Tower: data structures in Quantum superposition

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.

Twist: sound reasoning for purity and entanglement in Quantum programs

“…To implement Example 1.2, the developer must explicitly construct gate-level circuits with the correct effect, which are complex in practice [66; 91]. Limited Support QML [5], Silq [20], and Tower [107] support an if construct for binary branching in superposition, whose circuit is known to the compiler. They do not support any other construct, such as iteration, in superposition.…”

Quantum Data Science: Leveraging Data Analytics for Advancing Quantum Computing

“…The following section focuses on Quantum Error Correction and Noise Mitigation [22], covering error correction codes, noise characterization, and mitigation strategies crucial for robust quantum computing. The subsequent section addresses Quantum Software Development Tools and Frameworks [4,11], surveying quantum programming languages [16,25,27,28], development frameworks [5,9,15,17], and simulation tools for designing and optimizing quantum algorithms [2,3,13,19].…”