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The PennyLane Guide to Hamiltonian Simulation

Hamiltonian simulation is a set of quantum computing routines that simulate the dynamics of physical systems, with promising applications in industry. This collection guides you through modern Hamiltonian Simulation algorithms, starting from the basics and increasing in complexity.

Explore a variety of Hamiltonian Simulation techniques.

Preliminaries

Discover the most accessible and effective quantum algorithms for simulating the time evolution of quantum systems, ideal for those new to the field.


Block encoding

Unitary operators are the cornerstone of quantum computing, but what about non-unitary operations? Learn how block encoding enables you to represent and manipulate arbitrary matrices within quantum algorithms. They are the foundation for more advanced Hamiltonian Simulation methods.


Qubitization

While Hamiltonians are inherently Hermitian, efficient quantum simulation requires unitary operators. Qubitization leverages block-encoding techniques to embed qubit Hamiltonians into unitaries, speeding up simulation on quantum computers.


Quantum singular value transformation

By applying polynomials to block encodings, the Quantum Singular Value Transformation (QSVT) provides a unifying framework for numerous quantum algorithms. Its impact is particularly significant in Hamiltonian simulation, providing advanced and efficient techniques.


Documentation