Related papers: Reflections for quantum query algorithms
Learning low dimensional representation is a crucial issue for many machine learning tasks such as pattern recognition and image retrieval. In this article, we present a quantum algorithm and a quantum circuit to efficiently perform…
The polynomial and the adversary methods are the two main tools for proving lower bounds on query complexity of quantum algorithms. Both methods have found a large number of applications, some problems more suitable for one method, some for…
Nonlinear spectroscopy is a cornerstone of quantum science, providing unique access to multi-point correlations, quantum coherence, and couplings that are invisible to linear methods. However, classical simulation of these phenomena is…
Quantum Bit String Comparators (QBSC) operate on two sequences of n-qubits, enabling the determination of their relationships, such as equality, greater than, or less than. This is analogous to the way conditional statements are used in…
Despite the promise that fault-tolerant quantum computers can efficiently solve classically intractable problems, it remains a major challenge to find quantum algorithms that may reach computational advantage in the present era of noisy,…
Low-rank methods for semidefinite programming (SDP) have gained a lot of interest recently, especially in machine learning applications. Their analysis often involves determinant-based or Schatten-norm penalties, which are hard to implement…
The fundamental question considered in algorithms on strings is that of indexing, that is, preprocessing a given string for specific queries. By now we have a number of efficient solutions for this problem when the queries ask for an exact…
Demonstrating quantum advantage has been a pressing challenge in the field. Most claimed quantum speedups rely on a subroutine in which classical information can be accessed in a coherent quantum manner, which imposes a crucial constraint…
We study randomized and quantum query (a.k.a. decision tree) complexity for all total Boolean functions, with emphasis to derandomization and dequantization (removing quantumness from algorithms). Firstly, we show that $D(f) = O(Q_1(f)^3)$…
We present novel algorithms for design and design space exploration. The designs discovered by these algorithms are compositions of function types specified in component libraries. Our algorithms reduce the design problem to quantified…
Representing signals with sparse vectors has a wide range of applications that range from image and video coding to shape representation and health monitoring. In many applications with real-time requirements, or that deal with…
We design an efficient data structure for computing a suitably defined approximate depth of any query point in the arrangement $\mathcal{A}(S)$ of a collection $S$ of $n$ halfplanes or triangles in the plane or of halfspaces or simplices in…
We study and extend the semidefinite programming (SDP) hierarchies introduced in [Phys. Rev. Lett. 115, 020501] for the characterization of the statistical correlations arising from finite dimensional quantum systems. First, we introduce…
Quantum processors are now able to run quantum circuits that are infeasible to simulate classically, creating a need for benchmarks that assess a quantum processor's rate of errors when running these circuits. Here, we introduce a general…
It is known that the dual of the general adversary bound can be used to build quantum query algorithms with optimal complexity. Despite this result, not many quantum algorithms have been designed this way. This paper shows another example…
Many important computer science problems can be reduced to clause satisfaction problem. We are given $n$ Boolean variables $x_{k}$ and $m$ clauses $c_{j}$ where each clause is a function of values of some of the variables. We want to find…
Properties of Boolean functions can often be tested much faster than the functions can be learned. However, this advantage usually disappears when testers are limited to random samples of a function $f$--a natural setting for data…
Providing an optimal path to a quantum annealing algorithm is key to finding good approximate solutions to computationally hard optimization problems. Reinforcement is one of the strategies that can be used to circumvent the exponentially…
Grover's quantum search algorithm provides a quadratic speedup over the classical one. The computational complexity is based on the number of queries to the oracle. However, depth is a more modern metric for noisy intermediate-scale quantum…
Indirect trajectory optimization methods such as Differential Dynamic Programming (DDP) have found considerable success when only planning under dynamic feasibility constraints. Meanwhile, nonlinear programming (NLP) has been the…