graph and its choice of inputs and outputs.
The class of patterns having flow is stable under composition and
tensorization, and has unitary embeddings as realizations. The restricted class
of patterns having both flow and reverse flow, supports an operation of
adjunction, and has all and only unitaries as realizations.Comment: 8 figures, keywords: measurement based quantum computing,
deterministic computing; Published version, including a new section on
circuit decompositio
Consistency of Automated Market Makers
Decentralised Finance has popularised Automated Market Makers (AMMs), but surprisingly little research has been done on their consistency. Can a single attacker extract risk-free revenue from an AMM, regardless of price or other users\u27 behaviour? In this paper, we investigate the consistency of a large class of AMMs, including the most widely used ones, and show that consistency holds
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