Related papers: Exact distributed quantum algorithm for generalize…
This paper gives the first separation of quantum and classical pure (i.e., non-cryptographic) computing abilities with no restriction on the amount of available computing resources, by considering the exact solvability of a celebrated…
We provide algorithms for efficiently addressing quantum memory in parallel. These imply that the standard circuit model can be simulated with low overhead by the more realistic model of a distributed quantum computer. As a result, the…
We study a generalization of entanglement testing which we call the "hidden cut problem." Taking as input copies of an $n$-qubit pure state which is product across an unknown bipartition, the goal is to learn precisely where the state is…
Unstructured search remains as one of the significant challenges in computer science, as classical search algorithms become increasingly impractical for large-scale systems due to their linear time complexity. Quantum algorithms, notably…
Accurate computation of multiple eigenvalues of quantum Hamiltonians is essential in quantum chemistry, materials science, and molecular spectroscopy. Estimating excited-state energies is challenging for classical algorithms due to…
Quantum sampling, a fundamental subroutine in numerous quantum algorithms, involves encoding a given probability distribution in the amplitudes of a pure state. Given the hefty cost of large-scale quantum storage, we initiate the study of…
Almost all of the most successful quantum algorithms discovered to date exploit the ability of the Fourier transform to recover subgroup structure of functions, especially periodicity. The fact that Fourier transforms can also be used to…
Simon's algorithm is a polynomial period-finding algorithm that has been used to exploit the algebraic structure of specific symmetric ciphers, showing that exponential speedups in their cryptanalysis are theoretically possible. While the…
In this Letter, we construct the quantum algorithms for the Simon problem and the period-finding problem, which do not require initializing the auxiliary qubits involved in the process of functional evaluation but are as efficient as the…
Distributed optimization for resource allocation problems is investigated and a sub-optimal continuous-time algorithm is proposed. Our algorithm has lower order dynamics than others to reduce burdens of computation and communication, and 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…
Randomized algorithms are crucial subroutines in quantum computing, but the requirement to execute many types of circuits on a real quantum device has been challenging to their extensive implementation. In this study, we propose an…
Due to Shor's algorithm, quantum computers are a severe threat for public key cryptography. This motivated the cryptographic community to search for quantum-safe solutions. On the other hand, the impact of quantum computing on secret key…
It is believed that there is no efficient classical algorithm to determine the linear structure of Boolean function. We investigate an extension of Simon's period-finding quantum algorithm, and propose an efficient quantum algorithm to…
The simulation of large-scale classical systems in exponentially small space on quantum computers has gained attention. The prior work demonstrated that a quantum algorithm offers an exponential speedup over any classical algorithm in…
This paper presents a quantum algorithm for efficiently computing partial sums and specific weighted partial sums of quantum state amplitudes. Computation of partial sums has important applications, including numerical integration,…
The distributed subgradient method (DSG) is a widely discussed algorithm to cope with large-scale distributed optimization problems in the arising machine learning applications. Most exisiting works on DSG focus on ideal communication…
The quantum hidden subgroup approach is an actively studied approach to solve combinatorial problems in quantum complexity theory. With the success of the Shor's algorithm, it was hoped that similar approach may be useful to solve the other…
We propose a general learning algorithm for solving optimization problems, based on a simple strategy of trial and adaptation. The algorithm maintains a probability distribution of possible solutions (configurations), which is updated…
We investigate the boundary between classical and quantum computational power. This work consists of two parts. First we develop new classical simulation algorithms that are centered on sampling methods. Using these techniques we generate…