相关论文: Quantum lower bounds by quantum arguments
The field of quantum algorithms aims to find ways to speed up the solution of computational problems by using a quantum computer. A key milestone in this field will be when a universal quantum computer performs a computational task that is…
Quantum computation appears to offer significant advantages over classical computation and this has generated a tremendous interest in the field. In this thesis we consider the application of quantum computers to scientific computing and…
The quantum approximate optimization algorithm, also known in its generalization as the quantum alternating operator ansatz, (QAOA) is a heuristic hybrid quantum-classical algorithm for finding high-quality approximate solutions to…
The quantum version of communication complexity allows the two communicating parties to exchange qubits and/or to make use of prior entanglement (shared EPR-pairs). Some lower bound techniques are available for qubit communication…
Combinatorial optimization is anticipated to be one of the primary use cases for quantum computation in the coming years. The Quantum Approximate Optimization Algorithm (QAOA) and Quantum Annealing (QA) can potentially demonstrate…
We introduce new combinatorial quantities for concept classes, and prove lower and upper bounds for learning complexity in several models of query learning in terms of various combinatorial quantities. Our approach is flexible and powerful…
The nature of quantum computation is discussed. It is argued that, in terms of the amount of information manipulated in a given time, quantum and classical computation are equally efficient. Quantum superposition does not permit quantum…
The problem of minimizing the maximum of $N$ convex, Lipschitz functions plays significant roles in optimization and machine learning. It has a series of results, with the most recent one requiring $O(N\epsilon^{-2/3} + \epsilon^{-8/3})$…
Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct…
It is well known that quantum, randomized and deterministic (sequential) query complexities are polynomially related for total boolean functions. We find that significantly larger separations between the parallel generalizations of these…
The phenomenon of quantum entanglement is fundamental to the implementation of quantum computation, and requires at least two qubits for its demonstration. However, both Deutsch algorithm and Grover's search algorithm for two bits do not…
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…
We study the entanglement of a multipartite quantum state. An inequality between the bipartite concurrence and the multipartite concurrence is obtained. More effective lower and upper bounds of the multipartite concurrence are obtained. By…
Some quantum algorithms have "quantum speedups": improved time complexity as compared with the best-known classical algorithms for solving the same tasks. Can we understand what fuels these speedups from an entropic perspective? Information…
As a cornerstone of automated reasoning, equational reasoning finds equivalences between symbolic expressions and fuels advances across scientific disciplines. Yet, its potential remains limited by the exponential growth of equivalent…
In the exact quantum query model a successful algorithm must always output the correct function value. We investigate the function that is true if exactly $k$ or $l$ of the $n$ input bits given by an oracle are 1. We find an optimal…
Many proofs in discrete mathematics and theoretical computer science are based on the probabilistic method. To prove the existence of a good object, we pick a random object and show that it is bad with low probability. This method is…
Many quantum information measures can be written as an optimization of the quantum relative entropy between sets of states. For example, the relative entropy of entanglement of a state is the minimum relative entropy to the set of separable…
The standard quantum search algorithm lacks a feature, enjoyed by many classical algorithms, of having a fixed-point, i.e. a monotonic convergence towards the solution. Here we present two variations of the quantum search algorithm, which…
The Maximum Matching problem has a quantum query complexity lower bound of $\Omega(n^{3/2})$ for graphs on $n$ vertices represented by an adjacency matrix. The current best quantum algorithm has the query complexity $O(n^{7/4})$, which is…