[Paper Review] symQV: Automated Symbolic Verification of Quantum Programs

Fabian Bauer-Marquart, Stefan Leue+1 more|arXiv (Cornell University)|Dec 5, 2022

Quantum Computing Algorithms and Architecture4 citations

TL;DR

symQV is a symbolic execution framework that enables automated, push-button verification of quantum programs against first-order logic specifications using SMT solving. It supports symbolic input qubits and scales to 24-qubit programs (2^24 state space) via a novel abstraction technique, making it the first fully automated tool for symbolic verification of general quantum programs with formal specifications.

ABSTRACT

We present symQV, a symbolic execution framework for writing and verifying quantum computations in the quantum circuit model. symQV can automatically verify that a quantum program complies with a first-order specification. We formally introduce a symbolic quantum program model. This allows to encode the verification problem in an SMT formula, which can then be checked with a delta-complete decision procedure. We also propose an abstraction technique to speed up the verification process. Experimental results show that the abstraction improves symQV's scalability by an order of magnitude to quantum programs with 24 qubits (a 2^24-dimensional state space).

Motivation & Objective

• To address the lack of automated, symbolic verification tools for quantum programs that support general first-order specifications.
• To enable verification of quantum programs with arbitrary symbolic input qubits, avoiding the need to fix inputs to specific values.
• To overcome the exponential memory overhead of quantum state simulation by introducing a symbolic and abstracted verification approach.
• To provide a scalable, sound, and fully automated verification framework comparable to classical symbolic verification tools like CPAchecker.
• To support essential quantum algorithms such as teleportation, QFT, Grover's diffusion, and quantum phase estimation with formal correctness guarantees.

Proposed method

• Formalizes a symbolic quantum program model that captures quantum circuits with symbolic input parameters.
• Encodes the verification problem as a δ-complete SMT formula using complex amplitudes and unitary operations.
• Applies a novel abstraction technique to over-approximate quantum state evolution, reducing state space explosion while preserving verification soundness.
• Uses SMT solvers to check whether all symbolic input values satisfy the given first-order specification.
• Supports symbolic execution by tracking amplitude variables (real and imaginary parts) through unitary operations and measurements.
• Generates counterexamples when verification fails, aiding in debugging quantum programs.

Experimental results

Research questions

• RQ1 Can symbolic execution be effectively adapted to quantum programs to verify compliance with formal specifications?
• RQ2 How can the exponential state space of quantum programs be managed during automated verification?
• RQ3 Can abstraction techniques be applied to quantum verification without compromising soundness?
• RQ4 To what extent can automated symbolic verification scale to practical quantum algorithms with symbolic inputs?
• RQ5 Can the framework verify standard quantum algorithms like teleportation and QFT with full generality and correctness?

Key findings

• symQV successfully verifies quantum programs with up to 24 symbolic input qubits, corresponding to a 2^24-dimensional state space.
• The abstraction technique improves scalability by an order of magnitude, enabling verification of larger quantum programs.
• The framework supports full symbolic execution, allowing verification across all possible input values without fixing inputs to specific values.
• symQV correctly verifies key quantum algorithms including teleportation, quantum Fourier transform, Grover's diffusion, and quantum phase estimation.
• When verification fails, symQV generates counterexamples that help identify bugs in the quantum program.
• The approach is sound and fully automated, providing a push-button verification workflow similar to classical symbolic verification tools.