49,401 research outputs found
Complexity-Theoretic Limitations on Blind Delegated Quantum Computation
Blind delegation protocols allow a client to delegate a computation to a
server so that the server learns nothing about the input to the computation
apart from its size. For the specific case of quantum computation we know that
blind delegation protocols can achieve information-theoretic security. In this
paper we prove, provided certain complexity-theoretic conjectures are true,
that the power of information-theoretically secure blind delegation protocols
for quantum computation (ITS-BQC protocols) is in a number of ways constrained.
In the first part of our paper we provide some indication that ITS-BQC
protocols for delegating computations in which the client and the
server interact only classically are unlikely to exist. We first show that
having such a protocol with bits of classical communication implies
that . We conjecture that this
containment is unlikely by providing an oracle relative to which . We then show that if an ITS-BQC protocol
exists with polynomial classical communication and which allows the client to
delegate quantum sampling problems, then there exist non-uniform circuits of
size , making polynomially-sized queries to
an oracle, for computing the permanent of an matrix.
The second part of our paper concerns ITS-BQC protocols in which the client and
the server engage in one round of quantum communication and then exchange
polynomially many classical messages. First, we provide a complexity-theoretic
upper bound on the types of functions that could be delegated in such a
protocol, namely . Then, we show that
having such a protocol for delegating -hard functions implies
.Comment: Improves upon, supersedes and corrects our earlier submission, which
previously included an error in one of the main theorem
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Complexity Theory
Computational Complexity Theory is the mathematical study of the intrinsic power and limitations of computational resources like time, space, or randomness. The current workshop focused on recent developments in various sub-areas including arithmetic complexity, Boolean complexity, communication complexity, cryptography, probabilistic proof systems, pseudorandomness, and quantum computation. Many of the developements are related to diverse mathematical ïŹelds such as algebraic geometry, combinatorial number theory, probability theory, quantum mechanics, representation theory, and the theory of error-correcting codes
Recommended from our members
Complexity Theory
Computational Complexity Theory is the mathematical study of the intrinsic power and limitations of computational resources like time, space, or randomness. The current workshop focused on recent developments in various sub-areas including arithmetic complexity, Boolean complexity, communication complexity, cryptography, probabilistic proof systems, pseudorandomness, and quantum computation. Many of the developments are related to diverse mathematical ïŹelds such as algebraic geometry, combinatorial number theory, probability theory, representation theory, and the theory of error-correcting codes
Exact and Efficient Simulation of Concordant Computation
Concordant computation is a circuit-based model of quantum computation for
mixed states, that assumes that all correlations within the register are
discord-free (i.e. the correlations are essentially classical) at every step of
the computation. The question of whether concordant computation always admits
efficient simulation by a classical computer was first considered by B. Eastin
in quant-ph/1006.4402v1, where an answer in the affirmative was given for
circuits consisting only of one- and two-qubit gates. Building on this work, we
develop the theory of classical simulation of concordant computation. We
present a new framework for understanding such computations, argue that a
larger class of concordant computations admit efficient simulation, and provide
alternative proofs for the main results of quant-ph/1006.4402v1 with an
emphasis on the exactness of simulation which is crucial for this model. We
include detailed analysis of the arithmetic complexity for solving equations in
the simulation, as well as extensions to larger gates and qudits. We explore
the limitations of our approach, and discuss the challenges faced in developing
efficient classical simulation algorithms for all concordant computations.Comment: 16 page
The Impact of Imperfect Timekeeping on Quantum Control
In order to unitarily evolve a quantum system, an agent requires knowledge of
time, a parameter which no physical clock can ever perfectly characterise. In
this letter, we study how limitations on acquiring knowledge of time impact
controlled quantum operations in different paradigms. We show that the quality
of timekeeping an agent has access to limits the gate complexity they are able
to achieve within circuit-based quantum computation. It also exponentially
impacts state preparation for measurement-based quantum computation. Another
area where quantum control is relevant is quantum thermodynamics. In that
context, we show that cooling a qubit can be achieved using a timer of
arbitrary quality for control: timekeeping error only impacts the rate of
cooling and not the achievable temperature. Our analysis combines techniques
from the study of autonomous quantum clocks and the theory of quantum channels
to understand the effect of imperfect timekeeping on controlled quantum
dynamics.Comment: 5 + 7 pages, 2 figure
Quark: A Gradient-Free Quantum Learning Framework for Classification Tasks
As more practical and scalable quantum computers emerge, much attention has
been focused on realizing quantum supremacy in machine learning. Existing
quantum ML methods either (1) embed a classical model into a target Hamiltonian
to enable quantum optimization or (2) represent a quantum model using
variational quantum circuits and apply classical gradient-based optimization.
The former method leverages the power of quantum optimization but only supports
simple ML models, while the latter provides flexibility in model design but
relies on gradient calculation, resulting in barren plateau (i.e., gradient
vanishing) and frequent classical-quantum interactions. To address the
limitations of existing quantum ML methods, we introduce Quark, a gradient-free
quantum learning framework that optimizes quantum ML models using quantum
optimization. Quark does not rely on gradient computation and therefore avoids
barren plateau and frequent classical-quantum interactions. In addition, Quark
can support more general ML models than prior quantum ML methods and achieves a
dataset-size-independent optimization complexity. Theoretically, we prove that
Quark can outperform classical gradient-based methods by reducing model query
complexity for highly non-convex problems; empirically, evaluations on the Edge
Detection and Tiny-MNIST tasks show that Quark can support complex ML models
and significantly reduce the number of measurements needed for discovering
near-optimal weights for these tasks.Comment: under revie
Variational Quantum Neural Networks (VQNNS) in Image Classification
Quantum machine learning has established as an interdisciplinary field to
overcome limitations of classical machine learning and neural networks. This is
a field of research which can prove that quantum computers are able to solve
problems with complex correlations between inputs that can be hard for
classical computers. This suggests that learning models made on quantum
computers may be more powerful for applications, potentially faster computation
and better generalization on less data. The objective of this paper is to
investigate how training of quantum neural network (QNNs) can be done using
quantum optimization algorithms for improving the performance and time
complexity of QNNs. A classical neural network can be partially quantized to
create a hybrid quantum-classical neural network which is used mainly in
classification and image recognition. In this paper, a QNN structure is made
where a variational parameterized circuit is incorporated as an input layer
named as Variational Quantum Neural Network (VQNNs). We encode the cost
function of QNNs onto relative phases of a superposition state in the Hilbert
space of the network parameters. The parameters are tuned with an iterative
quantum approximate optimisation (QAOA) mixer and problem hamiltonians. VQNNs
is experimented with MNIST digit recognition (less complex) and crack image
classification datasets (more complex) which converges the computation in
lesser time than QNN with decent training accuracy
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