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Programming Languages for Quantum Computing: Key Concepts and Frameworks

This document outlines the foundational principles of quantum programming languages (QPLs) as discussed by Vadim von Brzeski. It explores the Quantum RAM (QRAM) model, the sequence of quantum operations, and the need for reversibility in quantum computations. It contrasts two approaches: formal semantics with type systems and pragmatic implementations using classical simulators and popular programming languages like C++ and Haskell. Noteworthy examples include Quantum Lambda Calculus and Reversible Computation methodologies. The interplay of control, measurements, and entanglement in quantum states is also examined.

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Programming Languages for Quantum Computing: Key Concepts and Frameworks

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  1. Programming Languages for Quantum Computing“Just the High (qu)Bits” Vadim von Brzeski vvonbrze@ucsc.edu CS 203

  2. QRAM Model of QCClassical Control, Quantum Data Quantum Subsystem (QRAM) Sequence of Operations qureg Classical Control System Measurement • Typical Sequence of a Quantum Computation : • Initialize quantum subsystem • Perform sequence of operations (transformations) • Measure the result (one or more qubits) • Is the result correct ? No – Goto to Step 1. register(s) of n qubits in quantum superposition of all 2n possible states

  3. Constraints on a Quantum Program qubit q, p; bit b, c; ... q := p; ... ... b := p && p; quantum_op (p, p); ... ... c := p; quantum_op(p); .... .... quantum_op(q); All operations on quantum states must be reversible. No-cloning rule : cannot copy a quantum system that is in an unknown state. Operations must be on distinct states. Copy-by-value not allowed. An implicit measurement of qubit p. Collapses the quantum state of p (side-effect). quantum_op(p) will not yield expected result. If p and q are in an entangled quantum state, measuring p above also affects q. How do you ensure a quantum program is well-formed and well-typed ?

  4. Two Camps • Formalists • Define formal semantics and type systems for QPLs • Semantics of non-deterministic programs • “weakest precondition”  “greatest pre-expectation” • Quantum lambda calculi • Functional language domain • Focus on static checking • Pragmatists • Quantum simulators on classical computers • Extensions of popular imperative and functional languages • C++ • Haskell • Run-time checking

  5. Two Examples • Quantum Lambda Calculus (van Tonder) • Based on theory of linear lambda calculi • e :: = x | λx.e | e e | !e | λ!x.e • Linear term may appear in a function body exactly once • (λx. (x x)) is not valid since x is a linear term • Reversible Computation (Sanders & Zuliani, qGCL) • Set of rules (compiler) for transforming non-reversible programs to reversible programs Non-linear terms push x; x := e; pop x; x := e

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