相关论文: Quantum and Stochastic Branching Programs of Bound…

(Abridged.) Quantum computers promise to solve some problems exponentially faster than traditional computers, but we still do not fully understand why this is the case. While the most studied model of quantum computation uses qubits, which…

Within the framework of statistical learning theory it is possible to bound the minimum number of samples required by a learner to reach a target accuracy. We show that if the bound on the accuracy is taken into account, quantum machine…

We define a class of stochastic processes based on evolutions and measurements of quantum systems, and consider the complexity of predicting their long-term behavior. It is shown that a very general class of decision problems regarding…

We show that one can approximate the least fixed point solution for a multivariate system of monotone probabilistic polynomial equations in time polynomial in both the encoding size of the system of equations and in log(1/\epsilon), where…

As we enter the era of useful quantum computers we need to better understand the limitations of classical support hardware, and develop mitigation techniques to ensure effective qubit utilisation. In this paper we discuss three key…

Variational Quantum Algorithms are one of the most promising candidates to yield the first industrially relevant quantum advantage. Being capable of arbitrary function approximation, they are often referred to as Quantum Neural Networks…

This paper studies the 1-2-1 half-duplex network model, where two half-duplex nodes can communicate only if they point `beams' at each other; otherwise, no signal can be exchanged or interference can be generated. The main result of this…

It is a widely believed, though unproven, conjecture that the capability of postselection increases the language recognition power of both probabilistic and quantum polynomial-time computers. It is also unknown whether polynomial-time…

Quantum circuits that are classically simulatable tell us when quantum computation becomes less powerful than or equivalent to classical computation. Such classically simulatable circuits are of importance because they illustrate what makes…

Small numbers of qubits are one of the primary constraints on the near-term deployment of advantageous quantum computing. To mitigate this constraint, techniques have been developed to break up a large quantum computation into smaller…

We analyze Kumar's recent quadratic algebraic branching program size lower bound proof method (CCC 2017) for the power sum polynomial. We present a refinement of this method that gives better bounds in some cases. The lower bound relies on…

We present a classical protocol, using the matrix product state representation, to simulate cluster-state quantum computation at a cost polynomial in the number of qubits in the cluster and exponential in d -- the width of the cluster. We…

According to the statistical interpretation of quantum theory, quantum computers form a distinguished class of probabilistic machines (PMs) by encoding n qubits in 2n pbits (random binary variables). This raises the possibility of a…

In this paper, we study some bounds for nonconvex quadratically constrained quadratic programs. We propose two types of bounds for quadratically constrained quadratic programs, quadratic and cubic bounds. For quadratic bounds, we use affine…

In this paper we generalize N-fold integer programs and two-stage integer programs with N scenarios to N-fold 4-block decomposable integer programs. We show that for fixed blocks but variable N, these integer programs are polynomial-time…

We investigate the amount of noise required to turn a universal quantum gate set into one that can be efficiently modelled classically. This question is useful for providing upper bounds on fault tolerant thresholds, and for understanding…

Bosonic quantum systems operate in an infinite-dimensional Hilbert space, unlike discrete-variable quantum systems. This distinct mathematical structure leads to fundamental differences in quantum information processing, such as an…

The limit of infinite width allows for substantial simplifications in the analytical study of over-parameterised neural networks. With a suitable random initialisation, an extremely large network exhibits an approximately Gaussian…

We study the power of the bounded-width consistency algorithm in the context of the fixed-template Promise Constraint Satisfaction Problem (PCSP). Our main technical finding is that the template of every PCSP that is solvable in bounded…

Quantum convolutional neural networks (QCNNs) offer a promising architecture for near-term quantum machine learning by combining hierarchical feature extraction with modest parameter growth. However, any QCNN operating on classical data…