相关论文: Quantum Period Query Proves NP in BQP

A sequence of moments encode the corresponding probability distribution. Probing if quantum joint probability distribution can be retrieved from the associated set of moments -- realized in the sequential measurement of a dichotomic…

We investigate bicomplex Hamiltonian systems in the framework of an analogous version of the Schrodinger equation. Since in such a setting three different types of conjugates of bicomplex numbers appear, each is found to define in a natural…

We investigate the quantum recurrence phenomena in periodically driven systems. We calculate the classical period and the quantum recurrence time and develop their interdependence. We further predict the behavior of the recurrence phenomena…

An ideal quantum walk transitions from one vertex to another with perfect fidelity, but in physical systems, the particle may be hindered by potential energy barriers. Then the particle has some amplitude of tunneling through the barriers,…

This paper creates and analyses a new quantum algorithm called the Amplified Quantum Fourier Transform (Amplified-QFT) for solving the following problem: The Local Period Problem: Let L = {0,1...N-1} be a set of N labels and let A be a…

We use several techniques to probe the wave functions proposed to describe the ${\cal A}$ phases by Das, Das, and Mandal [Phys. Rev. Lett. 131, 056202 (2023); Phys. Rev. Lett. 132, 106501 (2024); Phys. Rev. B 110, L121303 (2024).]. As…

The widely held belief that BQP strictly contains BPP raises fundamental questions: if we cannot efficiently compute predictions for the behavior of quantum systems, how can we test their behavior? In other words, is quantum mechanics…

We present a hybrid classical-quantum computing paradigm where the quantum part strictly runs within the coherence time of a quantum annealer, a method we call variational coherent quantum annealing (VCQA). It involves optimizing the…

Quantum annealing (QA) is a promising method for solving combinatorial optimization problems whose solutions are embedded into a ground state of the Ising Hamiltonian. This method employs two types of Hamiltonians: a driver Hamiltonian and…

Entanglement lies at the core of quantum algorithms designed to solve problems that are intractable by classical approaches. One such algorithm, quantum annealing (QA), provides a promising path to a practical quantum processor. We have…

This paper discusses why the usual notion that quantum phase transitions can be mapped onto classical phase transitions in a higher dimension, and that this makes the former uninteresting from a fundamental theoretical point of view, is in…

In this paper we consider a generalization of quantum hash functions for arbitrary groups. We show that quantum hash function exists for arbitrary abelian group. We construct a set of "good" automorphisms --- a key component of quantum hash…

We use differentiable programming and gradient descent to find unitary matrices that can be used in the period finding algorithm to extract period information from the state of a quantum computer post application of the oracle. The standard…

The entropy of a black hole can differ from a quarter of the area of the horizon because of quantum corrections. The correction is related to the contribution to the Euclidean functional integral from quantum fluctuations but is not simply…

A recent publication on arXiv:1905.00668 suggests that the phase relationship within a frequency comb can be reconstructed from a heterodyne measurement using a reference comb. In principle, following this approach, such retrieval of…

We continue the study of a novel relation between quantum periods and TBA(Thermodynamic Bethe Ansatz)-like difference equations, generalize previous works to a large class of Calabi-Yau geometries described by three-term quantum operators.…

It is shown that determining whether a quantum computation has a non-zero probability of accepting is at least as hard as the polynomial time hierarchy. This hardness result also applies to determining in general whether a given quantum…

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…

We study optimal perfect distinguishability between a unitary and a general quantum operation. In 2-dimensional case we provide a simple sufficient and necessary condition for sequential perfect distinguishability and an analytical formula…

We introduce an algorithm for combinatorial search on quantum computers that is capable of significantly concentrating amplitude into solutions for some NP search problems, on average. This is done by exploiting the same aspects of problem…