Utility-scale quantum computing will require executing long, complex algorithms with end-to-end error rates far below what physical qubits can support directly. Error-corrected logical qubits are needed to achieve this goal. To make the progress on logical qubits measurable and comparable we introduce the definition of scalable logical qubits: logical qubits preserved for long computations by repeated quantum error correction, capable of fault-tolerant universal operations with low-latency real-time decoding and feedback, and replicable to the hundreds or thousands, as required by applications. We characterize these scalable logical qubits along four coupled dimensions: reliability, scale, capability, and performance, and discuss trade-offs among these dimensions.
Utility-scale quantum computing will require executing long, complex algorithms with end-to-end error rates far below what physical qubits can support directly. Error-corrected logical qubits are needed to achieve this goal. To make the progress on logical qubits measurable and comparable we introduce the definition of scalable logical qubits: logical qubits preserved for long computations by repeated quantum error correction, capable of fault-tolerant universal operations with low-latency real-time decoding and feedback, and replicable to the hundreds or thousands, as required by applications. We characterize these scalable logical qubits along four coupled dimensions: reliability, scale, capability, and performance, and discuss trade-offs among these dimensions.
Quantum computing has reached a pivotal inflection point with the recent demonstration ofbelow-threshold quantum error correction and the emergence of logical qubits that outperformtheir physical counterparts. This review synthesizes the remarkable progress achieved between2024 and 2026 across multiple quantum hardware platforms, including superconducting circuits,trapped ions, and neutral atom arrays. We examine the theoretical foundations of quantumerror correction codes, with particular emphasis on surface codes and the rapidly advancingquantum low-density parity-check (qLDPC) codes. Key experimental milestones are analyzed,including Google’s Willow chip demonstration of exponential error suppression, IBM’s modularfault-tolerant roadmap culminating in the Starling system, IonQ’s achievement of 48 logicalqubits with a 2:1 encoding ratio, and QuEra’s record-efficiency neutral atom error correctionapproaching the Teraquop regime. The review further explores critical enabling technologiessuch as real-time decoding architectures, magic state distillation protocols, and fault-tolerant gateimplementations. We discuss the remaining challenges in scaling to hundreds of logical qubits,achieving practical logical error rates of 10−10 to 10−15, and realizing end-to-end fault-tolerantalgorithms. By synthesizing these developments, this article provides a comprehensive assessmentof the field’s trajectory toward practical fault-tolerant quantum computing and identifies the keymilestones that will define the next phase of progress.
Vast numbers of qubits will be needed for large-scale quantum computing because of the overheads associated with error correction. We present a scheme for low-overhead fault-tolerant quantum computation based on quantum low-density parity-check (LDPC) codes, where long-range interactions enable many logical qubits to be encoded with a modest number of physical qubits. In our approach, logic gates operate via logical Pauli measurements that preserve both the protection of the LDPC codes and the low overheads in terms of the required number of additional qubits. Compared with surface codes with the same code distance, we estimate order-of-magnitude improvements in the overheads for processing around 100 logical qubits using this approach. Given the high thresholds demonstrated by LDPC codes, our estimates suggest that fault-tolerant quantum computation at this scale may be achievable with a few thousand physical qubits at comparable error rates to what is needed for current approaches.
Quantum computing holds the promise of solving problems that are intractable for classical computers, with applications ranging from optimization and materials simulation to cryptography. It achieves this by leveraging the exponentially scaling dimensionality of the space encoding quantum information and by executing algorithms on quantum registers in superposition states – a feature often referred to as quantum parallelism. However, while encoding information in computational units capable of exploring a continuous set of quantum states enables exponential scaling of computational power with system size, quantum systems are also more susceptible to errors than their classical counterparts. These errors take the form of both control errors, where miscalibration of the control pulses causes coherent errors on the qubit states, as well as incoherent errors due to energy relaxation and dephasing. Scaling quantum systems to run useful algorithms involving hundreds or thousands of logical qubits will require quantum error correction. In this approach, quantum information is redundantly encoded across an entangled state of many physical qubits. This has enabled experimental demonstrations across various platforms – including ion traps, superconducting circuits, and neutral atoms – showing that encoded quantum states can be preserved beyond the coherence times of the constituting physical qubits. However, quantum state preservation is only one component needed for scalable quantum computing. To execute algorithms, it is also necessary to implement quantum gates on and between encoded qubits, in a way that maintains fault tolerance by preserving the ability to correct errors as they occur during the computation. In the first part of this thesis, we demonstrate the implementation of an error-corrected quantum operation that entangles two logical qubits. This is achieved by performing lattice surgery on a distance-three surface code qubit, resulting in a logical Bell state encoded in distance-three repetition codes, which enable the correction of single bit-flip errors. We further introduce techniques to benchmark and characterize the performance of logical operations, including applying the protocol to arbitrary logical input states and performing logical quantum process tomography. Together, these results constitute one of the first realizations of error-corrected lattice surgery in superconducting circuits. While quantum error correction can correct errors provided they occur with sufficiently low frequency, it may fail when many qubits experience errors simultaneously. In the second part of this thesis, we therefore shift focus to a specific error mechanism known to cause correlated errors in superconducting circuits – quasiparticle-induced decoherence. In this case, various forms of energy deposition on the quantum device can break Cooper pairs into quasiparticles, which may subsequently diffuse to the tunnel junction and interact with the qubit state, thereby causing decoherence. In this thesis, we investigate the impact of quasiparticle tunneling on qubit performance, with a focus on infrared-induced quasiparticles. We compare the sensitivity of niobium-based qubits to those made from tantalum – a material that has gained interest in recent years following demonstrations of qubits with improved coherence times based on this material. Using a thermal radiator source, we show that the performance of tantalum qubits may be limited by infrared-induced quasiparticles in typical superconducting circuit experimental setups. By employing both ambient and in-line infrared filters, we investigate the effectiveness of different filtering strategies and develop best practices for engineering cryogenic environments for superconducting quantum processors. The results presented in this thesis contribute to the advancement of quantum computing based on superconducting circuits by implementing and characterizing quantum error-corrected operations, and by investigating quasiparticles as a source of decoherence, along with strategies to improve infrared filtering and signal conditioning in cryogenic environments for future fault-tolerant quantum computing.
Quantum error correction (QEC) has transitioned from a theoretical promise to an experimental reality, with recent demonstrations of below-threshold logical qubits marking a turning point in the quest for fault-tolerant quantum computing. Over the past five years, breakthroughs in surface code implementations, low-latency decoders, and improved physical qubit fidelities have brought us to the brink of scalable logical qubit systems. Yet the road to practical quantum advantage remains steep: correlated noise, cryogenic control complexity, and the resource overhead of magic state distillation still pose major barriers. Here, we synthesize recent progress across superconductng, trapped-ion, and neutral-atom platforms, assess the state-of the-art in topological and LDPC codes, and highlight engineering challenges that must be overcome to achieve systems with thousands of logical qubits. We argue that the 2025-2035 decade will be decisive for quantum computing, with success hinging on co-design of hardware, software, and algorithms. This perspective outlines a roadmap for the next generation of fault tolerant systems and discusses the societal and economic implications of entering the era of practical quantum advantage.
The promise of quantum computers hinges on the ability to scale to large system sizes, e.g., to run quantum computations consisting of more than 100 million operations fault-tolerantly. This in turn requires suppressing errors to levels inversely proportional to the size of the computation. As a step towards this ambitious goal, we present experiments on a trapped-ion QCCD processor where, through the use of fault-tolerant encoding and error correction, we are able to suppress logical error rates to levels below the physical error rates. In particular, we entangled logical qubits encoded in the [[7,1,3]] code with error rates 9.8 times to 500 times lower than at the physical level, and entangled logical qubits encoded in a [[12,2,4]] code based on Knill's C4/C6 scheme with error rates 4.7 times to 800 times lower than at the physical level, depending on the judicious use of post-selection. Moreover, we demonstrate repeated error correction with the [[12,2,4]] code, with logical error rates below physical circuit baselines corresponding to repeated CNOTs, and show evidence that the error rate per error correction cycle, which consists of over 100 physical CNOTs, approaches the error rate of two physical CNOTs. These results signify a transition from noisy intermediate scale quantum computing to reliable quantum computing, and demonstrate advanced capabilities toward large-scale fault-tolerant quantum computing.
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.