In this study, the ground-state structural and electronic band structure of cubic SrThO3 (space group Pm3̅m, No. 221) were comprehensively investigated through first-principles calculations within the framework of density functional theory (DFT) at ambient conditions, as implemented in the Quantum Espresso software and code. The structural and electronic characteristics of pristine SrThO3 were calculated using the Generalized Gradient Approximation (GGA) within the Perdew Burke Ernzerhof (PBE) exchange–correlation functional. The structural parameters show good agreement with previously reported theoretical data, validating the reliability of the adopted methodology. The electronic band gap was calculated as 1.986 eV with direct band characterization. This paper focused on the investigation of the structural model and electronic behavior of pristine SrThO3 for understanding potential use in optoelectronics devices.

Recent discoveries in asymptotically good quantum codes have intensified research on their application in quantum computation and fault-tolerant operations. This study focuses on the addressability problem within CSS codes: we ask what circuits might implement logical gates on strict subsets of logical qubits. With some notion of fault-tolerance, we prove several impossibility results: for CSS codes with non-zero rate, one cannot address a logical H , H S , S H , or C N O T to any non-empty strict subset of logical qubits using a circuit made only from 1-local Clifford gates.Furthermore, we show that one cannot permute the logical qubits in a code purely by permuting the physical qubits, if the rate of the code is (asymptotically) greater than 1/3 and the distance is at least 3. We can show a similar no-go result for C N O T s and C Z s between two such high-rate codes, albeit under a more restrictive assumption on the circuit, which we call "global" (though recent addressable CCZ gates use global circuits).This work pioneers the study of distance-preserving addressability in quantum codes, mainly by considering automorphisms of the code. This perspective offers new insights and potential directions for future research. We argue that studying this trade off between addressability and efficiency of the codes is essential to understand better how to do efficient quantum computation.

Fast native three-qubit gates and fault-tolerant quantum error correction with trapped Rydberg ions

Continuous-variable (CV) quantum key distribution (QKD) allows for quantum secure communication with the benefit of being close to classical coherent communication. In recent years, CV QKD protocols using a discrete number of displaced coherent states have been studied intensively as the modulation can be directly implemented with real devices with finite resolution. Until now, experiments only calculated key rates in the asymptotic regime. Here, we present a CV QKD system using discrete modulation that is especially designed for atmospheric channels. We use polarization encoding to exploit the nonbirefringent nature of the turbulent atmosphere. This allows to expand CV QKD networks beyond the existing fiber backbone. In a laboratory demonstration with a static 3-decibel loss channel, we implemented a recently developed security proof allowing to calculate composable finite-size key rates against independently and identically distributed collective attacks. We applied the full QKD protocol including a quantum random number generator, error correction, and privacy amplification to extract secret keys.

The Berkeley gate is a high-performance, two-qubit entangling operation with particular potential for quantum error correction and fault-tolerant protocols. However, harnessing this potential on current noisy intermediate-scale quantum (NISQ) processors, requires efficient compilation and robust performance under realistic noise conditions. In this work, we demonstrate a hardware-efficient implementation of the Berkeley gate on a superconducting quantum processor. Using quantum process tomography (QPT), we experimentally characterize its performance and benchmark it against a noiseless quantum simulator to evaluate its practical reliability in the NISQ era. Experimental measurements confirm the gate’s correct logical action, producing the target partially entangled state with a subspace confinement probability of P_{text {succ}}^{text {hardware}} approx 95.96% on real quantum hardware compared to 100% in quantum simulation. Results from QPT experiments show a simulated process fidelity of mathcal {F}_{text {process}}^{text {sim}} = 98.23%, while the experimental process fidelity on hardware is mathcal {F}_{text {process}}^{text {hardware}} = 91.76%. The observed discrepancy is analyzed in the context of device-specific noise sources, including qubit relaxation, dephasing, and state preparation and measurement (SPAM) errors. Our work provides a concrete fidelity benchmark for the Berkeley gate on superconducting hardware and quantify the impact of realistic noise on a non-trivial two-qubit operation, supporting its use in near-term algorithmic and error-correction applications.

Gauge theories are important descriptions for many physical phenomena and systems in quantum computation. Automorphism of gauge group naturally gives global symmetries of gauge theories. In this work we study such symmetries in gauge theories induced by automorphisms of the gauge group, when the gauge theories have nontrivial topological actions in different spacetime dimensions. We discover the automorphism symmetry can be extended, become a higher group symmetry, and/or become a non-invertible symmetry. We illustrate the discussion with various models in field theory and on the lattice. In particular, we use automorphism symmetry to construct new transversal non-Clifford logical gates in topological quantum codes. In particular, we show that 2+1d \mathbb{Z}_N ℤ N qudit Clifford stabilizer models can implement non-Clifford transversal logical gate in the 4th level \mathbb{Z}_N ℤ N qudit Clifford hierarchy for N≥ 3 N ≥ 3 , extending the generalized Bravyi-König bound proposed in [arXiv:2511.02900] for qubits.

Quantum devices can process data in a fundamentally different way than classical computers. To leverage this potential, many algorithms require the aid of a quantum Random Access Memory (QRAM), i.e. a module capable of efficiently loading datasets onto the quantum processor. However, a realisation of this building block is still outstanding due to its formidable resource requirements, which become even more demanding in quantum error-correction schemes. Here we show that the challenge of implementing QRAM can be entirely reduced to a state-preparation problem: since such resource-state is independent on the memory, our approach allows one to prepare it offline, opening the door to new design strategies. As an example, we introduce a heralded 'QRAM factory' which enables improved fidelities with high acceptance rate. More broadly, our results introduce the concept of resource-state QRAM: we study its performance in noisy settings, showing that it preserves the noise-resilience of standard QRAM, and discuss how it can be efficiently combined with quantum error-correction. Finally, we propose an implementation with neutral-atom hardware, where our analysis suggests that high-fidelity and low-latency queries can be implemented.

Quantum error correction will be essential for quantum computers to realise their full potential. As quantum computers advance towards demonstrating a universal fault-tolerant logical gate set, implementing scalable and low-latency real-time decoding will be crucial to avoid an exponential slowdown and maintain a fast logical clock rate. Here, we demonstrate low-latency feedback with a scalable FPGA decoder integrated into the control system of a superconducting quantum processor. We perform an 8-qubit stability experiment with up to 25 decoding rounds and a sub-microsecond mean decoding time per round, providing strong evidence that the backlog problem will be avoided when the decoder is operated as a streaming decoder on a superconducting hardware with the strictest speed requirements. We observe logical error suppression as the number of decoding rounds is increased. We also implement and time a fast-feedback experiment demonstrating a decoding response time of 9.6 μs for a total of 9 measurement rounds.

Performing quantum algorithms for critical problems in physics and chemistry requires substantially lower error rates than the physical error rates of present quantum computers. Achieving such low logical error rates requires quantum error correction1,2 and physical error rates below a critical threshold value3-8. We experimentally demonstrate on a trapped-ion quantum charge-coupled device (QCCD)9,10 improvements in logical error rates ranging from 11× to 800× compared with several physical circuit baselines, including quantum computation on multiple qubits. Our results hinge on two quantum error correction code constructions optimized for an ion-trap processor: a 12-qubit code encoding two qubits inspired by Knill11 and a 16-qubit tesseract colour code encoding four qubits12,13. These constructions are combined with a scalable method of error detection and post-selection to achieve reduced logical error rates. Our results show that state-of-the-art quantum devices are already able to make use of fault tolerance and error correction to strongly suppress errors in non-trivial quantum circuit computations.

Quantum error correction is essential for building utility-scale quantum computers that outperform classical machines, yet leading approaches incur substantial physical qubit overhead. Quantum low-density parity check (QLDPC) codes offer a promising alternative by significantly reducing the number of physical qubits required per logical qubit. However, existing work on QLDPC codes has focused primarily on quantum memories, with no efficient method known for implementing arbitrary logical Clifford operations at low circuit depth. Here, we introduce a new family of QLDPC codes that enables efficient implementation of the full Clifford group via transversal operations, allowing any m-qubit Clifford operation to be executed in at most O(m) syndrome extraction rounds. We run circuit-level simulations of depth-126 logical circuits to demonstrate the near-memory logical performance of these logical operations. In combination with known methods for implementing T gates, these results establish QLDPC codes as a viable route toward resource-efficient universal quantum computation.

Abstract Quantum computer emulators model the behavior and error rates of specific quantum processors. Without accurate noise models in these emulators, it is challenging for users to optimize and debug executable quantum programs prior to running them on the quantum computer, as device-specific noise is not properly accounted for. To overcome this challenge, we design a machine learning-driven approach to construct approximate device-specific emulators that applies to different hardware platforms. We apply supervised machine learning on a pre-generated library containing simulated gate set tomography training data. The machine learning model then analyses gate set tomography data from a target quantum computer to predict its noise model, which is in turn used to construct the device-specific emulator. We demonstrate the effectiveness of our protocol's emulator in estimating the unitary coupled cluster energy of the H2 molecule and compare the results with those from actual quantum hardware. Remarkably, our noise model captures device noise with high accuracy, achieving a percentage relative error of just 0.128% in expectation value relative to the actual quantum hardware. Importantly, we show that even without access to pulse-level control, noise from the quantum computer can nonetheless be characterized and independently validated by our protocol.

The standard Landauer bound sets the fundamental thermodynamic cost for information erasure under ideal conditions: weak system–bath coupling, quasistatic operation, and equilibrium reservoirs. However, realistic quantum error correction (QEC) operates in a profoundly different regime—finite-time syndrome extraction, strong coupling to cryogenic environments, and non-equilibrium dynamics. Here, we develop a unified thermodynamic framework for fault-tolerant quantum computing that incorporates corrections beyond the ideal Landauer limit. We derive a generalized bound on the heat dissipation per QEC cycle: , and scaling this result to large-scale quantum computers, we find that the total heat load grows polynomially with code distance but remains in the nanowatt range for million-qubit systems—well within the cooling power of modern dilution refrigerators. Applying our model to superconducting qubit architectures, we show that while strong coupling can add up to ∼20% to the ideal cost, finite-time effects contribute approximately at 100 ns and at 10 ns reset operations. Our results establish that the true thermodynamic cost of fault tolerance, while exceeding the naive Landauer estimate, does not pose a fundamental obstacle to scalability; the dominant engineering challenges lie in the heat load of control electronics and wiring, not in the fundamental dissipation of qubit reset.

Abstract Artificial Neural Networks (ANNs) are a promising approach to the decoding problem of Quantum Error Correction (QEC), but have observed consistent difficulty when generalising performance to larger QEC codes. Recent scalability-focused approaches have split the decoding workload by using local ANNs to perform initial syndrome processing and leaving final processing to a global residual decoder. We investigated ANN surface code decoding under a scheme exploiting the spatiotemporal structure of syndrome data. In particular, we present a vectorised method for surface code data simulation and benchmark decoding performance when such data defines a multi-label classification problem and generative modelling problem for rotated surface codes with circuit noise after each gate and idle timestep. Performance was found to generalise to rotated surface codes of sizes up to d = 97, with depolarisation parameter thresholds of up to 0.7% achieved, competitive with Minimum Weight Perfect Matching (MWPM). Improved timings, compared with MWPM alone, were found starting at code distances of d = 33 and d = 89 under noise models above and below threshold respectively. These results suggest promising prospects for ANN-based frameworks for surface code decoding with performance sufficient to support the demands expected from fault-tolerant resource estimates.

Recent advances in quantum communication and quantum error correction (QEC) have motivated hybrid architectures that exploit quantum resources to enhance multimedia transmission. However, practical quantum hardware remains constrained in qubit count, making it unrealistic to apply full scale QEC to every pixel of an image. To address this, we propose a hybrid framework combining Adaptive Multi-Qubit Encoding (AMQE) with selective Quantum Low-Density Parity-Check (QLDPC) protection. The proposed solution is demonstrated for the case of image data. Our work provides a resource-efficient pathway for high-quality quantum media transmission. The system partitions the image into blocks and assigns an importance score based on local variance. High-importance blocks structural features are encoded into multi-qubit superposition states and embedded into the logical subspace of a high-rate lifted-product QLDPC code. Low-importance blocks background are transmitted with lightweight AMQE encoding. We model the channel using realistic amplitude - damping noise. Numerical simulations show that this selective protection strategy decouples perceptual quality from physical noise limits. The proposed architecture maintains a Peak Signal-to-Noise Ratio (PSNR) above 40 dB in noise regimes where classical baselines fail. The framework also retains high-structural fidelity, maintaining the Structural Similarity Index Measure (SSIM) more than 0.98, confirming robust preservation of key visual features under amplitude - damping noise. Furthermore, we demonstrate that the proposed QLDPC architecture outperforms Quantum Polar codes at finite block lengths due to the steeper error suppression slope of the Belief Propagation - Ordered Statistics Decoding (BP - OSD).

Calculating the quantum weight enumerator polynomial (WEP) is a valuable tool for characterizing quantum error-correcting (QEC) codes, but it is computationally hard for large or complex codes. The Quantum LEGO (QL) framework provides a tensor network approach for WEP calculation, in some cases offering superpolynomial speedups over brute-force methods, provided the code exhibits area law entanglement, that a good QL layout is used, and an efficient tensor network contraction schedule is found. We analyze the performance of a hyper-optimized contraction schedule framework across QL layouts for diverse stabilizer code families. We find that the intermediate tensors in the QL networks for stabilizer WEPs are often highly sparse, invalidating the dense-tensor assumption of standard cost functions. To address this, we introduce an exact, polynomial-time Sparse Stabilizer Tensor (SST) cost function based on the rank of the parity check matrices for intermediate tensors. The SST cost function correlates perfectly with the true contraction cost, providing a significant advantage over the default cost function, which exhibits large uncertainty. Optimizing contraction schedules using the SST cost function yields substantial performance gains, achieving up to orders of magnitude improvement in actual contraction cost compared to using the dense tensor cost function. Furthermore, the precise cost estimation from the SST function offers an efficient metric to decide whether the QL-based WEP calculation is computationally superior to brute force for a given QL layout. These results, enabled by PlanqTN, a new open-source QL implementation, validate hyper-optimized contraction as a crucial technique for leveraging the QL framework to explore the QEC code design space.

Quantum Error Correction Faces Another Hurdle

Absolutely maximally entangled (AME) pure states of a system composed ofNparties are distinguished by the property that for any splitting at least one partial trace is maximally mixed. Due to maximal possible correlations between any two selected subsystems these states have numerous applications in various fields of quantum information processing including multi-user teleportation, quantum error correction and secret sharing. We present an updated survey of various techniques to generate such strongly entangled states, including those going beyond the standard construction of graph and stabilizer states. Our contribution includes, in particular, analysis of the degree of entanglement of reduced states obtained by partial trace of AME projectors, states obtained by a symmetric superposition of GHZ states, an orthogonal frequency square representation of the 'golden' AME state and an updated summary of the number of local unitary equivalence classes.

Realistic quantum information processing devices are inherently imperfect, leading to computational errors that require quantum error correction. Likewise, random bits generated by such devices are flawed and must be enhanced to be usable for applications such as generating cryptographic keys. This enhancement of randomness quality is achieved through a protocol known as randomness amplification1. Here we report on an experiment that implements such a protocol. Randomness amplification is device-independent, making no assumptions about the internal workings of the quantum devices. It requires executing a loophole-free Bell test2-4 within a specific parameter regime that involves both a high Bell violation and a high repetition rate. The experimental demonstration is made possible by a combination of theoretical advances, which allow for protocols with an experimentally realistic parameter regime, and experimental progress that achieves this regime with superconducting circuits. Crucially, randomness amplification has been proven to be impossible by purely classical means5. This experiment therefore demonstrates a definitive quantum advantage-leveraging quantum technology to accomplish a task unattainable by classical information processing.

Abstract Quantum error-correcting codes with asymptotically lower overheads than the surface code require nonlocal connectivity. Leveraging multilayer routing and long-range coupling capabilities in superconducting qubit hardware, we develop Hardware-Aware Layout, HAL: a robust, runtime-efficient heuristic algorithm that automates and optimizes the placement and routing of arbitrary codes. Using HAL, we generate around 150 explicit layouts of quantum low-density parity-check (qLDPC) codes. We study codes with topological structure and find that removing the periodic boundaries significantly lowers the hardware complexity with only a moderate reduction of logical efficiency. We also lay out highly nonlocal qLDPC code families that achieve competitive tradeoffs between hardware complexity and logical efficiency. Based on our findings, we anticipate many novel qLDPC codes to be realizable on near-term superconducting qubit hardware and inform future directions for the co-design of quantum devices and fault-tolerant architectures.

Quantum information is fragile and must be protected by a quantum error-correcting code for large-scale practical applications. Recently, highly efficient quantum codes have been discovered which require a high degree of spatial connectivity. This raises the question of how to realize these codes with minimal overhead under physical hardware connectivity constraints. Here, we introduce a general recipe to transform any quantum stabilizer code into a subsystem code that has local interactions, with weight and degree three, on a given graph. We call the subsystem codes produced by our recipe wire codes, and their code parameters depend on the input code and the given graph. Wire codes can be adapted to have a local implementation on any graph that supports a low-density embedding of the input Tanner graph, with an overhead that depends on the embedding. In particular, applying our results to a stabilizer code and a subdivision of its own Tanner graph, yields a quantum weight reduction procedure with a multiplicative qubit overhead and distance reduction that are linear in the input check degree and weight, respectively. Applying our results to hypercubic lattices leads to a construction of local subsystem codes with optimal scaling code parameters in any fixed spatial dimension. Similarly, applying our results to families of expanding graphs leads to local codes on these graphs with code parameters that depend on the degree of expansion. Our results constitute a general method to construct low-overhead subsystem codes on general graphs, which can be applied to adapt highly efficient quantum error correction procedures to hardware with restricted connectivity.