[Paper Review] InQuIR: Intermediate Representation for Interconnected Quantum Computers

S. Nishio, Ryo Wakizaka|arXiv (Cornell University)|Feb 1, 2023

Quantum Computing Algorithms and Architecture4 citations

TL;DR

This paper introduces InQuIR, a formally-specified intermediate representation for interconnected quantum computers that enables precise modeling of distributed quantum programs, including communication and computation across multiple processors. It provides a foundation for static verification, resource estimation, and tooling to detect issues like deadlock and qubit exhaustion, enhancing reusability and reliability of compiled quantum programs across heterogeneous architectures.

ABSTRACT

Various physical constraints limit the number of qubits that can be implemented in a single quantum processor, and thus it is necessary to connect multiple quantum processors via quantum interconnects. While several compiler implementations for interconnected quantum computers have been proposed, there is no suitable representation as their compilation target. The lack of such representation impairs the reusability of compiled programs and makes it difficult to reason formally about the complicated behavior of distributed quantum programs. We propose InQuIR, an intermediate representation that can express communication and computation on distributed quantum systems. InQuIR has formal semantics that allows us to describe precisely the behaviors of distributed quantum programs. We give examples written in InQuIR to illustrate the problems arising in distributed programs, such as deadlock. We present a roadmap for static verification using type systems to deal with such a problem. We also provide software tools for InQuIR and evaluate the computational costs of quantum circuits under various conditions. Our tools are available at https://github.com/team-InQuIR/InQuIR.

Motivation & Objective

• To address the lack of a standardized compilation target for distributed quantum programs running on interconnected quantum processors.
• To enable formal reasoning about complex behaviors in distributed quantum programs, such as communication patterns, resource consumption, and runtime errors.
• To improve reusability and portability of compiled quantum programs across different quantum hardware architectures.
• To support static verification techniques—particularly type systems—for detecting errors like deadlock and qubit exhaustion before execution.
• To provide a software toolchain for performance evaluation, resource estimation, and compilation from existing formats like OpenQASM to InQuIR.

Proposed method

• Designing InQuIR as a formal intermediate representation with a well-defined syntax and operational semantics for distributed quantum computation.
• Defining instruction sets that model remote quantum operations, entanglement distribution (e.g., EPR pairs), and qubit management across processors.
• Introducing a dependency-aware execution model that tracks data and communication dependencies to model asynchronous program behavior.
• Proposing a type system based on linear types and multiparty session types to statically verify deadlock freedom and resource consumption.
• Implementing a software toolchain including a compiler frontend from OpenQASM, a runtime evaluator, and a resource estimator for circuit cost analysis.
• Using formal semantics to enable precise reasoning about program behavior, including error states such as qubit memory exhaustion and communication deadlocks.

Experimental results

Research questions

• RQ1 How can we formally represent distributed quantum programs that span multiple interconnected quantum processors?
• RQ2 What are the key failure modes—such as deadlock or resource exhaustion—in distributed quantum programs, and how can they be modeled?
• RQ3 Can a type system be designed to statically detect runtime errors like deadlock in asynchronous distributed quantum programs?
• RQ4 How can resource consumption (e.g., qubits, EPR pairs, circuit depth) be estimated and optimized in a portable, architecture-agnostic intermediate representation?
• RQ5 What is the feasibility of using InQuIR as a compilation target for both NISQ and fault-tolerant quantum computing systems?

Key findings

• InQuIR successfully models complex distributed quantum behaviors, including remote operations, entanglement distribution, and communication protocols across multiple processors.
• The formal semantics of InQuIR allow precise, machine-checkable reasoning about program execution, enabling accurate modeling of asynchronous and concurrent behaviors.
• The paper demonstrates concrete examples of runtime errors such as deadlock and qubit memory exhaustion, showing how they can be detected through formal analysis.
• A roadmap for static verification using linear types and multiparty session types is proposed, offering a path to prevent deadlock and resource misuse at compile time.
• The implemented toolchain enables performance evaluation and resource estimation for InQuIR programs, with support for compilation from OpenQASM and extensibility to other input formats.
• InQuIR is general enough to support future architectures, including fault-tolerant quantum computing and NUMA-like models, with potential for dynamic rescheduling extensions.