# Q Sharp

__: Programming lang. for quantum algorithms__

**Short description**Paradigm | Quantum, functional, imperative |
---|---|

Designed by | Microsoft Research (quantum architectures and computation group; QuArC) |

Developer | Microsoft |

First appeared | December 11, 2017 |

Typing discipline | Static, strong |

Platform | Common Language Infrastructure |

License | MIT License^{[1]} |

Filename extensions | .qs |

Website | docs |

Influenced by | |

C#, F#, Python |

**Q#** (pronounced as *Q sharp*) is a domain-specific programming language used for expressing quantum algorithms.^{[2]} It was initially released to the public by Microsoft as part of the Quantum Development Kit.^{[3]}

## History

Historically, Microsoft Research had two teams interested in quantum computing, the QuArC team based in Redmond,^{[4]} directed by Krysta Svore, that explored the construction of quantum circuitry, and Station Q initially located in Santa Barbara and directed by Michael Freedman, that explored topological quantum computing.^{[5]}^{[6]}

During a Microsoft Ignite Keynote on September 26, 2017, Microsoft announced that they were going to release a new programming language geared specifically towards quantum computers.^{[7]} On December 11, 2017, Microsoft released Q# as a part of the Quantum Development Kit.^{[3]}

At Build 2019, Microsoft announced that it would be open-sourcing the Quantum Development Kit, including its Q# compilers and simulators.^{[8]}

Bettina Heim currently leads the Q# language development effort.^{[9]}^{[10]}

## Usage

Q# is available as a separately downloaded extension for Visual Studio,^{[11]} but it can also be run as an independent tool from the Command line or Visual Studio Code. The Quantum Development Kit ships with a quantum simulator which is capable of running Q#.^{[12]}

In order to invoke the quantum simulator, another .NET programming language, usually C#, is used, which provides the (classical) input data for the simulator and reads the (classical) output data from the simulator.^{[13]}

## Features

A primary feature of Q# is the ability to create and use qubits for algorithms. As a consequence, some of the most prominent features of Q# are the ability to entangle and introduce superpositioning to qubits via Controlled NOT gates and Hadamard gates, respectively, as well as Toffoli Gates, Pauli X, Y, Z Gate, and many more which are used for a variety of operations; see the list at the article on quantum logic gates.^{[14]}

The hardware stack that will eventually come together with Q# is expected to implement Qubits as topological qubits. The quantum simulator that is shipped with the Quantum Development Kit today is capable of processing up to 32 qubits on a user machine and up to 40 qubits on Azure.^{[15]}

## Documentation and resources

Currently, the resources available for Q# are scarce, but the official documentation is published: Microsoft Developer Network: Q#. Microsoft Quantum Github repository is also a large collection of sample programs implementing a variety of Quantum algorithms and their tests.

Microsoft has also hosted a Quantum Coding contest on Codeforces here: Microsoft Q# Coding Contest - Codeforces, and also provided related material to help answer the questions in the blog posts, plus the detailed solutions in the tutorials.

Microsoft hosts a set of learning exercises to help learn Q# on GitHub: microsoft/QuantumKatas with links to resources, and answers to the problems.

## Syntax

Q# is syntactically related to both C# and F# yet also has some significant differences.

### Similarities with C#

- Uses
`namespace`

for code isolation - All statements end with a
`;`

- Curly braces are used for statements of scope
- Single line comments are done using
`//`

- Variable data types such as
`Int`

`Double`

`String`

and`Bool`

are similar, although capitalised (and Int is 64-bit)^{[16]} - Qubits are allocated and disposed inside a
`using`

block. - Lambda functions using the
`=>`

operator. - Results are returned using the
`return`

keyword.

### Similarities with F#

- Variables are declared using either
`let`

or`mutable`

^{[2]} - First-order functions
- Modules, which are imported using the
`open`

keyword - The datatype is declared after the variable name
- The range operator
`..`

`for … in`

loops- Every operation/function has a return value, rather than
`void`

. Instead of`void`

, an empty Tuple`()`

is returned. - Definition of record datatypes (using the
`newtype`

keyword, instead of`type`

).

### Differences

- Functions are declared using the
`function`

keyword - Operations on the quantum computer are declared using the
`operation`

keyword - Lack of multiline comments
- Asserts instead of throwing exceptions
- Documentation is written in Markdown instead of XML-based documentation tags

## Example

The following source code is a multiplexer from the official Microsoft Q# library repository.

// Copyright (c) Microsoft Corporation. // Licensed under the MIT License. namespace Microsoft.Quantum.Canon { open Microsoft.Quantum.Intrinsic; open Microsoft.Quantum.Arithmetic; open Microsoft.Quantum.Arrays; open Microsoft.Quantum.Diagnostics; open Microsoft.Quantum.Math; /// # Summary /// Applies a multiply-controlled unitary operation $U$ that applies a /// unitary $V_j$ when controlled by n-qubit number state $\ket{j}$. /// /// $U = \sum^{N-1}_{j=0}\ket{j}\bra{j}\otimes V_j$. /// /// # Input /// ## unitaryGenerator /// A tuple where the first element `Int` is the number of unitaries $N$, /// and the second element `(Int -> ('T => () is Adj + Ctl))` /// is a function that takes an integer $j$ in $[0,N-1]$ and outputs the unitary /// operation $V_j$. /// /// ## index /// $n$-qubit control register that encodes number states $\ket{j}$ in /// little-endian format. /// /// ## target /// Generic qubit register that $V_j$ acts on. /// /// # Remarks /// `coefficients` will be padded with identity elements if /// fewer than $2^n$ are specified. This implementation uses /// $n-1$ auxiliary qubits. /// /// # References /// - [ *Andrew M. Childs, Dmitri Maslov, Yunseong Nam, Neil J. Ross, Yuan Su*, /// arXiv:1711.10980](https://arxiv.org/abs/1711.10980) operation MultiplexOperationsFromGenerator<'T>(unitaryGenerator : (Int, (Int -> ('T => Unit is Adj + Ctl))), index: LittleEndian, target: 'T) : Unit is Ctl + Adj { let (nUnitaries, unitaryFunction) = unitaryGenerator; let unitaryGeneratorWithOffset = (nUnitaries, 0, unitaryFunction); if Length(index!) == 0 { fail "MultiplexOperations failed. Number of index qubits must be greater than 0."; } if nUnitaries > 0 { let auxiliary = []; Adjoint MultiplexOperationsFromGeneratorImpl(unitaryGeneratorWithOffset, auxiliary, index, target); } } /// # Summary /// Implementation step of `MultiplexOperationsFromGenerator`. /// # See Also /// - Microsoft.Quantum.Canon.MultiplexOperationsFromGenerator internal operation MultiplexOperationsFromGeneratorImpl<'T>(unitaryGenerator : (Int, Int, (Int -> ('T => Unit is Adj + Ctl))), auxiliary: Qubit[], index: LittleEndian, target: 'T) : Unit { body (...) { let nIndex = Length(index!); let nStates = 2^nIndex; let (nUnitaries, unitaryOffset, unitaryFunction) = unitaryGenerator; let nUnitariesLeft = MinI(nUnitaries, nStates / 2); let nUnitariesRight = MinI(nUnitaries, nStates); let leftUnitaries = (nUnitariesLeft, unitaryOffset, unitaryFunction); let rightUnitaries = (nUnitariesRight - nUnitariesLeft, unitaryOffset + nUnitariesLeft, unitaryFunction); let newControls = LittleEndian(Most(index!)); if nUnitaries > 0 { if Length(auxiliary) == 1 and nIndex == 0 { // Termination case (Controlled Adjoint (unitaryFunction(unitaryOffset)))(auxiliary, target); } elif Length(auxiliary) == 0 and nIndex >= 1 { // Start case let newauxiliary = Tail(index!); if nUnitariesRight > 0 { MultiplexOperationsFromGeneratorImpl(rightUnitaries, [newauxiliary], newControls, target); } within { X(newauxiliary); } apply { MultiplexOperationsFromGeneratorImpl(leftUnitaries, [newauxiliary], newControls, target); } } else { // Recursion that reduces nIndex by 1 and sets Length(auxiliary) to 1. let controls = [Tail(index!)] + auxiliary; use newauxiliary = Qubit(); use andauxiliary = Qubit[MaxI(0, Length(controls) - 2)]; within { ApplyAndChain(andauxiliary, controls, newauxiliary); } apply { if nUnitariesRight > 0 { MultiplexOperationsFromGeneratorImpl(rightUnitaries, [newauxiliary], newControls, target); } within { (Controlled X)(auxiliary, newauxiliary); } apply { MultiplexOperationsFromGeneratorImpl(leftUnitaries, [newauxiliary], newControls, target); } } } } } adjoint auto; controlled (controlRegister, ...) { MultiplexOperationsFromGeneratorImpl(unitaryGenerator, auxiliary + controlRegister, index, target); } adjoint controlled auto; } /// # Summary /// Applies multiply-controlled unitary operation $U$ that applies a /// unitary $V_j$ when controlled by n-qubit number state $\ket{j}$. /// /// $U = \sum^{N-1}_{j=0}\ket{j}\bra{j}\otimes V_j$. /// /// # Input /// ## unitaryGenerator /// A tuple where the first element `Int` is the number of unitaries $N$, /// and the second element `(Int -> ('T => () is Adj + Ctl))` /// is a function that takes an integer $j$ in $[0,N-1]$ and outputs the unitary /// operation $V_j$. /// /// ## index /// $n$-qubit control register that encodes number states $\ket{j}$ in /// little-endian format. /// /// ## target /// Generic qubit register that $V_j$ acts on. /// /// # Remarks /// `coefficients` will be padded with identity elements if /// fewer than $2^n$ are specified. This version is implemented /// directly by looping through n-controlled unitary operators. operation MultiplexOperationsBruteForceFromGenerator<'T>(unitaryGenerator : (Int, (Int -> ('T => Unit is Adj + Ctl))), index: LittleEndian, target: 'T) : Unit is Adj + Ctl { let nIndex = Length(index!); let nStates = 2^nIndex; let (nUnitaries, unitaryFunction) = unitaryGenerator; for idxOp in 0..MinI(nStates,nUnitaries) - 1 { (ControlledOnInt(idxOp, unitaryFunction(idxOp)))(index!, target); } } /// # Summary /// Returns a multiply-controlled unitary operation $U$ that applies a /// unitary $V_j$ when controlled by n-qubit number state $\ket{j}$. /// /// $U = \sum^{2^n-1}_{j=0}\ket{j}\bra{j}\otimes V_j$. /// /// # Input /// ## unitaryGenerator /// A tuple where the first element `Int` is the number of unitaries $N$, /// and the second element `(Int -> ('T => () is Adj + Ctl))` /// is a function that takes an integer $j$ in $[0,N-1]$ and outputs the unitary /// operation $V_j$. /// /// # Output /// A multiply-controlled unitary operation $U$ that applies unitaries /// described by `unitaryGenerator`. /// /// # See Also /// - Microsoft.Quantum.Canon.MultiplexOperationsFromGenerator function MultiplexerFromGenerator(unitaryGenerator : (Int, (Int -> (Qubit[] => Unit is Adj + Ctl)))) : ((LittleEndian, Qubit[]) => Unit is Adj + Ctl) { return MultiplexOperationsFromGenerator(unitaryGenerator, _, _); } /// # Summary /// Returns a multiply-controlled unitary operation $U$ that applies a /// unitary $V_j$ when controlled by n-qubit number state $\ket{j}$. /// /// $U = \sum^{2^n-1}_{j=0}\ket{j}\bra{j}\otimes V_j$. /// /// # Input /// ## unitaryGenerator /// A tuple where the first element `Int` is the number of unitaries $N$, /// and the second element `(Int -> ('T => () is Adj + Ctl))` /// is a function that takes an integer $j$ in $[0,N-1]$ and outputs the unitary /// operation $V_j$. /// /// # Output /// A multiply-controlled unitary operation $U$ that applies unitaries /// described by `unitaryGenerator`. /// /// # See Also /// - Microsoft.Quantum.Canon.MultiplexOperationsBruteForceFromGenerator function MultiplexerBruteForceFromGenerator(unitaryGenerator : (Int, (Int -> (Qubit[] => Unit is Adj + Ctl)))) : ((LittleEndian, Qubit[]) => Unit is Adj + Ctl) { return MultiplexOperationsBruteForceFromGenerator(unitaryGenerator, _, _); } /// # Summary /// Computes a chain of AND gates /// /// # Description /// The auxiliary qubits to compute temporary results must be specified explicitly. /// The length of that register is `Length(ctrlRegister) - 2`, if there are at least /// two controls, otherwise the length is 0. internal operation ApplyAndChain(auxRegister : Qubit[], ctrlRegister : Qubit[], target : Qubit) : Unit is Adj { if Length(ctrlRegister) == 0 { X(target); } elif Length(ctrlRegister) == 1 { CNOT(Head(ctrlRegister), target); } else { EqualityFactI(Length(auxRegister), Length(ctrlRegister)); let controls1 = ctrlRegister[0..0] + auxRegister; let controls2 = Rest(ctrlRegister); let targets = auxRegister + [target]; ApplyToEachA(ApplyAnd, Zipped3(controls1, controls2, targets)); } } }

## References

- ↑ "Introduction to Q#". University of Washington. https://courses.cs.washington.edu/courses/cse490q/20au/hws/qsharp-intro.pdf.
- ↑
^{2.0}^{2.1}QuantumWriter. "The Q# Programming Language" (in en-us). https://docs.microsoft.com/en-us/quantum/quantum-qr-intro?view=qsharp-preview. - ↑
^{3.0}^{3.1}"Announcing the Microsoft Quantum Development Kit" (in en-US). https://cloudblogs.microsoft.com/quantum/2017/12/11/announcing-microsoft-quantum-development-kit/. - ↑ "Solving the quantum many-body problem with artificial neural networks". 15 February 2017. https://cloudblogs.microsoft.com/quantum/2017/02/15/solving-the-quantum-many-body-problem-with-artificial-neural-networks/.
- ↑ Scott Aaronson's blog, 2013, 'Microsoft: From QDOS to QMA in less than 35 years', https://scottaaronson.blog/?p=1471
- ↑ "What are the Q# programming language & QDK? - Azure Quantum" (in en-us). https://learn.microsoft.com/en-us/azure/quantum/overview-what-is-qsharp-and-qdk.
- ↑ "Microsoft announces quantum computing programming language" (in en-US). https://cloudblogs.microsoft.com/quantum/2017/09/26/microsoft-announces-quantum-computing-programming-language/.
- ↑ Microsoft is open-sourcing its Quantum Development Kit
- ↑ "The Women of QuArC". 30 March 2019. https://devblogs.microsoft.com/qsharp/the-women-of-quarc/.
- ↑ "Intro to Q# - Intro to Quantum Software Development". https://stem.mitre.org/quantum/software-tools/intro-qsharp.html.
- ↑ QuantumWriter. "Setting up the Q# development environment" (in en-us). https://docs.microsoft.com/en-us/quantum/quantum-installconfig?view=qsharp-preview.
- ↑ Akdogan, Erman (23 October 2022). "Quantum computing is coming for finance & crypto" (in en). https://medium.datadriveninvestor.com/quantum-computing-is-coming-for-finance-crypto-b56c0255cb09.
- ↑ "This Week in Programming: Get Quantum with Q Sharp". 16 December 2017. https://thenewstack.io/week-programming-get-quantum-q-sharp/.
- ↑ "Qubit Gate - an overview". https://www.sciencedirect.com/topics/engineering/qubit-gate.
- ↑ "Microsoft previews quantum computing development kit". https://www2.cio.com.au/article/631142/microsoft-previews-quantum-computing-development-kit/.
- ↑ "Types in Q# - Microsoft Quantum". https://docs.microsoft.com/en-us/quantum/user-guide/language/types.

## External links

Original source: https://en.wikipedia.org/wiki/Q Sharp.
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