Related papers: Exponential Separation between Quantum and Classic…
The completeness of quantum mechanics in predictive power is a central question in its foundational study. While most investigations focus on two-dimensional systems, high-dimensional systems are more general and widely applicable. Building…
Finite-difference methods are a class of algorithms designed to solve black-box optimization problems by approximating a gradient of the target function on a set of directions. In black-box optimization, the non-smooth setting is…
Introduced by Darwiche (2011), sentential decision diagrams (SDDs) are essentially as tractable as ordered binary decision diagrams (OBDDs), but tend to be more succinct in practice. This makes SDDs a prominent representation language, with…
In this paper, we investigate the problem of \textit{episodic reinforcement learning} with quantum oracles for state evolution. To this end, we propose an \textit{Upper Confidence Bound} (UCB) based quantum algorithmic framework to…
This paper revisits the ordered statistics decoding (OSD). It provides a comprehensive analysis of the OSD algorithm by characterizing the statistical properties, evolution and the distribution of the Hamming distance and weighted Hamming…
Quantum algorithms have emerged as a promising tool to solve combinatorial optimization problems. The quantum walk optimization algorithm (QWOA) is one such variational approach that has recently gained attention. In the broader context of…
We study the gradient-based training of large-depth residual networks (ResNets) from standard random initializations. We show that infinite-depth ResNets behave as if they were infinitely wide, regardless of their actual width. More…
Solving linear ordinary differential equations (ODE) is one of the most promising applications for quantum computers to demonstrate exponential advantages. The challenge of designing a quantum ODE algorithm is how to embed non-unitary…
Reliability-based design optimization (RBDO) approaches aim to identify the best design of an engineering problem, whilst the probability of failure (PoF) remains below an acceptable value. Thus, the incorporation of the sharpest bounds on…
Sequential Quantum State Discrimination (SQSD) can be naturally framed as a sequential decision-making problem: at each time step, an agent must decide whether to perform an additional measurement to gather more information or to conclude…
The width measure treedepth, also known as vertex ranking, centered coloring and elimination tree height, is a well-established notion which has recently seen a resurgence of interest. Since graphs of bounded treedepth are more restricted…
We introduced decomposable negation normal form (DNNF) recently as a tractable form of propositional theories, and provided a number of powerful logical operations that can be performed on it in polynomial time. We also presented an…
Recent theoretical results in quantum machine learning have demonstrated a general trade-off between the expressive power of quantum neural networks (QNNs) and their trainability; as a corollary of these results, practical exponential…
Kernel methods augmented with random features give scalable algorithms for learning from big data. But it has been computationally hard to sample random features according to a probability distribution that is optimized for the data, so as…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
A binary string of length $2^k$ induces the Boolean function of $k$ variables whose Shannon expansion is the given binary string. This Boolean function then is representable via a unique reduced ordered binary decision diagram (ROBDD). The…
Classical optimization is a cornerstone of the success of variational quantum algorithms, which often require determining the derivatives of the cost function relative to variational parameters. The computation of the cost function and its…
The hidden shift problem is a natural place to look for new separations between classical and quantum models of computation. One advantage of this problem is its flexibility, since it can be defined for a whole range of functions and a…
Applications of decision diagrams in quantum circuit analysis have been an active research area. Our work introduces FeynmanDD, a new method utilizing standard and multi-terminal decision diagrams for quantum circuit simulation and…
Despite significant effort, the quantum machine learning community has only demonstrated quantum learning advantages for artificial cryptography-inspired datasets when dealing with classical data. In this paper we address the challenge of…