相关论文: Lower Bounds for Quantum Search and Derandomizatio…

Search-base algorithms have widespread applications in different scenarios. Grover's quantum search algorithms and its generalization, amplitude amplification, provide a quadratic speedup over classical search algorithms for unstructured…

Given a random permutation $f: [N] \to [N]$ as a black box and $y \in [N]$, we want to output $x = f^{-1}(y)$. Supplementary to our input, we are given classical advice in the form of a pre-computed data structure; this advice can depend on…

We describe a method to upper bound the quantum query complexity of Boolean formula evaluation problems, using fundamental theorems about the general adversary bound. This nonconstructive method can give an upper bound on query complexity…

We provide a tight analysis of Grover's recent algorithm for quantum database searching. We give a simple closed-form formula for the probability of success after any given number of iterations of the algorithm. This allows us to determine…

We establish the first general connection between the design of quantum algorithms and circuit lower bounds. Specifically, let $\mathfrak{C}$ be a class of polynomial-size concepts, and suppose that $\mathfrak{C}$ can be PAC-learned with…

We provide simple but surprisingly useful direct product theorems for proving lower bounds on online algorithms with a limited amount of advice about the future. As a consequence, we are able to translate decades of research on randomized…

Lexicographically minimal string rotation is a fundamental problem in string processing that has recently garnered significant attention in quantum computing. Near-optimal quantum algorithms have been proposed for solving this problem,…

The problem of memory checking considers storing files on an unreliable public server whose memory can be modified by a malicious party. The main task is to design an online memory checker with the capability to verify that the information…

We study the complexity of quantum query algorithms that make p queries in parallel in each timestep. This model is in part motivated by the fact that decoherence times of qubits are typically small, so it makes sense to parallelize 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…

We study the quantum query complexity of two problems. First, we consider the problem of determining if a sequence of parentheses is a properly balanced one (a Dyck word), with a depth of at most $k$. We call this the $Dyck_{k,n}$ problem.…

We consider a generalization of the standard oracle model in which the oracle acts on the target with a permutation selected according to internal random coins. We describe several problems that are impossible to solve classically but can…

We introduce a novel deterministic quantum search algorithm that provides a practical alternative to conventional probabilistic search approaches. Our scheme eliminates the inherent uncertainty of quantum search without relying on arbitrary…

As the matching condition in Grover search algorithm is transgressed due to inevitable errors in phase inversions, it gives a reduction in maximum probability of success. With a given degree of maximum success, we have derive the…

The quantum SearchRank algorithm is a promising tool for a future quantum search engine based on PageRank quantization. However, this algorithm loses its functionality when the $N/M$ ratio between the network size $N$ and the number of…

We propose a quantum algorithm for closest pattern matching which allows us to search for as many distinct patterns as we wish in a given string (database), requiring a query function per symbol of the pattern alphabet. This represents a…

Quantum computers show potential for achieving computational advantage over classical computers, with many candidate applications in combinatorial optimisation. We present an application level benchmarking framework for near-term quantum…

Local Search problem, which finds a local minimum of a black-box function on a given graph, is of both practical and theoretical importance to combinatorial optimization, complexity theory and many other areas in theoretical computer…

Grover's algorithm is a primary algorithm offered as evidence that quantum computers can provide an advantage over classical computers. It involves an "oracle" specified for a given application whose structure is not part of the formal…

A previously developed quantum search algorithm for solving 1-SAT problems in a single step is generalized to apply to a range of highly constrained k-SAT problems. We identify a bound on the number of clauses in satisfiability problems for…