Quantum programming

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Quantum programming is the process of designing or assembling sequences of instructions, called quantum circuits, using gates, switches, and operators to manipulate a quantum system for a desired outcome or results of a given experiment. Quantum circuit algorithms can be implemented on integrated circuits, conducted with instrumentation, or written in a programming language for use with a quantum computer or a quantum processor.

Contents

With quantum processor based systems, quantum programming languages help express quantum algorithms using high-level constructs. [1] The field is deeply rooted in the open-source philosophy and as a result most of the quantum software discussed in this article is freely available as open-source software. [2]

Quantum computers, such as those based on the KLM protocol, a linear optical quantum computing (LOQC) model, use quantum algorithms (circuits) implemented with electronics, integrated circuits, instrumentation, sensors, and/or by other physical means.[ not verified in body ]

Other circuits designed for experimentation related to quantum systems can be instrumentation and sensor based.[ not verified in body ]

Quantum instruction sets

Quantum instruction sets are used to turn higher level algorithms into physical instructions that can be executed on quantum processors. Sometimes these instructions are specific to a given hardware platform, e.g. ion traps or superconducting qubits.

cQASM

cQASM, [3] also known as common QASM, is a hardware-agnostic quantum assembly language which guarantees the interoperability between all the quantum compilation and simulation tools. It was introduced by the QCA Lab at TUDelft.

Quil

Quil is an instruction set architecture for quantum computing that first introduced a shared quantum/classical memory model. It was introduced by Robert Smith, Michael Curtis, and William Zeng in A Practical Quantum Instruction Set Architecture. [4] Many quantum algorithms (including quantum teleportation, quantum error correction, simulation, [5] [6] and optimization algorithms [7] ) require a shared memory architecture.

OpenQASM

OpenQASM [8] is the intermediate representation introduced by IBM for use with Qiskit and the IBM Q Experience.

Blackbird

Blackbird [9] [10] is a quantum instruction set and intermediate representation used by Xanadu Quantum Technologies and Strawberry Fields. It is designed to represent continuous-variable quantum programs that can run on photonic quantum hardware.

Quantum software development kits

Quantum software development kits provide collections of tools to create and manipulate quantum programs. [11] They also provide the means to simulate the quantum programs or prepare them to be run using cloud-based quantum devices and self-hosted quantum devices.

SDKs with access to quantum processors

The following software development kits can be used to run quantum circuits on prototype quantum devices, as well as on simulators.

Perceval

An open-source project created by Quandela  [ fr ] for designing photonic quantum circuits and developing quantum algorithms, based on Python. Simulations are run either on the user's own computer or on the cloud. Perceval is also used to connect to Quandela's cloud-based photonic quantum processor. [12] [13]

Ocean

An Open Source suite of tools developed by D-Wave. Written mostly in the Python programming language, it enables users to formulate problems in Ising Model and Quadratic Unconstrained Binary Optimization formats (QUBO). Results can be obtained by submitting to an online quantum computer in Leap, D-Wave's real-time Quantum Application Environment, customer-owned machines, or classical samplers.[ citation needed ]

A sample code using projectq with Python QProg1-Refreshed.png
A sample code using projectq with Python

ProjectQ

An Open Source project developed at the Institute for Theoretical Physics at ETH, which uses the Python programming language to create and manipulate quantum circuits. [14] Results are obtained either using a simulator, or by sending jobs to IBM quantum devices.

Qrisp

Qrisp [15] is an Open Source project coordinated by the Eclipse Foundation [16] and developed in Python programming by Fraunhofer FOKUS [17] Qrisp is a high-level programming language for creating and compiling quantum algorithms. Its structured programming model enables scalable development and maintenance. The expressive syntax is based on variables instead of qubits, with the QuantumVariable as core class, and functions instead of gates. Additional tools, such as a performant simulator and automatic uncomputation, complement the extensive framework. Furthermore, it is platform independent, since it offers alternative compilation of elementary functions down to the circuit level, based on device-specific gate sets.

Qiskit

An Open Source project developed by IBM. [18] Quantum circuits are created and manipulated using Python. Results are obtained either using simulators that run on the user's own device, simulators provided by IBM or prototype quantum devices provided by IBM. As well as the ability to create programs using basic quantum operations, higher level tools for algorithms and benchmarking are available within specialized packages. [19] Qiskit is based on the OpenQASM standard for representing quantum circuits. It also supports pulse level control of quantum systems via QiskitPulse standard. [20]

Qibo

An open source full-stack API for quantum simulation, quantum hardware control and calibration developed by multiple research laboratories, including QRC, CQT and INFN. Qibo is a modular framework which includes multiple backends for quantum simulation and hardware control. [21] [22] This project aims at providing a platform agnostic quantum hardware control framework with drivers for multiple instruments [23] and tools for quantum calibration, characterization and validation. [24] This framework focuses on self-hosted quantum devices by simplifying the software development required in labs.

Forest

An open source project developed by Rigetti, which uses the Python programming language to create and manipulate quantum circuits. Results are obtained either using simulators or prototype quantum devices provided by Rigetti. As well as the ability to create programs using basic quantum operations, higher level algorithms are available within the Grove package. [25] Forest is based on the Quil instruction set.

t|ket>

A quantum programming environment and optimizing compiler developed by Cambridge Quantum Computing that targets simulators and several quantum hardware back-ends, released in December 2018. [26]

Strawberry Fields

An open-source Python library developed by Xanadu Quantum Technologies for designing, simulating, and optimizing continuous variable (CV) quantum optical circuits. [27] [28] Three simulators are provided - one in the Fock basis, one using the Gaussian formulation of quantum optics, [29] and one using the TensorFlow machine learning library. Strawberry Fields is also the library for executing programs on Xanadu's quantum photonic hardware. [30] [31]

PennyLane

An open-source Python library developed by Xanadu Quantum Technologies for differentiable programming of quantum computers. [32] [33] [34] [35] PennyLane provides users the ability to create models using TensorFlow, NumPy, or PyTorch, and connect them with quantum computer backends available from IBMQ, Google Quantum, Rigetti, Quantinuum [36] and Alpine Quantum Technologies. [37] [38]

Quantum Development Kit

A project developed by Microsoft [39] as part of the .NET Framework. Quantum programs can be written and run within Visual Studio and VSCode using the quantum programming language Q#. Programs developed in the QDK can be run on Microsoft's Azure Quantum, [40] and run on quantum computers from Quantinuum, [36] IonQ, and Pasqal. [41]

Cirq

An Open Source project developed by Google, which uses the Python programming language to create and manipulate quantum circuits. Programs written in Cirq can be run on IonQ, Pasqal, [41] Rigetti, and Alpine Quantum Technologies. [37]

Quantum programming languages

There are two main groups of quantum programming languages: imperative quantum programming languages and functional quantum programming languages.

Imperative languages

The most prominent representatives of the imperative languages are QCL, [42] LanQ [43] and Q|SI>. [44]

Ket

Ket [45] is an open-source embedded language designed to facilitate quantum programming, leveraging the familiar syntax and simplicity of Python. It serves as an integral component of the Ket Quantum Programming Platform, [46] seamlessly integrating with a Rust runtime library and a quantum simulator. Maintained by Quantuloop, the project emphasizes accessibility and versatility for researchers and developers. The following example demonstrates the implementation of a Bell state using Ket:

fromketimport*a,b=quant(2)# Allocate two quantum bitsH(a)# Put qubit `a` in a superpositioncnot(a,b)# Entangle the two qubits in the Bell statem_a=measure(a)# Measure qubit `a`, collapsing qubit `b` as wellm_b=measure(b)# Measure qubit `b`# Assert that the measurement of both qubits will always be equalassertm_a.value==m_b.value

QCL

Quantum Computation Language (QCL) is one of the first implemented quantum programming languages. [47] The most important feature of QCL is the support for user-defined operators and functions. Its syntax resembles the syntax of the C programming language and its classical data types are similar to primitive data types in C. One can combine classical code and quantum code in the same program.

Quantum pseudocode

Quantum pseudocode proposed by E. Knill is the first formalized language for description of quantum algorithms. It was introduced and, moreover, was tightly connected with a model of quantum machine called Quantum Random Access Machine (QRAM).

Q#

A language developed by Microsoft to be used with the Quantum Development Kit. [48]

Q|SI>

Q|SI> is a platform embedded in .Net language supporting quantum programming in a quantum extension of while-language. [44] [49] This platform includes a compiler of the quantum while-language [50] and a chain of tools for the simulation of quantum computation, optimisation of quantum circuits, termination analysis of quantum programs, [51] and verification of quantum programs. [52] [53]

Q language

Q Language is the second implemented imperative quantum programming language. [54] Q Language was implemented as an extension of C++ programming language. It provides classes for basic quantum operations like QHadamard, QFourier, QNot, and QSwap, which are derived from the base class Qop. New operators can be defined using C++ class mechanism.

Quantum memory is represented by class Qreg.

Qregx1;// 1-qubit quantum register with initial value 0Qregx2(2,0);// 2-qubit quantum register with initial value 0

The computation process is executed using a provided simulator. Noisy environments can be simulated using parameters of the simulator.

qGCL

Quantum Guarded Command Language (qGCL) was defined by P. Zuliani in his PhD thesis. It is based on Guarded Command Language created by Edsger Dijkstra.

It can be described as a language of quantum programs specification.

QMASM

Quantum Macro Assembler (QMASM) is a low-level language specific to quantum annealers such as the D-Wave. [55]

Scaffold

Scaffold is C-like language, that compiles to QASM and OpenQASM. It is built on top of the LLVM Compiler Infrastructure to perform optimizations on Scaffold code before generating a specified instruction set. [56] [57]

Silq

Silq is a high-level programming language for quantum computing with a strong static type system, developed at ETH Zürich. [58] [59]

LQP

The Logic of Quantum Programs (LQP) is a dynamic quantum logic, capable of expressing important features of quantum measurements and unitary evolutions of multi-partite states, and provides logical characterizations of various forms of entanglement. The logic has been used to specify and verify the correctness of various protocols in quantum computation. [60] [61]

Functional languages

Efforts are underway to develop functional programming languages for quantum computing. Functional programming languages are well-suited for reasoning about programs. Examples include Selinger's QPL, [62] and the Haskell-like language QML by Altenkirch and Grattage. [63] [64] Higher-order quantum programming languages, based on lambda calculus, have been proposed by van Tonder, [65] Selinger and Valiron [66] and by Arrighi and Dowek. [67]

QFC and QPL

QFC and QPL are two closely related quantum programming languages defined by Peter Selinger. They differ only in their syntax: QFC uses a flow chart syntax, whereas QPL uses a textual syntax. These languages have classical control flow but can operate on quantum or classical data. Selinger gives a denotational semantics for these languages in a category of superoperators.

QML

QML is a Haskell-like quantum programming language by Altenkirch and Grattage. [68] [63] Unlike Selinger's QPL, this language takes duplication, rather than discarding, of quantum information as a primitive operation. Duplication in this context is understood to be the operation that maps to , and is not to be confused with the impossible operation of cloning; the authors claim it is akin to how sharing is modeled in classical languages. QML also introduces both classical and quantum control operators, whereas most other languages rely on classical control.

An operational semantics for QML is given in terms of quantum circuits, while a denotational semantics is presented in terms of superoperators, and these are shown to agree. Both the operational and denotational semantics have been implemented (classically) in Haskell. [69]

LIQUi|>

LIQUi|> (pronounced liquid) is a quantum simulation extension on the F# programming language. [70] It is currently being developed by the Quantum Architectures and Computation Group (QuArC) [71] part of the StationQ efforts at Microsoft Research. LIQUi|> seeks to allow theorists to experiment with quantum algorithm design before physical quantum computers are available for use. [72]

It includes a programming language, optimization and scheduling algorithms, and quantum simulators. LIQUi|> can be used to translate a quantum algorithm written in the form of a high-level program into the low-level machine instructions for a quantum device. [73]

Quantum lambda calculi

Quantum lambda calculi are extensions of the classical lambda calculus introduced by Alonzo Church and Stephen Cole Kleene in the 1930s. The purpose of quantum lambda calculi is to extend quantum programming languages with a theory of higher-order functions.

The first attempt to define a quantum lambda calculus was made by Philip Maymin in 1996. [74] His lambda-q calculus is powerful enough to express any quantum computation. However, this language can efficiently solve NP-complete problems, and therefore appears to be strictly stronger than the standard quantum computational models (such as the quantum Turing machine or the quantum circuit model). Therefore, Maymin's lambda-q calculus is probably not implementable on a physical device [ citation needed ].

In 2003, André van Tonder defined an extension of the lambda calculus suitable for proving correctness of quantum programs. He also provided an implementation in the Scheme programming language. [75]

In 2004, Selinger and Valiron defined a strongly typed lambda calculus for quantum computation with a type system based on linear logic. [76]

Quipper

Quipper was published in 2013. [77] [78] It is implemented as an embedded language, using Haskell as the host language. [79] For this reason, quantum programs written in Quipper are written in Haskell using provided libraries. For example, the following code implements preparation of a superposition

importQuipperspos::Bool->CircQubitsposb=doq<-qinitbr<-hadamardqreturnr

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This glossary of quantum computing is a list of definitions of terms and concepts used in quantum computing, its sub-disciplines, and related fields.

References

  1. ↑ Jarosław Adam Miszczak (2012). High-level Structures in Quantum Computing. Morgan & Claypool Publishers. ISBN   9781608458516.
  2. ↑ "Comprehensive list of quantum open-source projects". Github. Retrieved January 27, 2022.
  3. ↑ Bertels, K.; Almudever, C. G.; Hogaboam, J. W.; Ashraf, I.; Guerreschi, G. G.; Khammassi, N. (May 24, 2018). "cQASM v1.0: Towards a Common Quantum Assembly Language". arXiv: 1805.09607v1 [quant-ph].
  4. ↑ Smith, Robert S.; Curtis, Michael J.; Zeng, William J. (2016). "A Practical Quantum Instruction Set Architecture". arXiv: 1608.03355 [quant-ph].
  5. ↑ McClean, Jarrod R.; Romero, Jonathan; Babbush, Ryan; Aspuru-Guzik, Alán (February 4, 2016). "The theory of variational hybrid quantum-classical algorithms". New Journal of Physics. 18 (2): 023023. arXiv: 1509.04279 . Bibcode:2016NJPh...18b3023M. doi:10.1088/1367-2630/18/2/023023. ISSN   1367-2630. S2CID   92988541.
  6. ↑ Rubin, Nicholas C.; Curtis, Michael J.; Zeng, William J. (2016). "A Hybrid Classical/Quantum Approach for Large-Scale Studies of Quantum Systems with Density Matrix Embedding Theory". arXiv: 1610.06910 [quant-ph].
  7. ↑ Farhi, Edward; Goldstone, Jeffrey; Gutmann, Sam (2014). "A Quantum Approximate Optimization Algorithm". arXiv: 1411.4028 [quant-ph].
  8. ↑ qiskit-openqasm: OpenQASM specification, International Business Machines, July 4, 2017, retrieved July 6, 2017
  9. ↑ "Blackbird Quantum Assembly Language — Blackbird 0.2.0 documentation". quantum-blackbird.readthedocs.io. Retrieved June 24, 2019.
  10. ↑ Weedbrook, Christian; Amy, Matthew; Bergholm, Ville; Quesada, Nicolás; Izaac, Josh; Killoran, Nathan (March 11, 2019). "Strawberry Fields: A Software Platform for Photonic Quantum Computing". Quantum. 3: 129. arXiv: 1804.03159 . Bibcode:2019Quant...3..129K. doi:10.22331/q-2019-03-11-129. S2CID   54763305.
  11. ↑ Häner, Thomas; Steiger, Damian S.; Svore, Krysta; Troyer, Matthias (2018). "A software methodology for compiling quantum programs". Quantum Science and Technology. 3 (2): 020501. arXiv: 1604.01401 . Bibcode:2018QS&T....3b0501H. doi:10.1088/2058-9565/aaa5cc. ISSN   2058-9565. S2CID   1922315.
  12. ↑ "La puissance d'un ordinateur quantique testée en ligne (The power of a quantum computer tested online)". Le Monde.fr. Le Monde. November 22, 2022.
  13. ↑ Heurtel, Nicolas; Fyrillas, Andreas; de Gliniasty, Grégoire; Le Bihan, Raphaël; Malherbe, Sébastien; Pailhas, Marceau; Bertasi, Eric; Bourdoncle, Boris; Emeriau, Pierre-Emmanuel; Mezher, Rawad; Music, Luka; Belabas, Nadia; Valiron, Benoît; Senellart, Pascale; Mansfield, Shane; Senellart, Jean (February 21, 2023). "Perceval: A Software Platform for Discrete Variable Photonic Quantum Computing". Quantum. 7: 931. arXiv: 2204.00602 . Bibcode:2023Quant...7..931H. doi:10.22331/q-2023-02-21-931. S2CID   247922568.
  14. ↑ "Home".
  15. ↑ "Qrisp official website".
  16. ↑ "Eclipse Foundation (website)".
  17. ↑ "Fraunhofer FOKUS (website)".
  18. ↑ "qiskit.org". qiskit.org.
  19. ↑ "Qiskit Overview" . Retrieved February 10, 2021.
  20. ↑ McKay, David C.; Alexander, Thomas; Bello, Luciano; Biercuk, Michael J.; Bishop, Lev; Chen, Jiayin; Chow, Jerry M.; Córcoles, Antonio D.; Egger, Daniel; Filipp, Stefan; Gomez, Juan; Hush, Michael; Javadi-Abhari, Ali; Moreda, Diego; Nation, Paul; Paulovicks, Brent; Winston, Erick; Wood, Christopher J.; Wootton, James; Gambetta, Jay M. (2018). "Qiskit Backend Specifications for OpenQASM and OpenPulse Experiments". arXiv: 1809.03452 [quant-ph].
  21. ↑ Efthymiou, Stavros; Ramos-Calderer, Sergi; Bravo-Prieto, Carlos; Pérez-Salinas, Adrián; García-Martín, Diego; Garcia-Saez, Artur; Latorre, José Ignacio; Carrazza, Stefano (January 1, 2022). "Qibo: a framework for quantum simulation with hardware acceleration". Quantum Science and Technology. 7 (1): 015018. arXiv: 2009.01845 . Bibcode:2022QS&T....7a5018E. doi:10.1088/2058-9565/ac39f5. hdl:2434/887963. ISSN   2058-9565. S2CID   221507478.
  22. ↑ Efthymiou, Stavros; Lazzarin, Marco; Pasquale, Andrea; Carrazza, Stefano (September 22, 2022). "Quantum simulation with just-in-time compilation". Quantum. 6: 814. arXiv: 2203.08826 . Bibcode:2022Quant...6..814E. doi: 10.22331/q-2022-09-22-814 . S2CID   247518955.
  23. ↑ "Qibolab". November 2, 2022 – via GitHub.
  24. ↑ "Qibocal". November 1, 2022 – via GitHub.
  25. ↑ "Welcome to the Documentation for Grove! — Grove 1.7.0 documentation". grove-docs.readthedocs.io.
  26. ↑ "pytket". GitHub . January 22, 2022.
  27. ↑ "Strawberry Fields — Strawberry Fields 0.8.0 documentation". strawberryfields.readthedocs.io. Retrieved September 25, 2018.
  28. ↑ Killoran, Nathan; Izaac, Josh; Quesada, Nicolás; Bergholm, Ville; Amy, Matthew; Weedbrook, Christian (2019). "Strawberry Fields: A Software Platform for Photonic Quantum Computing". Quantum. 3: 129. arXiv: 1804.03159 . Bibcode:2019Quant...3..129K. doi:10.22331/q-2019-03-11-129. S2CID   54763305.
  29. ↑ Weedbrook, Christian; Pirandola, Stefano; García-Patrón, Raúl; Cerf, Nicolas J.; Ralph, Timothy C.; Shapiro, Jeffrey H.; Lloyd, Seth (May 1, 2012). "Gaussian quantum information". Reviews of Modern Physics. 84 (2): 621–669. arXiv: 1110.3234 . Bibcode:2012RvMP...84..621W. doi:10.1103/RevModPhys.84.621. S2CID   119250535.
  30. ↑ "Hardware — Strawberry Fields". strawberryfields.ai. Retrieved March 26, 2021.
  31. ↑ "In the Race to Hundreds of Qubits, Photons May Have "Quantum Advantage"". IEEE Spectrum: Technology, Engineering, and Science News. March 5, 2021. Retrieved March 26, 2021.
  32. ↑ "PennyLane Documentation — PennyLane 0.14.1 documentation". pennylane.readthedocs.io. Retrieved March 26, 2021.
  33. ↑ "AWS joins PennyLane, an open-source framework that melds machine learning with quantum computing". SiliconANGLE. February 17, 2021. Retrieved March 26, 2021.
  34. ↑ "SD Times Open-Source Project of the Week: PennyLane". SD Times. February 26, 2021. Retrieved March 26, 2021.
  35. ↑ Salamone, Salvatore (December 13, 2020). "Real-time Analytics News Roundup for Week Ending December 12". RTInsights. Retrieved March 26, 2021.
  36. 1 2 "Accelerating Quantum Computing". www.quantinuum.com.
  37. 1 2 "Home". AQT | ALPINE QUANTUM TECHNOLOGIES.
  38. ↑ "Plugins and ecosystem — PennyLane". pennylane.ai. Retrieved March 26, 2021.
  39. ↑ "Azure Quantum documentation, QDK & Q# API reference - Azure Quantum". learn.microsoft.com.
  40. ↑ "What is Azure Quantum? - Azure Quantum". learn.microsoft.com. January 11, 2023.
  41. 1 2 "PASQAL". PASQAL.
  42. ↑ Bernhard Omer. "The QCL Programming Language".
  43. ↑ Hynek Mlnařík. "LanQ – a quantum imperative programming language".
  44. 1 2 Liu, Shusen; Zhou, li; Guan, Ji; He, Yang; Duan, Runyao; Ying, Mingsheng (May 9, 2017). "Q|SI>: A Quantum Programming Language". Scientia Sinica Informationis. 47 (10): 1300. arXiv: 1710.09500 . doi:10.1360/N112017-00095. S2CID   9163705.
  45. ↑ Da Rosa, Evandro Chagas Ribeiro; De Santiago, Rafael (January 31, 2022). "Ket Quantum Programming". ACM Journal on Emerging Technologies in Computing Systems. 18 (1): 1–25. doi:10.1145/3474224. ISSN   1550-4832.
  46. ↑ "Ket Quantum Programming". quantumket.org. Retrieved May 18, 2023.
  47. ↑ "QCL - A Programming Language for Quantum Computers". tuwien.ac.at. Retrieved July 20, 2017.
  48. ↑ "Introduction to Q# & Quantum Development Kit - Azure Quantum". learn.microsoft.com. March 30, 2023.
  49. ↑ Ying, Mingsheng (January 2012). "Floyd–hoare Logic for Quantum Programs". ACM Trans. Program. Lang. Syst. 33 (6): 19:1–19:49. doi: 10.1145/2049706.2049708 . ISSN   0164-0925. S2CID   416960.
  50. ↑ Ying, Mingsheng; Feng, Yuan (2010). "A Flowchart Language for Quantum Programming". IEEE Transactions on Software Engineering. 37 (4): 466–485. doi:10.1109/TSE.2010.94. ISSN   0098-5589. S2CID   5879273.
  51. ↑ Ying, Mingsheng; Yu, Nengkun; Feng, Yuan; Duan, Runyao (2013). "Verification of quantum programs". Science of Computer Programming. 78 (9): 1679–1700. arXiv: 1106.4063 . doi:10.1016/j.scico.2013.03.016. S2CID   18913620.
  52. ↑ Ying, Mingsheng; Ying, Shenggang; Wu, Xiaodi (2017), "Invariants of quantum programs: Characterisations and generation", ACM SIGPLAN Notices, 52: 818–832, doi:10.1145/3093333.3009840, hdl: 10453/127333
  53. ↑ Liu, Tao; Li, Yangjia; Wang, Shuling; Ying, Mingsheng; Zhan, Naijun (2016). "A Theorem Prover for Quantum Hoare Logic and its Applications". arXiv: 1601.03835 [cs.LO].
  54. ↑ "Software for the Q language". November 23, 2001. Archived from the original on June 20, 2009. Retrieved July 20, 2017.
  55. ↑ Scott Pakin, "A Quantum Macro Assembler", Proceedings of the 20th Annual IEEE High Performance Extreme Computing Conference 2016
  56. ↑ Javadi-Abhari, Ali. "Scaffold: Quantum Programming Language". Princeton University-Department of Computer Science. Princeton University. Retrieved September 22, 2020.
  57. ↑ Litteken, Andrew (May 28, 2020). "An updated LLVM-based quantum research compiler with further OpenQASM support". Quantum Science and Technology. 5 (3): 034013. Bibcode:2020QS&T....5c4013L. doi: 10.1088/2058-9565/ab8c2c . OSTI   1803951. S2CID   219101628.
  58. ↑ "What is Silq?". silq.ethz.ch. Retrieved June 21, 2020.
  59. ↑ Bichsel, Benjamin; Baader, Maximilian; Gehr, Timon; Vechev, Martin (June 11, 2020). "Silq: A high-level quantum language with safe uncomputation and intuitive semantics". Proceedings of the 41st ACM SIGPLAN Conference on Programming Language Design and Implementation. London UK: ACM. pp. 286–300. doi:10.1145/3385412.3386007. ISBN   978-1-4503-7613-6. S2CID   219397029.
  60. ↑ A. Baltag and S. Smets, "LQP: The Dynamic Logic of Quantum Information", Mathematical Structures in Computer Science 16(3):491-525, 2006.
  61. ↑ Baltag, Alexandru; Bergfeld, Jort; Kishida, Kohei; Sack, Joshua; Smets, Sonja; Zhong, Shengyang (2014). "PLQP & Company: Decidable Logics for Quantum Algorithms". International Journal of Theoretical Physics. 53 (10): 3628–3647. Bibcode:2014IJTP...53.3628B. doi:10.1007/s10773-013-1987-3. S2CID   254573992.
  62. ↑ Peter Selinger, "Towards a quantum programming language", Mathematical Structures in Computer Science 14(4):527-586, 2004.
  63. 1 2 Jonathan Grattage: QML Research (website)
  64. ↑ T. Altenkirch, V. Belavkin, J. Grattage, A. Green, A. Sabry, J. K. Vizzotto, QML: A Functional Quantum Programming Language Archived 2006-07-10 at the Wayback Machine (website)
  65. ↑ Andre van Tonder, "A Lambda Calculus for Quantum Computation", SIAM J. Comput., 33(5), 1109–1135. (27 pages), 2004. Also available from arXiv:quant-ph/0307150
  66. ↑ Peter Selinger and Benoît Valiron, "A lambda calculus for quantum computation with classical control", Mathematical Structures in Computer Science 16(3):527-552, 2006.
  67. ↑ Pablo Arrighi, Gilles Dowek, "Linear-algebraic lambda-calculus: higher-order, encodings and confluence", 2006
  68. ↑ "QML: A Functional Quantum Programming Language". September 26, 2007. Archived from the original on September 26, 2007.
  69. ↑ Jonathan Grattage, QML: A Functional Quantum Programming Language (compiler) Archived 2016-03-05 at the Wayback Machine , 2005–2008
  70. ↑ "The Language Integrated Quantum Operations Simulator". github.io. Retrieved July 20, 2017.
  71. ↑ Quantum Architectures and Computation Group (QuArC), https://www.microsoft.com/en-us/research/group/quantum-architectures-and-computation-group-quarc/, 2011
  72. ↑ "StationQ". microsoft.com. Retrieved July 20, 2017.
  73. ↑ "Language-Integrated Quantum Operations: LIQUi|>". Microsoft . 2016.
  74. ↑ Philip Maymin, "Extending the Lambda Calculus to Express Randomized and Quantumized Algorithms", 1996
  75. ↑ André van Tonder. "A lambda calculus for quantum computation (website)". Archived from the original on March 5, 2016. Retrieved October 2, 2007.
  76. ↑ Peter Selinger, Benoˆıt Valiron, "Quantum Lambda Calculus"
  77. ↑ "The Quipper Language".
  78. ↑ Alexander S. Green; Peter LeFanu Lumsdaine; Neil J. Ross; Peter Selinger; Benoît Valiron. "The Quipper Language (website)".
  79. ↑ Alexander S. Green; Peter LeFanu Lumsdaine; Neil J. Ross; Peter Selinger; Benoît Valiron (2013). "An Introduction to Quantum Programming in Quipper". Reversible Computation. Lecture Notes in Computer Science. Vol. 7948. pp. 110–124. arXiv: 1304.5485 . doi:10.1007/978-3-642-38986-3_10. ISBN   978-3-642-38985-6. S2CID   9135905.

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