Lecture

Quantum Phase Estimation: Basics and Applications

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Description

This lecture covers the fundamentals of Quantum Phase Estimation (QPE), including the concept of unitary operators on n-qubits and eigenvectors. It explores the estimation task and its applications in quantum computing, focusing on approximations and known eigenvectors. The lecture delves into the challenges of estimating quantum phases accurately and the implications of only having approximate knowledge. Various scenarios are discussed, such as the impact of different digit accuracies and the high probability estimates. The lecture also touches upon the Fourier Transform and its role in QPE, emphasizing the importance of accurate estimations in quantum algorithms.

Official source

Ontological neighbourhood

Theoretical computer science

Theory of computation: Quantum computing

Related concepts (31)

Quantum computing

A quantum computer is a computer that exploits quantum mechanical phenomena. At small scales, physical matter exhibits properties of both particles and waves, and quantum computing leverages this behavior, specifically quantum superposition and entanglement, using specialized hardware that supports the preparation and manipulation of quantum states. Classical physics cannot explain the operation of these quantum devices, and a scalable quantum computer could perform some calculations exponentially faster than any modern "classical" computer.

Quantum algorithm

In quantum computing, a quantum algorithm is an algorithm which runs on a realistic model of quantum computation, the most commonly used model being the quantum circuit model of computation. A classical (or non-quantum) algorithm is a finite sequence of instructions, or a step-by-step procedure for solving a problem, where each step or instruction can be performed on a classical computer. Similarly, a quantum algorithm is a step-by-step procedure, where each of the steps can be performed on a quantum computer.

Quantum Fourier transform

In quantum computing, the quantum Fourier transform (QFT) is a linear transformation on quantum bits, and is the quantum analogue of the discrete Fourier transform. The quantum Fourier transform is a part of many quantum algorithms, notably Shor's algorithm for factoring and computing the discrete logarithm, the quantum phase estimation algorithm for estimating the eigenvalues of a unitary operator, and algorithms for the hidden subgroup problem. The quantum Fourier transform was discovered by Don Coppersmith.

Shor's algorithm

Shor's algorithm is a quantum algorithm for finding the prime factors of an integer. It was developed in 1994 by the American mathematician Peter Shor. It is one of the few known quantum algorithms with compelling potential applications and strong evidence of superpolynomial speedup compared to best known classical (that is, non-quantum) algorithms. On the other hand, factoring numbers of practical significance requires far more qubits than available in the near future.

Quantum phase estimation algorithm

In quantum computing, the quantum phase estimation algorithm is a quantum algorithm to estimate the phase corresponding to an eigenvalue of a given unitary operator. Because the eigenvalues of a unitary operator always have unit modulus, they are characterized by their phase, and therefore the algorithm can be equivalently described as retrieving either the phase or the eigenvalue itself. The algorithm was initially introduced by Alexei Kitaev in 1995.

Related lectures (64)

Shor's Algorithm: Quantum Circuit & Period Finding

Covers Shor's algorithm for period finding in quantum computing, explaining the quantum circuit and algorithm used.

Quantum Computing: Hardware Technologies and Applications

Explores quantum computing hardware technologies, applications, classical computing development, investments, and societal impact.

Quantum and Nanocomputing

Delves into quantum computing fundamentals, including entanglement, quantum gates, and algorithms, emphasizing unitary transformations and quantum coherence.

Bloch sphere representation and Larmor precession

Covers the Bloch sphere representation and Larmor precession in spin 1/2 systems.