Measurement-conditioned classical control in Pauli propagation

Extend Pauli propagation to support measurement-conditioned classical control and adaptive execution, thereby enabling backward observable evolution for quantum circuits whose subsequent operations depend on measurement outcomes.

Background

PPVM combines generalized tableau simulation, which supports adaptive execution and measurement-conditioned feed-forward, with Pauli propagation, which evolves observables backward through the adjoint circuit and computes expectation values without measurement sampling. The two backends therefore provide complementary capabilities: generalized tableaux retain the quantum state and can respond to classical measurement outcomes, whereas Pauli propagation efficiently evaluates observables but currently lacks measurement-conditioned classical control.

The unresolved problem is to incorporate measurement-conditioned classical control into backward operator evolution. This would extend Pauli propagation beyond fixed circuits and parameterized classical loops to adaptive quantum programs in which measurement results determine later operations, an important capability for realistic quantum-control and fault-tolerant protocols.

References

Although it avoids storing a full state vector, its cost can grow exponentially with the number of non-Clifford gates. Pauli propagation offers a complementary approach, evolving observables through the adjoint circuit with cost controlled by truncation. Atom loss can be incorporated through adjoint loss channels, while extending Pauli propagation to measurement-conditioned classical control remains an open problem.

— PPVM: A Circuit Simulation Framework for Digital Twins of Quantum Processors  (2610.18225 - Luo et al., 13 Oct 2026) in Section 1, Introduction