Tower: Data Structures in Quantum Superposition

TL;DR

This paper introduces Tower, a quantum programming language with data structures supporting superposition, reversibility, and efficiency, enabling practical quantum algorithms that rely on complex data manipulations.

Contribution

It presents Core Tower, Boson, and Tower, pioneering tools and data structures for quantum programming with reversible, history-independent, and bounded-time operations.

Findings

First reversible, history-independent quantum memory allocator.

First implementation of quantum data structures like sets satisfying all properties.

Executable quantum library of data structures including lists, stacks, queues, and sets.

Abstract

Emerging quantum algorithms for problems such as element distinctness, subset sum, and closest pair demonstrate computational advantages by relying on abstract data structures. Practically realizing such an algorithm as a program for a quantum computer requires an efficient implementation of the data structure whose operations correspond to unitary operators that manipulate quantum superpositions of data. To correctly operate in superposition, an implementation must satisfy three properties -- reversibility, history independence, and bounded-time execution. Standard implementations, such as the representation of an abstract set as a hash table, fail these properties, calling for tools to develop specialized implementations. In this work, we present Core Tower, the first language for quantum programming with random-access memory. Core Tower enables the developer to implement data structures as pointer-based, linked data. It features a reversible semantics enabling every valid program to be translated to a unitary quantum circuit. We present Boson, the first memory allocator that supports reversible, history-independent, and constant-time dynamic memory allocation in quantum superposition. We also present Tower, a language for quantum programming with recursively defined data structures. Tower features a type system that bounds all recursion using classical parameters as is necessary for a program to execute on a quantum computer. Using Tower, we implement Ground, the first quantum library of data structures, including lists, stacks, queues, strings, and sets. We provide the first executable implementation of sets that satisfies all three mandated properties of reversibility, history independence, and bounded-time execution.