Twist: sound reasoning for purity and entanglement in Quantum programs

Abstract

Quantum programming languages enable developers to implement algorithms for quantum computers that promise computational breakthroughs in classically intractable tasks. Programming quantum computers requires awareness of entanglement , the phenomenon in which measurement outcomes of qubits are correlated. Entanglement can determine the correctness of algorithms and suitability of programming patterns. In this work, we formalize purity as a central tool for automating reasoning about entanglement in quantum programs. A pure expression is one whose evaluation is unaffected by the measurement outcomes of qubits that it does not own, implying freedom from entanglement with any other expression in the computation. We present Twist, the first language that features a type system for sound reasoning about purity. The type system enables the developer to identify pure expressions using type annotations. Twist also features purity assertion operators that state the absence of entanglement in the output of quantum gates. To soundly check these assertions, Twist uses a combination of static analysis and runtime verification. We evaluate Twist’s type system and analyses on a benchmark suite of quantum programs in simulation, demonstrating that Twist can express quantum algorithms, catch programming errors in them, and support programs that existing languages disallow, while incurring runtime verification overhead of less than 3.5%.

Advances in Quantum Computation and Quantum Technologies: A Design Automation Perspective

“…These are merely some of the key safety guarantees made by recent quantum programming languages. Others include guaranteeing that qubits are separable from the rest of the state, as in the Twist programming language [71], through a mixture of static annotations and dynamic assertions and checks. λ Q# [72], a proposed formal core for Q#, uses singleton types to guarantee that multiple aliases of a qubit aren't passed to the same operation, while enforcing stack discipline.…”

Birkhoff-von Neumann Quantum Logic as an Assertion Language for Quantum Programs

“…Quantum Hoare Logic: The rapid progress of quantum computing hardware in the last decade has stimulated recent intensive research on quantum programming methodology. In particular, several program logics have been defined [6,7,3,13,25,48,49,4,46,58,28,31] and various verification and analysis techniques have been developed [41,40,10,17,18,22,47,45,56,38,55,53] for quantum programs (see also surveys [52,29,8]). Among them, D'Hondt and Panangaden [12] introduced the notion of quantum weakest precondition, where a quantum predicate is considered as a physical observable with eigenvalues in the unit interval, which can be mathematically modelled as a Hermitian operator between the zero and identity operators, and is often called an effect in the quantum foundations literature.…”