SymFT, a high-throughput simulator for Clifford-dominated circuits with Pauli rotations, stochastic Pauli noise, mid-circuit Pauli measurements, and measurement-record-controlled Pauli feedback, achieves state-of-the-art sampling performance.
Abstract
Fault-tolerant protocols often consist largely of stabilizer subcircuits, yet the non-Clifford operations required for universality make exact sampling costly. We present SymFT, a high-throughput simulator for Clifford-dominated circuits with Pauli rotations, stochastic Pauli noise, mid-circuit Pauli measurements, and measurement-record-controlled Pauli feedback. It combines two ideas. First, symbolic Clifford--Pauli frame factorization reduces branch-probability sampling to Pauli rotations and measurement projectors, with noise and feedback represented by symbolic signs. Since the residual Clifford and Pauli frames are unitary, they do not affect branch probabilities and need not be applied in every shot. Second, adaptive stabilizer-coordinate planning uses a shared stabilizer--destabilizer tableau to define the basis and stores only the active non-stabilizer degrees of freedom in a dynamically sized dense active-state vector. It resolves basis changes once and emits direct multi-coordinate sampling instructions, thereby avoiding per-shot tableau updates and localization-induced Clifford transformations of the dense vector. Across the tested pure-Clifford and near-Clifford circuits, SymFT achieves state-of-the-art sampling performance. On a single CPU core, it achieves a $2.51\text{--}2.56\times$ speedup over Stim for surface-code circuits and a $1.86\text{--}3.51\times$ speedup over Clifft for magic-state cultivation and distillation circuits. For the tested cultivation circuits, its GPU sampling throughput also exceeds that of our previous simulator, SOFT, by more than two orders of magnitude.
It is shown cut-count minimization is an unreliable proxy in practice: a globally cleaner partition can reduce cross-cut count yet increase wall-clock time, because it imbalances T-gate density across halves and inflates per-half stabilizer-frame size.
A measurement of what diagrammatic post-processing recovers from structural redundancy in the Solovay-Kitaev algorithm, which optimizes for numerical convergence rather than circuit economy, and its output carries structural redundancy that a gate-level compiler cannot see.
Dulari De Silva, Anuradha Mahasinghe, Chon‐Fai Kam et al.· 0 citations
Hardware teams building fault-tolerant quantum computers (FTQCs) must decide which imperfections to suppress, and that decision requires the logical performance of the architecture under the device's actual noise. Hardware noise often departs from the stochastic Pauli models used by scalable stabilizer simulators: superconducting transmons leak out of the computational subspace, neutral atoms scatter through intermediate states, trapped ions heat as their motional modes absorb phonons, and miscalibrated controls over-rotate coherently. We present Plaquette, a theoretical framework and software suite that computes the logical performance of fault-tolerant architectures directly from the physics of such imperfections. In Plaquette, a hardware error model is specified once, as Kraus operators, Hamiltonian-Lindblad dynamics, or an experimentally reconstructed quantum channel, and is compiled automatically into the exact or approximate representation required by each of four sampler classes: stabilizer sampling for Pauli noise, the new XPauli sampler for leakage and environment sectors, near-Clifford samplers for coherent errors, and full-state simulation for exact reference calculations. We validate the XPauli and near-Clifford samplers against full-state simulation, which they can match within statistical uncertainty while Pauli twirling can fall short depending on the error model. We demonstrate the framework on three error models: leakage in superconducting qubits, intermediate-state scattering in neutral atoms, and heating in trapped ions. The size of the discrepancy between Plaquette and Clifford-only simulations varies with platform and noise process, so reliable thresholds, error budgets, and overhead estimates require the most accurate simulation available. Plaquette provides a direct path from the open-system physics of a device to the logical performance of the FTQC built on it.
Raul Conchello Vendrell, Carlos D'iaz L'opez, Ish Dhand et al.· 0 citations
We introduce a family of quantum circuits that possess standard indicators of classical simulation hardness including high entanglement entropy, magic, and non-Gaussianity, yet admit efficient classical simulation via matrix product states (MPS). Our construction uses logical circuits of high-rate Calderbank-Shor-Steane (CSS) codes with enhanced symmetries. Using code automorphisms and transversal diagonal gates from higher levels of the Clifford hierarchy, we realize nonlocal logical Clifford and non-Clifford gates, showing how error-correcting codes can compile complex logical circuits into simple physical operations. Simulation efficiency rests on two properties: (i) diagonal transversal gates do not increase bond dimension, and (ii) permutations are tracked classically via on-the-fly relabeling, avoiding costly SWAP networks. Unlike Clifford or matchgate simulation, our method accepts a broad class of initial states, including dense entangled, magic, and non-Gaussian inputs, provided the encoded state retains an efficient MPS representation. We also release an exact phase-polynomial backend for monomial subfamilies, whose cost is set by higher-degree phase terms rather than entanglement growth. We demonstrate the method on an infinite polar CSS code family, showing bond dimension stays bounded by the encoding cost regardless of circuit depth. These results show that for some circuit families, standard resource measures are individually insufficient to indicate simulation hardness. As a near-term application, we use the compiled MPS as a classical reference for direct fidelity estimation of a quantum device running nontrivial logical circuits. Pauli sampling on the encoded reference, with a Clifford pushback through the known encoder, provides the ideal expectation values, so the logical output fidelity can be estimated from local Pauli readout alone, without costly state tomography.
Aydin Deger, Stergios Koutsioumpas, Mark A. Webster et al.· 0 citations
The contrast between settings is the central finding: when approximate outputs can be rescued by post-processing, the transformer succeeds; when exact discrete correctness is required, autoregressive drift limits reliability, with both inference-time search and data scaling as effective levers while training-side fine-tuning and model-level diversification are not.
Quantum gate teleportation is a key technique in fault-tolerant quantum computation that uses resource states to implement logical gates. Here, we develop a theory of quantum gate teleportation protocols that implement non-Clifford gates on arbitrary input states without revealing any information about them; we refer to these protocols as magic gate teleportation (MGT). We uncover a hidden structure within MGT -- after backpropagating the Pauli measurements, MGT protocols can be viewed as encoding the input state into a stabilizer code heralded by the measurement outcomes, followed by a logical non-Clifford gate. Using this structure, we construct MGT protocols for any resource state obtained by applying commuting Pauli rotations to a stabilizer state, and provide an efficient algorithm for synthesizing their circuit implementations. Conversely, we prove that useful resource states for MGT, i.e., states that can be used for non-Clifford gates through MGT protocols, are necessarily Clifford-equivalent to diagonal states; in particular, the output state distilled from the $[\![5, 1, 3]\!]$ protocol is not useful for MGT. Finally, we identify conditions under which the feedforward operators can be implemented by Pauli operators, shedding light on the paradigm of algorithmic fault tolerance and simplifying the feedforward operations needed for quantum computing.
Yunzhe Zheng, A. Zang, Aleksander Kubica· 1 citation
