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Despite rapid progress in the field, it is still challenging to discover new ways to take advantage of quantum computation: all quantum algorithms need to be designed by hand, and quantum mechanics is notoriously counterintuitive. In this…

Quantum Physics · Physics 2023-05-04 Leopoldo Sarra , Kevin Ellis , Florian Marquardt

We introduce a novel scheme of quantum recursive programming, in which large unitary transformations, i.e. quantum gates, can be recursively defined using quantum case statements, which are quantum counterparts of conditionals and case…

Programming Languages · Computer Science 2023-11-06 Mingsheng Ying , Zhicheng Zhang

We describe a family of recursive methods for the synthesis of qubit permutations on quantum computers with limited qubit connectivity. Two objectives are of importance: circuit size and depth. In each case we combine a scalable heuristic…

Quantum Physics · Physics 2023-08-25 Cynthia Chen , Bruno Schmitt , Helena Zhang , Lev S. Bishop , Ali Javadi-Abhari

Quantum unitary synthesis addresses the problem of translating abstract quantum algorithms into sequences of hardware-executable quantum gates. Solving this task exactly is infeasible in general due to the exponential growth of the…

Quantum Physics · Physics 2026-02-19 Lukas Theißinger , Thore Gerlach , David Berghaus , Christian Bauckhage

A key challenge of quantum programming is uncomputation: the reversible deallocation of qubits. And while there has been much recent progress on automating uncomputation, state-of-the-art methods are insufficient for handling today's…

Programming Languages · Computer Science 2024-06-21 Hristo Venev , Timon Gehr , Dimitar Dimitrov , Martin Vechev

Recursive techniques have recently been introduced into quantum programming so that a variety of large quantum circuits and algorithms can be elegantly and economically programmed. In this paper, we present a proof system for formal…

Quantum Physics · Physics 2024-11-08 Mingsheng Ying , Zhicheng Zhang

We introduce Qunity, a new quantum programming language designed to treat quantum computing as a natural generalization of classical computing. Qunity presents a unified syntax where familiar programming constructs can have both quantum and…

Programming Languages · Computer Science 2025-08-08 Finn Voichick , Liyi Li , Robert Rand , Michael Hicks

Quantum computers have leaped from the theoretical realm into a race to large-scale implementations. This is due to the promise of revolutionary speedups, where achieving such speedup requires designing an algorithm that harnesses the…

Quantum recursive programming has been recently introduced for describing sophisticated and complicated quantum algorithms in a compact and elegant way. However, implementation of quantum recursion involves intricate interplay between…

Quantum Physics · Physics 2025-06-17 Zhicheng Zhang , Mingsheng Ying

With the growing interest in quantum programs, ensuring their correctness is a fundamental challenge. Although constraint-solving techniques can overcome some limitations of traditional testing and verification, they have not yet been…

Quantum Physics · Physics 2026-02-25 Shangzhou Xia , Haitao Fu , Jianjun Zhao

We present a scalable, robust approach to creating quantum programs of arbitrary size and complexity. The approach is based on the true abstraction of the problem. The quantum program is expressed in terms of a high-level model together…

Quantum programs today are written at a low level of abstraction - quantum circuits akin to assembly languages - and the unitary parts of even advanced quantum programming languages essentially function as circuit description languages.…

Programming Languages · Computer Science 2025-12-02 Chris Heunen , Louis Lemonnier , Christopher McNally , Alex Rice

We introduce isQ, a new software stack for quantum programming in an imperative programming language, also named isQ. The aim of isQ is to make the programmers write quantum programs as conveniently as possible. In particular: 1) The isQ…

Quantum Physics · Physics 2023-11-22 Jingzhe Guo , Huazhe Lou , Riling Li , Wang Fang , Junyi Liu , Peixun Long , Shenggang Ying , Mingsheng Ying

Quantum gates are the fundamental instructions of digital quantum computers. Current programming languages, systems, and software development toolkits identify these operational gates by their titles, which requires a shared understanding…

Programming Languages · Computer Science 2025-01-17 Ed Younis

While the ability to build quantum computers is improving dramatically, developing quantum algorithms is limited and relies on human insight and ingenuity. Although a number of quantum programming languages have been developed, it is…

Software Engineering · Computer Science 2022-10-07 Kentaro Murakami , Jianjun Zhao

Most existing quantum programming languages are based on the quantum circuit model of computation, as higher-level abstractions are particularly challenging to implement - especially ones relating to quantum control flow. The Qunity…

Programming Languages · Computer Science 2025-10-14 Mikhail Mints , Finn Voichick , Leonidas Lampropoulos , Robert Rand

Uncomputation is an essential part of reversible computing and plays a vital role in quantum computing. Using this technique, memory resources can be safely deallocated without performing a nonreversible deletion process. For the case of…

Quantum Physics · Physics 2023-07-24 Raphael Seidel , Nikolay Tcholtchev , Sebastian Bock , Manfred Hauswirth

Recent research in multi-valued logic for quantum computing has shown practical advantages for scaling up a quantum computer. Multivalued quantum systems have also been used in the framework of quantum cryptography, and the concept of a…

Quantum Physics · Physics 2007-05-23 Faisal Shah Khan , Marek Perkowski

In the Noisy Intermediate Scale Quantum (NISQ) era, finding implementations of quantum algorithms that minimize the number of expensive and error prone multi-qubit gates is vital to ensure computations produce meaningful outputs. Unitary…

Quantum Physics · Physics 2023-06-12 Mathias Weiden , Ed Younis , Justin Kalloor , John Kubiatowicz , Costin Iancu

The quantum computer has become contemporary reality, with the first two-qubit machine of mere decades ago transforming into cloud-accessible devices with tens, hundreds, or -- in a few cases -- even thousands of qubits. While such hardware…

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