# Classical Simulations of Low Magic Quantum Dynamics

## TL;DR

This paper introduces classical algorithms for simulating low-magic quantum circuits, especially those with frequent measurements, enabling analysis of larger systems and complex phenomena like measurement-induced phase transitions.

## Contribution

The authors develop new classical simulation algorithms tailored for low-magic, measurement-rich quantum circuits, expanding the capacity to study larger and more complex quantum dynamics.

## Key findings

- Simulated all-to-all monitored quantum circuits with low T-gate rates.
- Characterized measurement-induced phase transitions in entanglement, purification, and magic.
- Demonstrated the utility of algorithms for low-magic, high-entanglement dynamics.

## Abstract

We develop classical simulation algorithms for adaptive quantum circuits that produce states with low levels of ``magic'' (i.e., non-stabilizerness). These algorithms are particularly well-suited to circuits with high rates of Pauli measurements, such as those encountered in quantum error correction and monitored quantum circuits. The measurements serve to limit the buildup of magic induced by non-Clifford operations arising from generic noise processes or unitary gates, respectively. Our algorithms also allow a systematic truncation procedure to achieve approximate simulation. To benchmark our approach, we study the dynamics of all-to-all monitored quantum circuits with a sub-extensive rate of T-gates per unit of circuit depth, where we can simulate previously inaccessible system sizes and depths. We characterize measurement-induced phase transitions in the output wavefunction, including in the entanglement, purification, and magic. We outline the utility of our algorithms to simulate dynamics with low magic and high entanglement, complementary to the leading matrix-product state approaches.