Clifft: Fast Exact Simulation of Near-Clifford Quantum Circuits

TL;DR

Clifft is an open-source quantum circuit simulator that efficiently handles near-Clifford circuits by dynamically managing active state space, enabling large-scale, exact simulations of fault-tolerant quantum protocols.

Contribution

It introduces a novel architecture that shifts exponential costs to a dynamic active subspace, allowing efficient, exact simulation of complex quantum circuits including magic state cultivation.

Findings

Achieves up to orders-of-magnitude throughput improvements over GPU simulators.

Enables exact end-to-end simulation of magic state cultivation over hundreds of billions of shots.

Shows that escape-stage failures influence the discrepancy between true and proxy T-gate circuits.

Abstract

Exact classical simulation of fault-tolerant quantum circuits remains limited by a tradeoff between exponential state vector scaling, exponential $T$-count scaling in stabilizer-rank approaches, and per-shot tracking overhead in sparse generalized stabilizer simulators. In this work, we introduce Clifft, an open-source simulator that shifts the dominant exponential cost from the total qubit count to a dynamic active subspace by factoring the quantum state into an offline Clifford frame, an online Pauli frame, and a dynamically sized active state vector. This architecture resolves deterministic Clifford coordinate transformations ahead of time, generalizing Stim's compile-once, sample-many execution model to circuits with non-Clifford operations. Consequently, exponential simulation costs are determined by the peak active virtual dimension, which expands during non-Clifford operations and contracts during measurements. Clifft remains within a constant factor of standard tools in the pure-Clifford and non-Clifford limits, while delivering up to orders-of-magnitude throughput gains over GPU-accelerated near-Clifford simulators on low-magic fault-tolerant benchmarks. Executing on commodity CPUs and exposing a Stim-like API, Clifft enables, to our knowledge, the first exact end-to-end simulation of magic state cultivation including the escape stage, over hundreds of billions of shots. These simulations show that escape-stage failures suppress the discrepancy between the true $T$-gate circuit and its $S$-proxy at low decoder-gap thresholds, while at high thresholds the full-protocol behavior approaches the larger discrepancy observed in the cultivation stages alone.