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Quantum approximate optimization is one of the promising candidates for useful quantum computation, particularly in the context of finding approximate solutions to Quadratic Unconstrained Binary Optimization (QUBO) problems. However, the…
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…
This paper considers the quantum query complexity of {\it $\eps$-biased oracles} that return the correct value with probability only $1/2 + \eps$. In particular, we show a quantum algorithm to compute $N$-bit OR functions with…
Solving linear systems of equations is essential for many problems in science and technology, including problems in machine learning. Existing quantum algorithms have demonstrated the potential for large speedups, but the required quantum…
In classical computation, a problem can be solved in multiple steps where calculated results of each step can be copied and used repeatedly. While in quantum computation, it is difficult to realize a similar multi-step computation process…
Quantum fingerprinting is a technique that maps classical input word to a quantum state. The obtained quantum state is much shorter than the original word, and its processing uses less resources, making it useful in quantum algorithms,…
We consider the problem of estimating the expected outcomes of Monte Carlo processes whose outputs are described by multidimensional random variables. We tightly characterize the quantum query complexity of this problem for various choices…
We revisit the so-called compressed oracle technique, introduced by Zhandry for analyzing quantum algorithms in the quantum random oracle model (QROM). To start off with, we offer a concise exposition of the technique, which easily extends…
Quantum spatial search has been widely studied with most of the study focusing on quantum walk algorithms. We show that quantum walk algorithms are extremely sensitive to systematic errors. We present a recursive algorithm which offers…
Quantum computation has attracted much attention since it was shown by Shor and Grover the possibility to implement quantum algorithms able to realize, respectively, factoring and searching in a faster way than any other known classical…
We develop a quantum algorithm to solve combinatorial optimization problems through quantum simulation of a classical annealing process. Our algorithm combines techniques from quantum walks, quantum phase estimation, and quantum Zeno…
Recent advancements in large language models (LLMs) have significantly improved their reasoning abilities, particularly through techniques involving search and backtracking. Backtracking naturally scales test-time compute by enabling…
Perceptrons, which perform binary classification, are the fundamental building blocks of neural networks. Given a data set of size~$N$ and margin~$\gamma$ (how well the given data are separated), the query complexity of the best-known…
We provide a detailed estimate for the logical resource requirements of the quantum linear system algorithm (QLSA) [Phys. Rev. Lett. 103, 150502 (2009)] including the recently described elaborations [Phys. Rev. Lett. 110, 250504 (2013)].…
Quantum oracles are widely adopted in problems, like query oracle in Grover's algorithm, cipher in quantum cryptanalytic and data encoder in quantum machine learning. Notably, the bit-flip oracle, capable of flipping the state based on a…
The current era of quantum computing has yielded several algorithms that promise high computational efficiency. While the algorithms are sound in theory and can provide potentially exponential speedup, there is little guidance on how to…
The presence of stochastic elements in combinatorial optimization problems makes them particularly challenging, as such problems quickly become intractable for classical computers even at relatively small sizes. In this work, we propose a…
We prove that the generic quantum speedups for brute-force search and counting only hold when the process we apply them to can be efficiently inverted. The algorithms speeding up these problems, amplitude amplification and amplitude…
Major obstacles remain to the implementation of macroscopic quantum computing: hardware problems of noise, decoherence, and scaling; software problems of error correction; and, most important, algorithm construction. Finding truly quantum…
In the search with wildcards problem [Ambainis, Montanaro, Quantum Inf.~Comput.'14], one's goal is to learn an unknown bit-string $x \in \{-1,1\}^n$. An algorithm may, at unit cost, test equality of any subset of the hidden string with a…