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Markus Müller

Publications and source records attributed to Markus Müller.

At least 19 recordsLinked to original sources
arXiv2026

Calibrating LLM Judges for Human and AI Conversations

Measuring how successful a conversation is remains difficult, even for humans judging spoken dialogue. We evaluate state-of-the-art LLMs as pointwise and pairwise judges of conversational success on CANDOR, finding pointwise scoring correlates moderately with human ratings, while pairwise comparison suffers from long transcripts and positional bias. Since this leaves judge scores incomparable across models, we propose a small anchor set and a calibration function that calibrates any judge onto a shared, interpretable scale. We further release the Voice Arena Goal Dataset (VA), 200 task-oriented human-AI and human-agent conversations with pairwise annotations, revealing a substantial gap between current judges and human-level discrimination. Using VA, we test whether CANDOR-fitted calibration transfers to human-AI conversations, finding it brings judges onto a shared scale despite never observing VA during fitting.

cs.HC↗
arXiv2026

Modular fault-tolerant quantum computing on a non-CSS code

Modularization promises to break down the design and implementation complexity of large scale quantum processors into smaller manageable subtasks. In this approach, quantum channels, realized for instance through physical rerouting of qubits or quantum teleportation, connect multiple modules. Each of those modules hosts a subset of qubits, e.g. multiple logical qubits, and provides quantum operations on them. In this work, we implement for the first time all logical operations required for modular fault-tolerant universal quantum computing with a non-Calderbank-Shor-Steane (CSS) code, the perfect $[[5, 1, 3]]$ code, on a trapped-ion quantum computer. This code is the smallest quantum error-correcting (QEC) code capable of correcting any single-qubit error, making it a compact alternative to larger CSS codes. We demonstrate logical state teleportation and a full suite of fault-tolerant operations required for universal logical control, including logical state preparation, QEC with real-time feedback, logical measurements, magic-state preparation, logical entangling operations, and magic-state injection. Moreover, we characterize the logical spectator error picked up by idling logical qubits during quantum operations on distinct qubit registers and demonstrate a logical Pauli quantum process tomography that minimizes required sampling resources for logical tomography.

quant-ph↗
arXiv2026

Performance of the spin qubit shuttling architecture for a surface code implementation

Qubit shuttling promises to advance some quantum computing platforms to the qubit register sizes needed for effective quantum error correction (QEC), but also introduces additional errors whose impact must be evaluated. The established method to investigate the performance of QEC codes in a realistic scenario is to employ a standard noise model known as circuit-level noise, where all quantum operations are modeled as noisy. In the present work, we take this noise model and single out the effect of shuttling errors by introducing them as an additional so-called error location. This hardware abstraction is motivated by the SpinBus architecture and allows a systematic numerical investigation to map out the resulting two-dimensional parameter space. To this end, we take the Surface code and perform large scale simulations, most notably extracting the threshold across said two-dimensional parameter space. We study two scenarios for shuttling errors, depolarization on the one hand and dephasing on the other hand. For a purely dephasing shuttling error, we find a threshold of several percent, provided that all other operations have a high fidelity. The qubit overhead needed to reach a logical error rate of $10^{-12}$ (known as the "teraquop" regime~\cite{Gidney2021Jul}) increases only moderately for shuttling error rates up to about 1 \% per shuttling operation. The error rates at which practically useful, i.e. well below threshold error correction is predicted to be possible are comfortably higher than what is expected to be achievable for spin qubits. Our results thus show that it is reasonable to expect shuttling operations to fall below threshold already at surprisingly large error rates. With realistic efforts in the near term, this offers positive prospects for spin qubit based quantum processors as a viable avenue for scalable fault-tolerant error-corrected quantum computing.

quant-ph↗
arXiv2026

Reducing Decoding Latency in Quantum Error Correction by Early Starting Clustering

In quantum error correction, fast low-latency decoding is essential for fault-tolerant quantum computation, as delays in processing syndrome data can lead to the backlog problem. Existing decoders, including parallelizable approaches such as Union-Find, begin decoding only after all stabilizer measurement outcomes from an error-correction cycle have been received, inherently introducing a delay before decoding begins. We introduce Cluster-As-You-Go (CAYG), a modification of the Union-Find decoder that processes syndrome information during stabilizer measurements by clustering and correcting errors as they appear. This approach reduces the size of the remaining decoding problem at the end of the quantum error correction cycle and, consequently, the time required to complete the decoding process. While this early start of clustering incurs a modest reduction in decoding accuracy, it preserves the decoder's scalability. Surface-code simulations show that the resulting reduction in post-measurement idling can outweigh the accuracy loss, yielding an improved speed-accuracy trade-off. These results demonstrate that real-time, early-starting decoding during QEC cycles is both feasible and can be advantageous for quantum error correction. Demonstrated here for the surface code, CAYG is broadly applicable to other quantum error-correcting codes, which allow for clustering-based decoding approaches, and is extensible to dedicated real-time decoding hardware.

quant-ph↗
arXiv2026

Fault-tolerant $|\sqrt{ \mathrm{T} }\rangle$ state preparation and injection for more efficient fine-grained quantum circuit synthesis

Magic-state injection is a standard route to realize universal fault-tolerant quantum computation. Whereas the set of Clifford gates in combination with the non-Clifford T gate is a widely used universal gate set, extending the available set of non-Clifford primitives can reduce compilation overhead, provided that the additional primitives can be prepared fault-tolerantly with competitive resource costs and at sufficiently low logical noise rates. In this work, we introduce flag fault-tolerant protocols for preparing logical $|\sqrt{\mathrm{T}} \rangle $ magic states on the 3D tetrahedral color code and its smaller morphed variant. Our simulations under circuit-level noise verify fault tolerance, quantify acceptance and logical error rates, and we reconstruct the effective logical channels of the corresponding circuits for gate injection via logical process tomography. We find that access to $\sqrt{\mathrm{T}}$ reduces the average space-time cost of synthesizing Haar-random single-qubit unitaries by approximately $20$-$30$% relative to the Clifford+T gate set across practically relevant approximation regimes. These results demonstrate how expanding the set of fault-tolerant non-Clifford primitives can improve computational efficiency and broaden the design space for universal quantum computation in the early fault-tolerant era.

quant-ph↗
arXiv2026

Towards logical entanglement creation in trivalent planar architectures

Low-overhead quantum error-correction schemes are essential for enabling quantum computation on registers containing multiple logical qubits. For planar architectures with limited nearest-neighbor qubit connectivity, the surface code has emerged as the leading paradigm. Recent theoretical and experimental work has shown that a physical-qubit connectivity of degree three is sufficient to implement fault-tolerant quantum error correction. In this work, we study lattice surgery in the context of such trivalent architectures and introduce scalable circuit constructions to implement it. Compared with the four-valent measurement scheme, the trivalent lattice-surgery protocol reduces the required resources by $\mathcal{O}(d)$ qubits out of a total qubit count of $\mathcal{O}(d^2)$ and by $\mathcal{O}(d)$ two-qubit gates out of a total two-qubit gate count of $\mathcal{O}(d^3)$. We benchmark the logical fidelity of both lattice-surgery schemes in terms of experimentally realistic simulations targeting an implementation with a fluxonium qubit based architecture and find a potential improvement of up to $\approx25\%$ for distance-three. These results open a way for scalable planar trivalent qubit architectures to host a surface-code-based logical quantum processor.

quant-ph↗
arXiv2026

Complementary 3D color codes for transversal quantum logic

Transversal logical gates provide a direct route to fault-tolerant quantum computation, but the Eastin-Knill theorem forbids a universal transversal gate set within a single quantum error-correcting code. We propose a hybrid architecture based on the tetrahedral three-dimensional color code and its Hadamard-transformed counterpart, which we call the H-tetrahedral code. The two encodings support complementary transversal non-Clifford operations. Combined with bitwise Hadamard transformations that switch between the two encodings and a one-way transversal logical CNOT from the tetrahedral code to the H-tetrahedral code, these operations realize an almost-universal transversal logical gate set that enables both the creation of entanglement and logical states with magic. We complete a universal gate set through a pieceably fault-tolerant round-robin construction of a logical controlled-$Z$ gate between two H-tetrahedral codes. This logical entangling gate is interleaved with reduced-overhead Steane-type syndrome extraction using logical two-dimensional color-code auxiliary qubits. Our construction provides a new route toward implementing classically hard-to-simulate quantum algorithms where magic and most entangling operations are transversal while the resource overhead is concentrated in a small number of non-transversal Clifford entangling operations.

quant-ph↗
arXiv2026

Machine Learning Optimal Quantum Error Correction Thresholds

As quantum computers remain susceptible to noise, QEC is essential for preserving logical information during computations. However, the performance of QEC codes breaks down beyond certain noise thresholds, revealing fundamental limits on their ability to protect quantum information. These limits can be characterized using information-theoretic measures such as the coherent information, which quantifies the maximum rate at which logical information can be reliably transmitted through a noisy quantum channel. In this work, we establish a direct connection between the CI and the binary cross-entropy loss used when training neural network decoders. Specifically, we show that the CI constitutes a sharp lower bound on the achievable loss for decoders that track logical operators across noisy channels. To this end, we develop a transformer-based neural network model based on maximum likelihood decoding. We train this network to estimate the CI and evaluate its performance on the surface code under three noise models: code capacity, phenomenological, and circuit-level noise. Our results demonstrate that the network accurately predicts CI and yields threshold estimates that closely match known theoretical limits. When used as a decoder, the network significantly outperforms the minimum weight perfect matching decoder in terms of logical error rate. We also introduce a novel soft post-selection scheme that independently treats uncertainty in both logical operators and relies on confidence-based filtering of the network's output. We prove that such post-selection strategies, based on the MLD cosets, are optimal, and demonstrate their scalability in terms of both logical error rate and abort probability. These findings establish transformer-based architectures as powerful tools for QEC and provide the first numerical evidence supporting the optimality and scalability of MLD-based post-selection.

quant-ph↗
arXiv2026

Lattice surgery for near-term experimental logical qubit entanglement creation in planar architectures

In the era of early fault-tolerant quantum computing, basic demonstrations of entanglement operations between a few logical qubits are at the frontier of recent developments in quantum computing. In this work, we describe in detail, at both the logical and physical qubit levels, a logical teleportation protocol between two surface code logical qubits based on lattice surgery. We address several aspects of the teleportation protocol pertinent to superconducting qubit architectures. We explore the modularity constraints in the number and location of stabilizer readouts and compare variants of the teleportation protocol in this regard. Additionally, we investigate potential performance improvements related to in-sequence decision logic and the optimal size of the interface region between two surface code patches on a superconducting chip. Based on our simulations, we show possible near-term improvements in lattice surgery protocols that facilitate fault-tolerant quantum computing in superconducting circuit architectures.

quant-ph↗
arXiv2026

PlanRAG-Audio: Planning and Retrieval Augmented Generation for Long-form Audio Understanding

Long-form audio understanding poses significant challenges for large audio language models (LALMs) due to the extreme length of audio sequences and the need to reason over heterogeneous acoustic cues distributed over time, such as speech content, speaker identity, emotion, and sound events. To address these challenges, we propose \textbf{PlanRAG-Audio}, a planning-based retrieval-augmented generation framework for scalable long-form audio understanding. Rather than having audio LALMs process entire recordings directly, PlanRAG-Audio explicitly plans which modalities and temporal spans are required for a given query, and retrieves only query-relevant information from a structured text and audio database. This retrieval planning enables effective reasoning over complex, cross-domain audio queries while substantially reducing the input length passed to the large language models. Experiments across a wide range of speech/audio retrieval demonstrate that PlanRAG-Audio improves reasoning accuracy and stabilizes performance as audio duration increases by decoupling inference cost from raw audio length.

eess.AS↗
arXiv2026

Syndrome resampling enhances quantum error correction thresholds

Quantum error correction (QEC) enables fault-tolerant quantum computation but requires operating quantum hardware at physical error rates below code-dependent thresholds, which remains challenging for current devices. We introduce syndrome resampling, a general method that increases QEC thresholds of any decoder and suppresses logical errors without additional hardware, decoding modifications, or code-specific assumptions beyond syndrome statistics. The method exploits the fact that syndromes with low probability are likely to lead to logical failure, therefore biasing syndrome averages towards most likely syndromes effectively increases logical fidelities. We establish a direct connection between the Rényi coherent information (RCI) and powers of the syndrome probability distribution, showing that resampling syndromes according to these powers combined with maximum likelihood decoding (MLD) realizes a family of optimal thresholds associated with phase transitions in the RCI. Numerical simulations of surface codes demonstrate that syndrome resampling substantially increases thresholds for both optimal and suboptimal decoders and reduces logical error rates by up to four orders of magnitude in experimentally relevant regimes. We further show that syndrome resampling can be effectively implemented from finite data and combined with decoding-based post-selection to achieve additional gains. Finally, applying the method to existing experimental QEC data yields up to two orders of magnitude reduction in logical error rates without requiring additional measurements. Our results provide a practical and decoder-agnostic route to improved logical fidelities in near-term QEC experiments.

quant-ph↗
arXiv2026

Multiqubit Rydberg Gates for Quantum Error Correction

Multiqubit gates that involve three or more qubits are usually thought to be of little significance for fault-tolerant quantum error correction because single gate faults can lead to errors of high Pauli weight. However, recent works have shown that multiqubit gates can be beneficial for measurement-free fault-tolerant quantum error correction and for fault-tolerant stabilizer readout in unrotated surface codes. In this work, we investigate multiqubit Rydberg gates that are useful for fault-tolerant quantum error correction in single-species neutral-atom platforms and can be implemented with global laser pulses that do not individually address atomic sites. We develop an open-source Python package to generate analytical, few-parameter pulses that implement the desired gates while minimizing gate errors due to Rydberg-state decay. The tool also allows us to identify parameter-optimal pulses, characterized by a minimal parameter count for the pulse ansatz. Measurement-free quantum error correction protocols require CCZ gates, which we analyze for atoms arranged in symmetric and asymmetric configurations. We investigate the performance of these schemes for various single-, two-, and three-qubit gate error rates, showing that break-even performance of measurement-free QEC is within reach of current hardware. Moreover, we study Floquet quantum error correction protocols that comprise two-body stabilizer measurements. Those can be realized using global three-qubit gates, and we show that this can lead to a significant reduction in shuttling operations. Simulations with realistic circuit-level noise indicate that applying three-qubit gates for stabilizer measurements in Floquet codes can yield competitive logical qubit performance in experimentally relevant error regimes.

quant-ph↗
arXiv2026

High-performance cellular automaton decoders for quantum repetition and toric code

Execution of quantum algorithms on large-scale quantum computers will require extremely low logical error rates, which necessitates the development of scalable decoding architectures. Local decoders are promising candidates for this task, as they avoid the communication and data processing bottlenecks inherent in global decoding strategies. Cellular automaton (CA) decoders represent a distinct class of local decoders, offering a path toward the low-latency, real-time decoding required for practical applications. In this work, we present SCALA (Signaling CA with Local Attraction), a novel non-hierarchical cellular automaton decoder for quantum repetition and toric codes. By evaluating SCALA alongside the hierarchical CA decoder proposed by Harrington, we provide a direct comparison between non-hierarchical and renormalization-group-style local decoding strategies. We characterize SCALA across three key metrics: Performance, scalability, and robustness. Our results show that SCALA achieves a code-capacity threshold of approximately $p_c\approx 7.5\%$ and provides strong sub-threshold scaling of about $p_L\propto p^{d/4}$ on the toric code. In terms of scalability, our non-hierarchical design ensures that the local computational resources remain independent of system size, yielding a modular local architecture suitable for hardware implementation. Finally, SCALA demonstrates strong robustness to qubit measurement errors and noise within the decoder itself, a critical advantage for real-time decoding on noisy hardware. Our results establish SCALA as a high-performance, scalable, and robust local decoder for scalable quantum error correction.

quant-ph↗
arXiv2026

Analog-Digital Quantum Computing with Quantum Annealing Processors

Quantum annealing processors typically control qubits in unison, attenuating quantum fluctuations uniformly until the applied system Hamiltonian is diagonal in the computational basis. This simplifies control requirements, allowing annealing QPUs to scale to much larger sizes than gate-based systems, but constraining the class of available operations. Here we expand the class by performing analog-digital quantum computing in a highly-multiplexed, superconducting quantum annealing processor. This involves evolution under a fixed many-body Hamiltonian that, in the weak-coupling regime, is well-described by an effective XY model, together with arbitrary-basis initialization and measurement via auxiliary qubits. Operationally, this is equivalent to implementing single-qubit gates at the beginning and end of an analog quantum evolution. We demonstrate this capability with several foundational applications: single-qubit and two-qubit coherent oscillations with varying initialization and measurement bases, a multi-qubit quantum walk with fermionic dispersion in line with theory, and Anderson localization in a disordered chain. These experiments open the door to a wide range of new possibilities in quantum computation and simulation, greatly expanding the applications of commercially available quantum annealing processors.

quant-ph↗
arXiv2026

Unitary fault-tolerant encoding of Pauli states in surface codes

In fault-tolerant quantum computation, the preparation of logical states is a ubiquitous subroutine, yet significant challenges persist even for the simplest states required. In the present work, we present a unitary, scalable, distance-preserving encoding scheme for preparing Pauli eigenstates in surface codes. Unlike previous unitary approaches whose fault-distance remains constant with increasing code distance, our scheme ensures that the protection offered by the code is preserved during state preparation. Building on strategies discovered by reinforcement learning for the surface-17 code, we generalize the construction to arbitrary code distances and both rotated and unrotated surface codes. The proposed encoding relies only on geometrically local gates, and is therefore fully compatible with planar 2D qubit connectivity, and it achieves circuit depth scaling as $\mathcal{O}(d)$, consistent with fundamental entanglement-generation bounds. We design explicit stabilizer-expanding circuits with and without ancilla-mediated connectivity and analyze their error-propagation behavior. Numerical simulations under depolarizing noise show that our unitary encoding without ancillas outperforms standard stabilizer-measurement-based schemes, reducing logical error rates by up to an order of magnitude. These results make the scheme particularly relevant for platforms such as trapped ions and neutral atoms, where measurements are costly relative to gates and idling noise is considerably weaker than gate noise. Our work bridges the gap between measurement-based and unitary encodings of surface-code states and opens new directions for distance-preserving state preparation in fault-tolerant quantum computation.

quant-ph↗
arXiv2025

Scaling roadmap for modular trapped-ion QEC and lattice-surgery teleportation

We present a footprint study for the scaling of modular quantum error correction (QEC) protocols designed for triangular color codes, including a lattice-surgery-based logical teleportation gadget, and compare the performance of various possible architectures based on trapped ions. The differences in these architectures arise from the technology that enables the connectivity between physical qubits and the modularity required for the QEC gadgets, which is either based on laser-beam deflectors focused to independent modules hosting mid-size ion crystals, or integrated photonics guided to segmented modules of the trap and allowing for the manipulation of smaller ion crystals. Our approach integrates the transpilation of the QEC gadgets into native trapped-ion primitives and a detailed account of the specific laser addressing and ion transport leading to different amounts of crosstalk errors, motional excitation and idle qubit errors. Combining a microscopically-informed noise model with an efficient Pauli-frame simulator and different scalable decoders, we assess the near-term performance of the color-code memory and teleportation protocols on these architectures. Our analysis demonstrates that modular color-code teleportation is achievable in these near-term trapped-ion architectures, and identifies the integrated-photonics connectivity as the most promising route for longer-term scaling.

quant-ph↗
arXiv2025

Decoding 3D color codes with boundaries

Practical large-scale quantum computation requires both efficient error correction and robust implementation of logical operations. Three-dimensional (3D) color codes are a promising candidate for fault-tolerant quantum computation due to their transversal non-Clifford gates, but efficient decoding remains challenging. In this work, we extend previous decoders for two-dimensional color codes [1], which are based on the restriction of the decoding problem to a subset of the qubit lattice, to three dimensions. Including boundaries of 3D color codes, we demonstrate that the 3D restriction decoder achieves optimal scaling of the logical error rate and a threshold value of 1.55(6)% for code-capacity bit- and phase-flip noise, which is almost a factor of two higher than previously reported for this family of codes [2, 3]. We furthermore present qCodePlot3D, a Python package for visualizing 2D and 3D color codes, error configurations, and decoding paths, which supports the development and analysis of such decoders. These advancements contribute to making 3D color codes a more practical option for exploring fault-tolerant quantum computation.

quant-ph↗
arXiv2025

Strong electron-electron interactions in a dilute weakly-localized metal near a metal-to-insulator transition

Because it is easily switched from insulator to metal either via chemical doping or electrical gating, silicon is at the core of modern information technology and remains a candidate platform for quantum computing. The metal-to-insulator transition in this material has therefore been one of the most studied phenomena in condensed matter physics, and has been revisited with considerable profit each time a new fabrication technology has been introduced. Here we take advantage of recent advances in creating ultra-thin layers of Bohr-atom-like dopants to realize the two-dimensional disordered Hubbard model at half-filling and its metal-to-insulator transition (MIT) as a function of mean distance between atoms. We use gas-phase dosing of dopant precursor molecules on silicon to create arsenic and phosphorus $δ$-layers as thin as 0.4~nm and as dilute as 10$^{13}$~cm$^{-2}$. On approaching the insulating state, the conventional weak localization effects, prevalent at high dopant densities and due to orbital motion of the electrons in the plane, become dominated by electron-electron interaction contributions which obey a paramagnetic Zeeman scaling law. The latter make a negative contribution to the conductance, and thus cannot be interpreted in terms of an emergent Kondo regime near the MIT.

quant-ph↗