相关论文: Quantum NP - A Survey

This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…

We investigate some particular completely positive maps which admit a stable commutative Von Neumann subalgebra. The restriction of such maps to the stable algebra is then a Markov operator. In the first part of this article, we propose a…

Quantum machine learning (QML) holds promise for accelerating pattern recognition, optimization, and data analysis, but the conditions under which it can truly outperform classical approaches remain unclear. Existing research often…

The polynomial hierarchy plays a central role in classical complexity theory. Here, we define a quantum generalization of the polynomial hierarchy, and initiate its study. We show that not only are there natural complete problems for the…

In this work we develop theoretical techniques for analysing the performance of the quantum approximate optimization algorithm (QAOA) when applied to random boolean constraint satisfaction problems (CSPs), and use these techniques to…

We study a quantum algorithm that consists of a simple quantum Markov process, and we analyze its behavior on restricted versions of Quantum 2-SAT. We prove that the algorithm solves this decision problem with high probability for n qubits,…

We introduce the reinforcement quantum annealing (RQA) scheme in which an intelligent agent interacts with a quantum annealer that plays the stochastic environment role of learning automata and tries to iteratively find better Ising…

The problem of estimating the spectral gap of a local Hamiltonian is known to be contained in the class $P^{QMA[log]}$: polynomial time with access to a logarithmic number of QMA queries. The problem was shown to be hard for…

This paper concerns quantum heuristics able to extend the domain of quantum computing, defining a promising way in the large number of well-known classical algorithms. Quantum approximate heuristics take advantage of alternation between a…

The quantum adiabatic theorem ensures that a slowly changing system, initially prepared in its ground state, will evolve to its final ground state with arbitrary precision. As a first result this thesis extends the original theorem to…

We consider the problem of learning local quantum Hamiltonians given copies of their Gibbs state at a known inverse temperature, following Haah et al. [2108.04842] and Bakshi et al. [arXiv:2310.02243]. Our main technical contribution is a…

We examine the computational complexity of testing and finding small plans in probabilistic planning domains with both flat and propositional representations. The complexity of plan evaluation and existence varies with the plan type sought;…

Quantum computation can be achieved by preparing an appropriate initial product state of qudits and then letting it evolve under a fixed Hamiltonian. The readout is made by measurement on individual qudits at some later time. This approach…

In the continuum limit (large number of qubits), adiabatic quantum algorithms display a remarkable similarity to sweeps through quantum phase transitions. We find that transitions of second or higher order are advantageous in comparison to…

Satisfiability problems play a central role in computer science and engineering as a general framework for studying the complexity of various problems. Schaefer proved in 1978 that truth satisfaction of propositional formulas given a…

Commuting local Hamiltonians provide a testing ground for studying many of the most interesting open questions in quantum information theory, including the quantum PCP conjecture and the existence of area laws. Although they are a…

The Local Hamiltonian problem is the problem of estimating the least eigenvalue of a local Hamiltonian, and is complete for the class QMA. The 1D problem on a chain of qubits has heuristics which work well, while the 13-state qudit case has…

All Hamiltonian complexity results to date have been proven by constructing a local Hamiltonian whose ground state -- or at least some low-energy state -- is a "computational history state", encoding a quantum computation as a superposition…

We prove that adiabatic computation is equivalent to standard quantum computation even when the adiabatic quantum system is restricted to be a set of particles on a one-dimensional chain. We give a construction that uses a 2-local…

Understanding the entanglement structure of local Hamiltonian ground spaces is a physically motivated problem, with applications ranging from tensor network design to quantum error-correcting codes. To this end, we study the complexity of…