# nLab quantum circuit diagram

Contents

### Context

#### Monoidal categories

monoidal categories

# Contents

## Idea

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.

## References

### 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)

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

General:

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:

QPL:

QML:

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.