arXiv subjects

Markus Müller

Publications and source records attributed to Markus Müller.

At least 19 recordsLinked to original sources

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.

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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.

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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.

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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.

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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.

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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.

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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 R\'enyi 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.

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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.

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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.

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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.

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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.

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arXiv2025

Fast Native Three-Qubit Gates and Fault-Tolerant Quantum Error Correction with Trapped Rydberg Ions

Trapped ions as one of the most promising quantum-information-processing platforms, yet conventional entangling gates mediated by collective motion remain slow and difficult to scale. Exciting trapped ions to high-lying electronic Rydberg states provides a promising route to overcome these limitations by enabling strong, long-range dipole-dipole interactions that support much faster multi-qubit operations. Here, we introduce the first scheme for implementing a native controlled-controlled-Z gate with microwave-dressed Rydberg ions by optimizing a single-pulse protocol that accounts for the finite Rydberg-state lifetime. The resulting gate outperforms standard decompositions into one- and two-qubit gates by achieving fidelities above 97% under realistic conditions, with execution times of about 2 microseconds at cryogenic temperatures. To explore the potential of trapped Rydberg ions for fault-tolerant quantum error correction, and to illustrate the utility of three-qubit Rydberg-ion gates in this context, we develop and analyze a proposal for fault-tolerant, measurement-free quantum error correction using the nine-qubit Bacon-Shor code. Our simulations confirm that quantum error correction can be performed in a fully fault-tolerant manner on a linear Rydberg-ion chain despite its limited qubit connectivity. These results establish native multiqubit Rydberg-ion gates as a valuable resource for fast, high-fidelity quantum computing and highlight their potential for fault-tolerant quantum error correction.

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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.

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arXiv2025

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.

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arXiv2025

Addressable fault-tolerant universal quantum gate operations for high-rate lift-connected surface codes

Quantum low-density parity check (qLDPC) codes are among the leading candidates to realize error-corrected quantum memories with low qubit overhead. Potentially high encoding rates and large distance relative to their block size make them appealing for practical suppression of noise in near-term quantum computers. In addition to increased qubit-connectivity requirements compared to more conventional topological quantum error correcting codes, qLDPC codes remain notoriously hard to compute with. In this work, we introduce a construction to implement all Clifford quantum gate operations on the recently introduced lift-connected surface (LCS) codes (Old et al. 2024). These codes can be implemented in a 3D-local architecture and achieve asymptotic scaling $[[n, \mathcal{O}(n^{1/3}), \mathcal{O}(n^{1/3})]]$. In particular, LCS codes realize favorable instances with small numbers of qubits: For the $[[15,3,3]]$ LCS code, we provide deterministic fault-tolerant (FT) circuits of the logical gate set $\{\overline{H}_i, \overline{H}_i, \overline{C_i X_j}\}_{i,j \in (0,1,2)}$ based on flag qubits. By adding a procedure for FT magic state preparation, we show quantitatively how to realize an FT universal gate set in $d=3$ LCS codes. Numerical simulations indicate that our gate constructions can attain pseudothresholds in the range $p_{\mathrm{th}} \approx 4.8\cdot 10^{-3}-1.2\cdot 10^{-2}$ for circuit-level noise. The schemes use a moderate number of qubits and are therefore feasible for near-term experiments, facilitating progress for fault-tolerant error corrected logic in high-rate qLPDC codes.

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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 $\delta$-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.

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arXiv2025

Demonstration of measurement-free universal fault-tolerant quantum computation

The ability to perform quantum error correction (QEC) and robust gate operations on encoded qubits opens the door to demonstrations of quantum algorithms. Contemporary QEC schemes typically require mid-circuit measurements with feed-forward control, which are challenging for qubit control, often slow, and susceptible to relatively high error rates. In this work, we propose and experimentally demonstrate a universal toolbox of fault-tolerant logical operations without mid-circuit measurements on a trapped-ion quantum processor. We present modular logical state teleportation between two four-qubit error-detecting codes without measurements during algorithm execution. Moreover, we realize a fault-tolerant universal gate set on an eight-qubit error-detecting code hosting three logical qubits, based on state injection, which can be executed by coherent gate operations only. We apply this toolbox to experimentally realize Grover's quantum search algorithm fault-tolerantly on three logical qubits encoded in eight physical qubits, with the implementation displaying clear identification of the desired solution states. Our work demonstrates the practical feasibility and provides first steps into the largely unexplored direction of measurement-free quantum computation.

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arXiv2025

Optimizing Superconducting Three-Qubit Gates for Surface-Code Error Correction

Quantum error correction (QEC) is one of the crucial building blocks for developing quantum computers that have significant potential for reaching a quantum advantage in applications. Prominent candidates for QEC are stabilizer codes for which periodic readout of stabilizer operators is typically implemented via successive two-qubit entangling gates, and is repeated many times during a computation. To improve QEC performance, it is thus beneficial to make the stabilizer readout faster and less prone to fault-tolerance-breaking errors. Here we design a 3-qubit CZZ gate for superconducting transmon qubits that maps the parity of two data qubits onto one measurement qubit in a single step. We find that the gate can be executed in a duration of $35\,$ns with a fidelity of F$=99.96 \, \%$. To optimize the gate, we use an error model obtained from the microscopic gate simulation to systematically suppress Pauli errors that are particularly harmful to the QEC protocol. Using this error model, we investigate the implementation of this 3-qubit gate in a surface code syndrome readout schedule. We find that for the rotated surface code, the implementation of CZZ gates increases the error threshold by nearly 50\% to $\approx 1.2\,\%$ and decreases the logical error rate, in the experimental relevant regime, by up to one order of magnitude, compared to the standard CZ readout protocol. We also show that for the unrotated surface code, strictly fault-tolerant readout schedules can be found. This opens a new perspective for below-threshold surface-code error correction, where it can be advantageous to use multi-qubit gates instead of two-qubit gates to obtain a better QEC performance.

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