Lecture

The Local Hamiltonian Problem

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Description

This lecture discusses the Local Hamiltonian Problem, focusing on the concept of QMA-Complete problems and the complexity of verifying quantum computations. It covers the delegation circuit, locality, 3-SAT, small eigenvalues, and the historical background of the problem dating back to the 1970s.

Official source

Ontological neighbourhood

Theoretical computer science

Theory of computation: Computational complexity theory

Related concepts (32)

Complexity class

In computational complexity theory, a complexity class is a set of computational problems "of related resource-based complexity". The two most commonly analyzed resources are time and memory. In general, a complexity class is defined in terms of a type of computational problem, a model of computation, and a bounded resource like time or memory. In particular, most complexity classes consist of decision problems that are solvable with a Turing machine, and are differentiated by their time or space (memory) requirements.

Computational complexity

In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to computation time (generally measured by the number of needed elementary operations) and memory storage requirements. The complexity of a problem is the complexity of the best algorithms that allow solving the problem. The study of the complexity of explicitly given algorithms is called analysis of algorithms, while the study of the complexity of problems is called computational complexity theory.

Electron acceptor

An electron acceptor is a chemical entity that accepts electrons transferred to it from another compound. It is an oxidizing agent that, by virtue of its accepting electrons, is itself reduced in the process. Electron acceptors are sometimes mistakenly called electron receptors. The electron accepting power of an acceptor molecule is measured by its electron affinity (A) which is the energy released when filling the lowest unoccupied molecular orbital (LUMO).

Qubit

In quantum computing, a qubit (ˈkjuːbɪt) or quantum bit is a basic unit of quantum information—the quantum version of the classic binary bit physically realized with a two-state device. A qubit is a two-state (or two-level) quantum-mechanical system, one of the simplest quantum systems displaying the peculiarity of quantum mechanics. Examples include the spin of the electron in which the two levels can be taken as spin up and spin down; or the polarization of a single photon in which the two states can be taken to be the vertical polarization and the horizontal polarization.

Computational complexity theory

In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other. A computational problem is a task solved by a computer. A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used.

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