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ScaffCC: Scalable Compilation and Analysis of Quantum Programs
Ali JavadiAbhari, Shruti Patil, Daniel Kudrow, Jeff Heckey, Alexey Lvov, Frederic T. Chong, Margaret Martonosi
TL;DR
ScaffCC addresses the gap between quantum algorithms of practical interest and feasible implementations. It provides a scalable LLVM-based logical-level compiler and analysis framework integrating classical compiler methods, reversible-logic synthesis, and quantum program analyses. The paper demonstrates scalable compilation and an accuracy–speed trade-off in critical-path analysis, while noting constraints from compiler scalability and lost parallelism at module boundaries.
Problem
ScaffCC addresses the gap between quantum algorithms of practical interest and what can be feasibly implemented.
Method
ScaffCC uses an LLVM-based logical-level compiler with scalable compilation algorithms, reversible-logic synthesis, and quantum program analyses.
Results
The paper demonstrates an accuracy–speed trade-off in critical-path analysis and presents compilation and analysis approaches intended for large quantum programs.
Takeaways & Limitations
ScaffCC bridges high-level quantum algorithm specifications and lower-level implementations while supporting larger quantum programs.
Takeaways & Limitations
Compiler scalability is pressured by the opportunity for deep optimization, and lost parallelism at module boundaries can cause longer schedules.
Abstract
from arXiv · showhide
We present ScaffCC, a scalable compilation and analysis framework based on LLVM, which can be used for compiling quantum computing applications at the logical level. Drawing upon mature compiler technologies, we discuss similarities and differences between compilation of classical and quantum programs, and adapt our methods to optimizing the compilation time and output for the quantum case. Our work also integrates a reversible-logic synthesis tool in the compiler to facilitate coding of quantum circuits. Lastly, we present some useful quantum program analysis scenarios and discuss their implications, specifically with an elaborate discussion of timing analysis for critical path estimation. Our work focuses on bridging the gap between high-level quantum algorithm specifi- cations and low-level physical implementations, while providing good scalability to larger and more interesting problems
1. Introduction
ScaffCC addresses the gap between quantum algorithms of practical interest and feasible implementations by providing a scalable LLVM-based compiler and analysis framework for the logical level. It combines quantum-specific compilation, classical compiler techniques, reversible-logic synthesis, and program analyses for large quantum programs.
- ScaffCC targets the persistent gap between practically interesting quantum algorithms and what can be feasibly implemented.
- The framework is designed to compile programs containing trillions of operations while supporting an extensible quantum program analysis toolbox.
- Quantum programs are statically analyzable, enabling aggressive constant propagation, deep optimization, and operation parallelization while increasing compiler scalability pressure.
- ScaffCC manages compilation scale through modular output and dynamic, instrumentation-driven compilation rather than relying only on multiple compile-time optimization passes.
- The compiler leverages LLVM and classical techniques such as loop unrolling, procedure cloning, and data-flow analysis for quantum programs.
- ScaffCC analyzes critical paths, qubit and operation usage, and no-cloning or entanglement constraints, while exposing an accuracy–speed trade-off in critical-path analysis.
- The framework integrates reversible-logic synthesis to describe and compile sub-circuits, addressing the difficulty of hand-coding mathematical library functions.
2. Quantum Computation
Quantum computation represents information in qubits and evolves it through reversible quantum operations, with measurement producing a classical answer. These properties impose compiler concerns involving entanglement, no-cloning, reversibility, and costly qubit resources.
- Qubits can occupy superposition states, allowing quantum operations to modify multiple basis-state combinations simultaneously.
- Entanglement creates dependencies between qubits, while no-cloning prevents copying an arbitrary quantum state.
- Measurement converts a probabilistic quantum state into a classical result by collapsing a qubit into |0⟩ or |1⟩.
- Quantum operations must be unitary, making the entire circuit reversible and requiring non-reversible sub-circuits to be detected or transformed.
- These quantum properties guide compiler checks for logical flaws, including possible entanglement and no-cloning violations.
- Quantum compilers must account for qubits as the most expensive resources during valid circuit generation.
3. Overview of ScaffCC
ScaffCC compiles Scaffold programs into logical-level QASM using LLVM, while supporting classical-to-quantum-gate synthesis and quantum-program analysis. Its design targets scalable translation from hierarchical high-level descriptions to analyzable quantum assembly for large benchmark programs.
- Compiler overview: ScaffCC compiles Scaffold programs into QASM at the logical level before synthesis into machine-dependent physical operations.The compiler separates high-level algorithm specification from later hardware-level implementation.
- Scaffold language: Scaffold combines quantum operations with classical control such as loops, and organizes circuits hierarchically into instantiable modules.Modules must ultimately represent reversible sub-circuits through unitary operations or compiler transformation.
- CTQG synthesis: ScaffCC supports Classical-To-Quantum-Gate modules by converting classical logical circuits into valid quantum code.These modules are separated during compilation and translated through a dedicated CTQG sub-compiler.
- QASM generation: The compiler extends QASM with hierarchical representations that retain manageable structure instead of fully flattening circuits containing 10^7 to 10^12 gates.These modifications aim to preserve scalability for large target programs.
- Code generation: ScaffCC balances per-module flattening for scheduling and mapping against retained abstraction needed to keep circuit generation tractable.Unitary operations are decomposed into supported QASM gates, including fixed sub-circuits for Toffoli operations.
- Program analysis: The framework supports correctness checks and circuit estimates through quantum program analyses, including timing analysis, across eight quantum algorithms.The study covers broad algorithmic themes such as Quantum Fourier Transform, classical oracles, random walks, and amplitude amplification.
4. Managing Scalability Through Choice of QASM Format
ScaffCC manages scalability by choosing among flat, hierarchical, and loop-retaining QASM formats. Retaining quantum loops substantially reduces output size, although benefits depend on loop structure and the benchmark’s use of CTQG modules.
- Loop retention: QASM-HL represents highly repeated operations with repeat loops and broad simultaneous operations with forall loops.Static analysis supplies repeat trip counts and forall qubit ranges from pure quantum blocks.
- Benchmark effects: For Grover’s and BWT algorithms, retaining repeat blocks changes exponential code growth with problem parameters into linear growth.Their high iteration counts make loop retention particularly effective.
- Benchmark effects: QASM-HL provides limited additional benefit for GSE and Shor’s programs because they contain few pure quantum loops with low trip counts.BF, CN, and SHA-1 also gain little when much of their output comes from the flat CTQG sub-compiler.
- QASM formats: QASM-HL reduces code size by retaining quantum loops, making compilation tractable for more programs.Across benchmarks, QASM-H already provides an average code-size advantage of approximately 200,000X over flat QASM.
5. Code Generation and Scaling
ScaffCC resolves classical control while avoiding whole-program flattening through static passes and execution-based instrumentation. The instrumentation-driven method scales better, compiling QASM-HL code in about 20 hours rather than several days for the pass-driven approach.
- Control-flow resolution: The fixed-trace nature of Scaffold programs allows classical control flow to be resolved in the compiler for specialized input parameters.Different module versions may be discovered statically or dynamically when parameters alter gate sets.
- Pass-driven approach: The pass-driven method repeatedly applies loop unrolling, procedure cloning, and inter-procedural constant propagation to specialize modules and partially execute classical control.The resulting program preserves modularity while being flattened on a per-module basis.
- Instrumentation-driven approach: The instrumentation-driven method executes classical portions to collect quantum operations, using separate quantum and classical modes and memoization to avoid repeated call sequences.Quantum instructions are printed in QASM-HL syntax while dead code is removed from the quantum version.
- Compilation scaling: The instrumentation-driven approach compiles QASM-HL code in ∼20 hours, whereas the pass-driven approach takes several days.Across quantum benchmarks, instrumentation-driven compilation has better overall scaling as problem sizes increase.
6. CTQG: Classical-To-Quantum-Gate Conversion
CTQG converts classical reversible logic into quantum gates and QASM, supporting simulation, arithmetic, control flow, and scalable compilation. Its instrumentation-driven approach improves compilation performance for larger benchmarks, averaging 3X faster than pass-driven compilation.
- CTQG compiles classical oracles into flat QASM and inserts precompiled oracle modules verbatim at each call site.The compiler can also simulate oracles on selected inputs for verification and debugging.
- CTQG supports reversible arithmetic, bit-string manipulation, ancilla allocation, conditionals, and bounded loops using reversible-gate synthesis.Bounded loops are unrolled, producing roughly the maximum iteration count times the loop-body gate count.
- Instrumentation-driven compilation averages 3X faster than pass-driven compilation and scales better for larger benchmarks.Pass-driven compilation can remain faster for small benchmarks.
- CTQG adders and subtracters use 6n −3 CNOT gates and 2n −2 Toffoli gates without ancillas, giving linear size in operand bit width.Its integer multiplier has size O(n^2) and also uses no ancilla signals.
- CTQG emits QASM in one pass without retaining prior gates, allowing circuits of 10^12–10^13 gates with runtime, rather than memory size, as the limiting factor.This streaming design supports very large generated circuits.
7. Quantum Program Analysis
ScaffCC applies compiler analyses to quantum programs for validity checks, entanglement tracking, resource estimation, and timing analysis. These analyses expose uncomputed ancillas and recover parallelism that modular designs can hide, while trading analysis speed against critical-path accuracy.
- 7. Quantum Program Analysis: ScaffCC’s analyses provide program validity checks and estimates of quantum algorithms’ timing and resource requirements.Resource estimates can support early algorithm comparison before physical-device implementation.
- 7.1. Entanglement Analysis: Data-flow analysis conservatively tracks potentially entangled qubits and annotates the output QASM-HL program.The analysis records interactions from multi-qubit operations and propagates prior entanglements.
- 7.1. Entanglement Analysis: The disentangled qubit check warns when a module ends with remnant ancillas, because uncomputed ancillas can alter data-qubit measurement probabilities.ScaffCC requires newly instantiated qubits to be uncomputed or measured at module termination.
- 7.2. Resource Analysis: Instrumentation-driven resource estimation performs better for larger programs by counting quantum operations per module and recursively aggregating them to parent modules.The approach collects resource counts through execution rather than only inspecting LLVM-IR.
- 7.3. Timing Analysis: Flattening improves critical-path estimates by exposing inter-module parallelism, while slack-aware scheduling yields shorter, more accurate paths at higher analysis cost.Modular analysis runs faster but can miss boundary parallelism; more flattening increases code size and runtime.
- 7.3. Timing Analysis: The timing-analysis methods can discover parallelism hidden by modular design, producing shorter reported critical paths closer to real schedules.The improved estimates come at the cost of longer analysis time.
8. Related Work
ScaffCC extends quantum compilation beyond small circuits by combining scalable compiler techniques, reversible-logic synthesis, and logical program analyses. Its related work emphasizes modularity, tractable optimization, entanglement and timing analysis, and trade-offs between compilation quality, code size, and analysis complexity.
- ScaffCC targets arbitrary-size quantum problems while supporting aggressive low-level optimization and full-program logical analyses.
- Modularization improves scalability, but modular inlining introduces a trade-off between compilation efficiency, output quality, and critical-time estimation accuracy.
- The scheduling framework combines fine-grained center alignment with coarse-grained slack filling to compress schedules and recover parallelism.
- Higher-complexity analysis and additional flattening improve accuracy, but flattening eventually causes substantial code-size growth on larger problems.
- ScaffCC integrates scalable reversible-logic synthesis, including integer arithmetic without ancillas, optimized analytic functions, and automatic ancilla management.
- Its analysis toolbox includes extensible entanglement and timing analyses, with conservative modular entanglement analysis intended to support algorithm design and debugging.
9. Conclusion
The paper demonstrates that large-scale quantum applications can be compiled using adapted classical techniques while exploiting quantum programs’ dual classical-quantum structure. It also contributes reversible-logic synthesis, correctness methods, and critical-path analysis, including an optimality–speed trade-off as code size increases.
- ScaffCC demonstrates the possibility of compiling large-scale quantum applications using classical techniques adapted to quantum programs.
- The framework proposes methods for program correctness checking and a novel approach to reversible-logic synthesis.
- Critical-path estimation can be optimized as code size increases, but its analysis exposes a trade-off between optimality and speed.
- These compilation and analysis methods are presented as steps toward mapping quantum algorithms onto physical quantum computers.