Related papers: A quantum algorithm to estimate the closeness to t…
We present a constructive method to create quantum circuits that implement oracles $|x\rangle|y\rangle|0\rangle^k \mapsto |x\rangle|y \oplus f(x)\rangle|0\rangle^k$ for $n$-variable Boolean functions $f$ with low $T$-count. In our method…
In Exact Quantum Query model, almost all of the Boolean functions for which non-trivial query algorithms exist are symmetric in nature. The most well known techniques in this domain exploit parity decision trees, in which the parity of two…
Two contrasting algorithmic paradigms for constraint satisfaction problems are successive local explorations of neighboring configurations versus producing new configurations using global information about the problem (e.g. approximating…
We consider minimization of a smooth nonconvex function with inexact oracle access to gradient and Hessian (without assuming access to the function value) to achieve approximate second-order optimality. A novel feature of our method is that…
The Quantum Approximate Optimization Algorithm (QAOA) is designed to run on a gate model quantum computer and has shallow depth. It takes as input a combinatorial optimization problem and outputs a string that satisfies a high fraction of…
Sequence classification algorithms, such as SVM, require a definition of distance (similarity) measure between two sequences. A commonly used notion of similarity is the number of matches between $k$-mers ($k$-length subsequences) in the…
We consider the problems of weighted constrained sampling and weighted model counting, where we are given a propositional formula and a weight for each world. The first problem consists of sampling worlds with a probability proportional to…
Orthogonal Monte Carlo (OMC) is a very effective sampling algorithm imposing structural geometric conditions (orthogonality) on samples for variance reduction. Due to its simplicity and superior performance as compared to its Quasi Monte…
We give a quantum algorithm for evaluating a class of boolean formulas (such as NAND trees and 3-majority trees) on a restricted set of inputs. Due to the structure of the allowed inputs, our algorithm can evaluate a depth $n$ tree using…
Given an implicit $n\times n$ matrix $A$ with oracle access $x^TA x$ for any $x\in \mathbb{R}^n$, we study the query complexity of randomized algorithms for estimating the trace of the matrix. This problem has many applications in quantum…
In this paper, we introduce a new quantum query lower bound framework. It is inspired by Zhandry's compressed oracle technique, but it also subsumes the polynomial method as a special case. Compared to Zhandry's technique, our approach has…
A leading proposal for verifying near-term quantum supremacy experiments on noisy random quantum circuits is linear cross-entropy benchmarking. For a quantum circuit $C$ on $n$ qubits and a sample $z \in \{0,1\}^n$, the benchmark involves…
This paper presents a complete algorithmic study of the decision Boolean Satisfiability Problem under the classical computation and quantum computation theories. The paper depicts deterministic and probabilistic algorithms, propositions of…
The Quantum Approximate Optimization Algorithm (QAOA) is an algorithmic framework for finding approximate solutions to combinatorial optimization problems, derived from an approximation to the Quantum Adiabatic Algorithm (QAA). In solving…
The general adversary dual is a powerful tool in quantum computing because it gives a query-optimal bounded-error quantum algorithm for deciding any Boolean function. Unfortunately, the algorithm uses linear qubits in the worst case, and…
We present several quantum algorithms for performing nearest-neighbor learning. At the core of our algorithms are fast and coherent quantum methods for computing distance metrics such as the inner product and Euclidean distance. We prove…
We revisit the well-studied problem of estimating the Shannon entropy of a probability distribution, now given access to a probability-revealing conditional sampling oracle. In this model, the oracle takes as input the representation of a…
Quantum simulation is a foundational application for quantum computers, projected to offer insights into complex quantum systems beyond the reach of classical computation. However, with the exception of Trotter-based methods, which suffer…
This paper depicts an algorithm for solving the Decision Boolean Satisfiability Problem using the binary numerical properties of a Special Decision Satisfiability Problem, parallel execution, object oriented, and short termination. The two…
We introduce a variational algorithm based on the quantum alternating operator ansatz (QAOA) for the approximate solution of computationally hard counting problems. Our algorithm, dubbed VQCount, is based on the equivalence between random…