Related papers: Classical-Quantum Separations in Certain Classes o…
In this paper, we consider decision trees that use both queries based on one attribute each and queries based on hypotheses about values of all attributes. Such decision trees are similar to ones studied in exact learning, where not only…
Noise is often regarded as anathema to quantum computation, but in some settings it can be an unlikely ally. We consider the problem of learning the class of $n$-bit parity functions by making queries to a quantum example oracle. In the…
Recent years have seen significant activity on the problem of using data for the purpose of learning properties of quantum systems or of processing classical or quantum data via quantum computing. As in classical learning, quantum learning…
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…
This manuscript presents the Quantum Finite Element Method (Q-FEM) developed for use in noisy intermediate-scale quantum (NISQ) computers and employs the variational quantum linear solver (VQLS) algorithm. The proposed method leverages the…
We present a logical separability analysis for a functional quantum computation language. This logic is inspired by previous works on logical analysis of aliasing for imperative functional programs. Both analyses share similarities notably…
Several well-studied models of access to data samples, including statistical queries, local differential privacy and low-communication algorithms rely on queries that provide information about a function of a single sample. (For example, a…
Given a Boolean function $f:\{0,1\}^n\to\{0,1\}$, the goal in the usual query model is to compute $f$ on an unknown input $x \in \{0,1\}^n$ while minimizing the number of queries to $x$. One can also consider a "distinguishing" problem…
We study quantum algorithms working on classical probability distributions. We formulate four different models for accessing a classical probability distribution on a quantum computer, which are derived from previous work on the topic, and…
Quantum versus classical separation plays a central role in understanding the advantages of quantum computation. In this paper, we present the first exponential separation between quantum and bounded-error randomized communication…
Dempster-Shafer Theory (DST) as an effective and robust framework for handling uncertain information is applied in decision-making and pattern classification. Unfortunately, its real-time application is limited by the exponential…
Resolution is the rule of inference at the basis of most procedures for automated reasoning. In these procedures, the input formula is first translated into an equisatisfiable formula in conjunctive normal form (CNF) and then represented as…
The complex systems with edge computing require a huge amount of multi-feature data to extract appropriate insights for their decision making, so it is important to find a feasible feature selection method to improve the computational…
Based on the recent breakthrough of Huang (2019), we show that for any total Boolean function $f$, $\bullet \quad \mathrm{deg}(f) = O(\widetilde{\mathrm{deg}}(f)^2)$: The degree of $f$ is at most quadratic in the approximate degree of $f$.…
In this work, we develop a highly efficient representation of functions and differential operators based on Fourier analysis. Using this representation, we create a variational hybrid quantum algorithm to solve static, Schr\"odinger-type,…
Most problems in uncertainty quantification, despite its ubiquitousness in scientific computing, applied mathematics and data science, remain formidable on a classical computer. For uncertainties that arise in partial differential equations…
This work studies the quantum query complexity of Boolean functions in a scenario where it is only required that the query algorithm succeeds with a probability strictly greater than 1/2. We show that, just as in the communication…
In this paper, we initiate study of the computational power of adaptive and non-adaptive monotone decision trees - decision trees where each query is a monotone function on the input bits. In the most general setting, the monotone decision…
We study the quantum query complexity of the Boolean hidden shift problem. Given oracle access to f(x+s) for a known Boolean function f, the task is to determine the n-bit string s. The quantum query complexity of this problem depends…
We consider quantum versions of two well-studied classical learning models: Angluin's model of exact learning from membership queries and Valiant's Probably Approximately Correct (PAC) model of learning from random examples. We give…