[Paper Review] Introduction to UniversalQCompiler

Raban Iten, Oliver Reardon-Smith+6 more|arXiv (Cornell University)|Apr 1, 2019

Quantum Computing Algorithms and Architecture35 references16 citations

TL;DR

UniversalQCompiler is an open-source Mathematica package that decomposes arbitrary quantum operations—such as isometries, quantum channels, POVMs, and instruments—into near-optimal sequences of single-qubit rotations and CNOT gates. It enables automated compilation of quantum protocols into quantum circuits with minimal CNOT counts, supports export to LaTeX and OpenQASM, and integrates with QI for analytic quantum information processing.

ABSTRACT

We introduce an open source software package UniversalQCompiler written in Mathematica that allows the decomposition of arbitrary quantum operations into a sequence of single-qubit rotations (with arbitrary rotation angles) and controlled-NOT (C-NOT) gates. Together with the existing package QI, this allows quantum information protocols to be analysed and then compiled to quantum circuits. Our decompositions are based on Phys. Rev. A 93, 032318 (2016), and hence, for generic operations, they are near optimal in terms of the number of gates required. UniversalQCompiler allows the compilation of any isometry (in particular, it can be used for unitaries and state preparation), quantum channel, positive-operator valued measure (POVM) or quantum instrument, although the run time becomes prohibitive for large numbers of qubits. The resulting circuits can be displayed graphically within Mathematica or exported to LaTeX. We also provide functionality to translate the circuits to OpenQASM, the quantum assembly language used, for instance, by the IBM Q Experience.

Motivation & Objective

• To automate the compilation of abstract quantum operations into physical quantum circuits for small-scale quantum systems.
• To provide a near-optimal decomposition of isometries, quantum channels, POVMs, and instruments into single-qubit rotations and CNOT gates.
• To enable seamless integration with existing quantum information tools via the QI package in Mathematica.
• To support interoperability with quantum hardware platforms through OpenQASM export and external transpilation pipelines.
• To offer specialized routines for optimizing special-form operations such as diagonal gates and uniformly-controlled gates.

Proposed method

• Employs decomposition techniques based on the Quantum Shannon Decomposition (Phys. Rev. A 93, 032318) to minimize CNOT gate counts.
• Represents quantum operations in Kraus or Choi matrix form and maps them to equivalent unitary evolutions via isometric extensions.
• Uses ancilla qubits to embed non-unitary operations (e.g., channels, POVMs) into unitary circuits for standard circuit compilation.
• Applies basic circuit simplification rules within the Mathematica environment to reduce gate sequences post-decomposition.
• Translates the resulting gate sequences into OpenQASM for use with IBM Q Experience and other quantum software stacks.
• Supports graphical visualization and LaTeX (Q-circuit) export for documentation and publication.

Experimental results

Research questions

• RQ1 How can arbitrary quantum operations—including non-unitary ones—be compiled into quantum circuits with minimal CNOT gate counts?
• RQ2 What is the performance of the decomposition method in terms of gate count and runtime for generic isometries and channels?
• RQ3 To what extent can the package handle special-form operations like diagonal or uniformly-controlled gates with improved efficiency?
• RQ4 How effectively can the generated circuits be interfaced with external tools such as transpilers or circuit optimizers?
• RQ5 What is the scalability of the decomposition method for larger quantum systems in terms of qubit count and runtime?

Key findings

• The decomposition method achieves CNOT counts within a constant factor (approximately two) of the theoretical lower bound for generic isometries.
• For generic quantum channels and POVMs, the decomposition is near-optimal in terms of CNOT count, based on the Quantum Shannon Decomposition framework.
• The package supports compilation of any isometry, including unitaries and state preparation, and handles quantum instruments and POVMs via isometric extensions.
• Circuit simplification rules are implemented directly in the package to reduce gate sequences post-decomposition.
• The package enables export of circuits to LaTeX (Q-circuit format) and OpenQASM, ensuring compatibility with major quantum software ecosystems.
• Runtime becomes prohibitive for large numbers of qubits, limiting practical use to small-scale systems (typically < 10 qubits).