nLab quantum circuit diagram



Quantum systems

quantum logic

quantum physics

quantum probability theoryobservables and states

quantum information

quantum computation

quantum algorithms:

Monoidal categories

monoidal categories

With symmetry

With duals for objects

With duals for morphisms

With traces

Closed structure

Special sorts of products



Internal monoids



In higher category theory



In quantum computation, a quantum circuit diagram is a kind of string diagram in finite-dimensional Hilbert spaces, typically used to express a sequence of low-level quantum gates acting on a finite number of qbits.

At the time of writing (2021) most of the actual programming of experimental quantum computers is conceived through quantum circuit diagrams, while more high-level quantum programming languages are are awaiting the rise of more powerful quantum hardware.


Quantum circuit diagrams

Textbook accounts:

Lecture notes:

  • John Preskill, Classical and quantum circuits (pdf), Chapter 5 in: Quantum Computation, lecture notes (web)

  • Ryan O’Donnell, Introduction to the Quantum Circuit Model, 2015 (pdf)

See also:

Survey, examples, and implementations:

With an eye towards quantum complexity theory:

  • Richard Cleve, Section 1.2 in: An Introduction to Quantum Complexity Theory (pdf)

Quantum programming languages

On quantum programming languages (programming languages for quantum computation):


See also:

Surveys of existing languages:

  • Simon Gay, Quantum programming languages: Survey and bibliography, Mathematical Structures in Computer Science16(2006) (doi:10.1017/S0960129506005378, pdf)

  • Sunita Garhwal, Maryam Ghorani , Amir Ahmad, Quantum Programming Language: A Systematic Review of Research Topic and Top Cited Languages, Arch Computat Methods Eng 28, 289–310 (2021) (doi:10.1007/s11831-019-09372-6)

Quantum programming via quantum logic understood as linear type theory interpreted in symmetric monoidal categories:

The corresponding string diagrams are known in quantum computation as quantum circuit diagrams:

functional programming languages for quantum computation:





On classically controlled quantum computation:

Quantum programming via dependent linear type theory/indexed monoidal (∞,1)-categories:

specifically with Quipper:

On quantum software verification:

with Quipper:

  • Linda Anticoli, Carla Piazza, Leonardo Taglialegne, Paolo Zuliani, Towards Quantum Programs Verification: From Quipper Circuits to QPMC, In: Devitt S., Lanese I. (eds) Reversible Computation. RC 2016. Lecture Notes in Computer Science, vol 9720. Springer, Cham (doi:10.1007/978-3-319-40578-0_16)

with QWIRE:

Last revised on September 19, 2021 at 06:30:01. See the history of this page for a list of all contributions to it.