Skip to content
A Small Quantum Intermediate Representation
Coq OCaml Python Makefile Shell
Branch: master
Clone or download
Fetching latest commit…
Cannot retrieve the latest commit at this time.
Type Name Latest commit message Commit time
Failed to load latest commit information.
examples updated Teleport example; made sure everything compiles with v8.10 Nov 8, 2019
hll-compiler updated documentation and benchmarks; changed SQIRE -> SQIR Oct 4, 2019
lib updating version of QWIRE Sep 10, 2019
Makefile added general 'optimize' function; updated code to run benchmarks Nov 19, 2019 updated code to run Qiskit benchmarks (and other misc. small edits) Nov 22, 2019


A Small Quantum Intermediate Representation for a verified compiler.

Compilation Instructions

Run make to compile the files in the core directory, make optimizer to compile code in the optimizer directory, make mapper to compile code in the mapper directory, and make examples to compile the code in the examples directory. Use make all to compile everything.

The development has been tested with Coq versions 8.9.1 and 8.10.1 on a MacBook Pro. make all should take about an hour.

Directory Contents


  • core/SQIR.v : General definition of the SQIR language.
  • core/UnitarySem.v : Semantics for unitary SQIR programs.
  • core/DensitySem.v : Density matrix semantics for general SQIR programs.
  • core/NDSem.v : Non-deterministic semantics for general SQIR programs.
  • core/Utilities.v : Utilities for describing composition of SQIR programs and classical state vectors.

We also rely on several files from the QWIRE development.


Compilation from higher-level languages to SQIR. Compilation from QWIRE is experimental (i.e. not done).

  • compiler/BooleanCompilation.v : Compilation from boolean expressions to unitary SQIR programs.
  • compiler/CompileFromQwire.v : Compilation from QWIRE to SQIR. (WIP)


Current progress on a verified optimizer for SQIR programs.

  • Utilities

    • optimizer/Equivalences.v : Verified circuit equivalences for peephole optimizations.
    • optimizer/ListRepresentation.v : List representation of unitary and non-unitary SQIR programs; includes utilities for manipulating program lists and gate-set-independent proofs when possible.
    • optimizer/PI4GateSet.v : Fixed gate set used in our optimizer; includes gate-set-specific proofs for utilities in ListRepresentation.v.
  • Optimizations on unitary programs

    • optimizer/GateCancellation.v : 'Single-qubit gate cancellation' and 'two-qubit gate cancellation' optimizations from Nam et al.
    • optimizer/HadamardReduction.v : 'Hadamard reduction' optimization from Nam et al.
    • optimizer/NotPropagation.v : 'Not propagation' preprocessing step from Nam et al.
    • optimizer/RotationMerging.v : 'Rotation merging using phase polynomials' optimization from Nam et al.
  • Optimizations on non-unitary programs

    • optimizer/RemoveZRotationBeforeMeasure.v : Remove single-qubit z-axis rotations before measurement operations.
    • optimizer/PropagateClassical.v : Track classical states to remove redundant measurements and CNOT operations.


Mapping algorithms for SQIR programs.

  • mapper/SimpleMapping.v: Simple mapping for an architecture described by a directed graph.
  • mapper/SimpleMappingWithLayout.v: Extends the simple mapping examples with an arbitrary initial layout. (WIP)
  • mapper/MappingExamples.v: Verified circuit mapping examples for linear nearest neighbor, 2D grid, and IBM Tenerife architectures.


Examples of verifying correctness properties of simple SQIR programs.

  • examples/Deutsch.v
  • examples/DeutschJozsa.v
  • examples/GHZ.v
  • examples/Superdense.v
  • examples/Teleport.v


Instructions for running SQIR optimizations on benchmark programs can be found in the README in the benchmarks directory.


A preliminary version of this work was presented at QPL 2019. For details, see the arXiv paper available here and code in the 'QPL2019' branch. A revised submission is in progress; contact the authors if you are interested in a draft.

This project is supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Quantum Testbed Pathfinder Program under Award Number DE-SC0019040.

You can’t perform that action at this time.