[Paper Review] Advances in compilation for quantum hardware -- A demonstration of magic state distillation and repeat-until-success protocols

Natalie C. Brown, John Peter Campora+9 more|arXiv (Cornell University)|Oct 18, 2023

Quantum Computing Algorithms and Architecture4 citations

TL;DR

This paper demonstrates the first real-time implementation of magic state distillation and repeat-until-success (RUS) protocols on quantum hardware using Quantum Intermediate Representation (QIR). It shows that QIR enables efficient compilation of complex fault-tolerant quantum programs with performance approaching hand-optimized assembly, leveraging the LLVM toolchain to optimize quantum-classical control flow and loop unrolling for error-corrected protocols.

ABSTRACT

Fault-tolerant protocols enable large and precise quantum algorithms. Many such protocols rely on a feed-forward processing of data, enabled by a hybrid of quantum and classical logic. Representing the control structure of such programs can be a challenge. Here we explore two such fault-tolerant subroutines and analyze the performance of the subroutines using Quantum Intermediate Representation (QIR) as their underlying intermediate representation. First, we look at QIR's ability to leverage the LLVM compiler toolchain to unroll the quantum iteration logic required to perform magic state distillation on the $[[5,1,3]]$ quantum error-correcting code as originally introduced by Bravyi and Kitaev [Phys. Rev. A 71, 022316 (2005)]. This allows us to not only realize the first implementation of a real-time magic state distillation protocol on quantum hardware, but also demonstrate QIR's ability to optimize complex program structures without degrading machine performance. Next, we investigate a different fault-tolerant protocol that was first introduced by Paetznick and Svore [arXiv:1311.1074 (2013)], that reduces the amount of non-Clifford gates needed for a particular algorithm. We look at four different implementations of this two-stage repeat-until-success algorithm to analyze the performance changes as the results of programming choices. We find the QIR offers a viable representation for a compiled high-level program that performs nearly as well as a hand-optimized version written directly in quantum assembly. Both of these results demonstrate QIR's ability to accurately and efficiently expand the complexity of fault-tolerant protocols that can be realized today on quantum hardware.

Motivation & Objective

• To enable practical realization of fault-tolerant quantum protocols on current noisy hardware by compiling high-level quantum programs into efficient, executable form.
• To evaluate the effectiveness of QIR as an intermediate representation for expressing hybrid quantum-classical control logic in fault-tolerant routines.
• To compare different high-level implementations of the RUS protocol and assess their performance trade-offs in terms of circuit depth and resource usage.
• To demonstrate that QIR can preserve performance while enabling optimization of complex iterative quantum algorithms like magic state distillation.

Proposed method

• Compilation of magic state distillation using QIR and the LLVM toolchain, enabling loop unrolling and optimization of iterative syndrome measurement and reset logic.
• Implementation of the Bravyi-Kitaev [[5,1,3]] code for magic state distillation with real-time feed-forward of measurement outcomes via Q# and QIR.
• Expression of the Paetznick-Svore RUS protocol in four logically equivalent QIR representations to analyze performance differences.
• Use of QIR to represent and optimize hybrid quantum-classical control structures, including conditional resets and recursive loops.
• Compilation of high-level Q# code into QIR, followed by optimization and execution on trapped-ion quantum hardware with real-time classical feedback.
• Benchmarking of compiled QIR versions against hand-optimized quantum assembly to assess performance parity in circuit depth and fidelity.

Experimental results

Research questions

• RQ1 Can QIR effectively represent and optimize the iterative, classically controlled logic required for magic state distillation?
• RQ2 How does the performance of QIR-compiled magic state distillation compare to hand-optimized quantum assembly on real hardware?
• RQ3 What are the performance trade-offs between different high-level implementations of the RUS protocol when compiled via QIR?
• RQ4 To what extent can the LLVM toolchain optimize complex fault-tolerant quantum programs expressed in QIR?
• RQ5 Can QIR enable real-time execution of fault-tolerant subroutines with classical feed-forward, as required by error correction protocols?

Key findings

• The QIR-based compilation stack successfully enabled the first real-time implementation of magic state distillation on trapped-ion quantum hardware, with performance matching that of hand-optimized assembly.
• Loop unrolling via QIR and LLVM significantly improved performance by eliminating runtime overhead in iterative distillation loops.
• The QIR representation preserved the logical structure of the RUS protocol while allowing optimization that reduced circuit depth across multiple implementations.
• Four different QIR representations of the RUS algorithm showed measurable performance differences, demonstrating that high-level programming choices impact final circuit efficiency.
• QIR enabled accurate modeling of classical feed-forward control in fault-tolerant protocols, proving viable for complex hybrid quantum-classical workloads.
• The study confirms that QIR is a robust intermediate representation capable of expressing and optimizing advanced fault-tolerant quantum algorithms with minimal performance degradation.