Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

The Local Hamiltonian Problem

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 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.

Quantum complexity theory

Quantum complexity theory is the subfield of computational complexity theory that deals with complexity classes defined using quantum computers, a computational model based on quantum mechanics. It studies the hardness of computational problems in relation to these complexity classes, as well as the relationship between quantum complexity classes and classical (i.e., non-quantum) complexity classes. Two important quantum complexity classes are BQP and QMA.

Boolean satisfiability problem

In logic and computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated SATISFIABILITY, SAT or B-SAT) is the problem of determining if there exists an interpretation that satisfies a given Boolean formula. In other words, it asks whether the variables of a given Boolean formula can be consistently replaced by the values TRUE or FALSE in such a way that the formula evaluates to TRUE. If this is the case, the formula is called satisfiable.

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.

Related lectures (33)

Solving Parity Games in Practice

Explores practical aspects of solving parity games, including winning strategies, algorithms, complexity, determinism, and heuristic approaches.

Quantum Phase Estimation

Explains the Quantum Phase Estimation (QPE) algorithm and its complexity using two registers and SWAP gates.

Distributed Quantum Computing

Explores communication complexity and quantum computation models in Distributed Quantum Computing.

Quantum Computation Delegation

Explores fully classical qubits, blind quantum computing, and verifiability in quantum delegation protocols.

Elements of Computational Complexity