The potential for scalable quantum computing depends on the viability of fault tolerance and quantum error correction, by which the entropy of environmental noise is removed during a quantum computation to maintain the physical reversibility of the computer’s logical qubits. However, the theory underlying quantum error correction applies a linguistic double standard to the words “noise” and “measurement” by treating environmental interactions during a quantum computation as inherently reversible, and environmental interactions at the end of a quantum computation as irreversible measurements. Specifically, quantum error correction theory models noise as interactions that are uncorrelated or that result in correlations that decay in space and/or time, thus embedding no permanent information to the environment. I challenge this assumption both on logical grounds and by discussing a hypothetical quantum computer based on “position qubits.” The technological difficulties of producing a useful scalable position-qubit quantum computer parallel the overwhelming difficulties in performing a double-slit interference experiment on an object comprising a million to a billion fermions.
The potential for scalable quantum computing depends on the viability of fault tolerance and quantum error correction, by which the entropy of environmental noise is removed during a quantum computation to maintain the physical reversibility of the computer’s logical qubits. However, the theory underlying quantum error correction applies a linguistic double standard to the words “noise” and “measurement” by treating environmental interactions during a quantum computation as inherently reversible, and environmental interactions at the end of a quantum computation as irreversible measurements. Specifically, quantum error correction theory models noise as interactions that are uncorrelated or that result in correlations that decay in space and/or time, thus embedding no permanent information to the environment. I challenge this assumption both on logical grounds and by discussing a hypothetical quantum computer based on “position qubits.” The technological difficulties of producing a useful scalable position-qubit quantum computer parallel the overwhelming difficulties in performing a double-slit interference experiment on an object comprising a million to a billion fermions.
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.
Over three decades after the formulation of early quantum algorithms, the realization of large-scale, fault-tolerant quantum computers remains constrained within the Noisy Intermediate-Scale Quantum (NISQ) regime. This paper critically re-evaluates the foundational assumptions underlying the Quantum Threshold Theorem and scalable Quantum Error Correction (QEC). We contrast classical error-suppression paradigms—specifically von Neumann’s majority-logic architecture for unreliable components—with the physical realities of continuous SU(2) symmetries in Hilbert space. We argue that the physical implementation of fault-tolerant quantum computing relies on a highly idealized model of uncorrelated, local Markovian noise, whose physical realizability at macroscopic scales remains contested. By examining interaction Hamiltonians in highly entangled macroscopic states, we demonstrate that collective decoherence channels and spatial noise correlations scale nonlinearly with register size n. This correlated phase drift acts as a directional force field—analogous to a long-wavelength hydrodynamic gradient across a field of coupled oscillators—rendering spatial averaging and independent syndrome measurements mathematically incapable of distinguishing systemic logic from collective environmental shifts. Consequently, we propose that universal quantum computers should not be conceptualized as scalable digital Turing machines, but rather as highly specialized, analog physical emulators bound by fundamental physical limits of continuous symmetry preservation.
A quantum computer is an information processing systems that utilizes invertible logic elements to perform reversible logic operations. It can also perform irreversible logic operations. Thus, in principle, it can compute the information transformation rule of any physical system for which the rules are known. A quantum computer can be designed to perform parallel computation on a massive scale, and therefore can have fast execution time. The basic structure of a quantum computer includes 1) a quantum register, or a configuration of quantum-mechanical energy states to store quantum bits (qubits) of information, 2) a quantum processor designed to induce quantum mechanical interactions between any arbitrary pair of qubits to perform a specified logic operations. 3) a quantum bus or network for transferring qubits from the registers to the processor and vice versa, and 4) a physical mechanisms for non-destructive measurements on the qubits. Quantum mechanical systems with the potential for realizing quantum computers include ion-trap quantum computers, cavity quantum electrodynamics quantum computers, photon-trap quantum computers, nuclear magnetic resonance quantum computers, and superconducting quantum computers. Decoherence [1 ,2] possesses the greatest challenge to the practical realization of quantum computers, because it causes the collapse of the quantum superposition states that contain the vital results of qubit manipulations. Decoherence processes are measurement-induced, noise-induced, and environment-induced [3] . Schemes to correct or circumvent the detrimental effects of decoherence in quantum processors fall into active error-correction schemes, and passive error-correction schemes [4]. Active error-correction schemes are designed to detect and correct for errors during computation. Algorithmic fault-tolerant computing [5, 6] is the most promising active-error correction scheme. In fault-tolerant computing, ancillary qubits are encoded into data blocks of the quantum registers. They are then used to detect errors. Once detected appropriate error-correction algorithms are then employed to rectify the errors. The implementation of fault-tolerant quantum computing has been hampered by the lack of practical universal set of quantum gates that can process an encoded data without propagating or introducing additional errors. Passive-error correction schemes [7] attempt to finding Hilbert subspaces that are intrinsically free of decoherence effects [8]. The key to quantum computing in such a decoherence-free subspace is the identification of mechanisms that can effect quantum mechanical interactions between the decoherence-free states without taking the system out of the decoherence-free environment. The challenge is to identify and employ physical processes that can achieve these goals.
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.
This review synthesizes current understanding of decoherence pathways across leading hardware platforms and explains why several experimentally observed noise features—drift, burst events, coherent components, correlated and non-Markovian structure, and leakage—can be disproportionately damaging for QEC. Decoherence remains the dominant impediment to scalable quantum computing because it is not a single error mechanism but a system-level phenomenon arising from materials defects, electromagnetic loss, control electronics, measurement backaction, and the broader environment in which a processor operates. Quantum error correction (QEC) is designed to algorithmically suppress physical noise, yet its practical success depends on how closely real devices satisfy the assumptions under which fault tolerance is proved: approximate locality, weak temporal correlations, sufficiently stochastic error statistics, low leakage, and reliable syndrome extraction. We then evaluate fundamental and engineering challenges that shape the viability of QEC at scale: syndrome measurement fidelity, correlated error suppression, decoding latency and classical co-processing, architectural constraints (connectivity, crosstalk, calibration overhead), and the resource cost of implementing a universal fault-tolerant gate set. Recent demonstrations of below-threshold behaviour and “break-even” regimes show that QEC is transitioning from theory to practice, but also clarify what remains unresolved: maintaining stable noise below fault-tolerance targets over long times, scaling to many logical qubits with low correlated-error rates, and integrating hardware-aware codes and decoders. We conclude with research priorities that treat decoherence and QEC as part of a co-designed stack spanning device physics, control, architecture, and algorithms.
Quantum computers have the potential to solve several interesting problems in polynomial \ntime for which no polynomial time classical algorithms have been found. However, \none of the major challenges in building quantum devices is that quantum systems are very \nsensitive to noise arising from undesired interactions with the environment. Noise can lead \nto errors which can corrupt the results of the computation. Quantum error correction is \none way to mitigate the effects of noise arising in quantum devices. \nWith a plethora of quantum error correcting codes that can be used in various settings, \none of the main challenges of quantum error correction is understanding how well various \ncodes perform under more realistic noise models that can be observed in experiments. \nThis thesis proposes a new decoding algorithm which can optimize threshold values of \nerror correcting codes under different noise models. The algorithm can be applied to \nany Markovian noise model. Further, it is shown that for certain noise models, logical \nClifford corrections can further improve a code's threshold value if the code obeys certain \nsymmetries. \n \nSince gates and measurements cannot in general be performed with perfect precision, \nthe operations required to perform quantum error correction can introduce more errors \ninto the system thus negating the benefits of error correction. Fault-tolerant quantum \ncomputing is a way to perform quantum error correction with imperfect operations while \nretaining the ability to suppress errors as long as the noise is below a code's threshold. \nOne of the main challenges in performing fault-tolerant error correction is the high resource \nrequirements that are needed to obtain very low logical noise rates. With the use of \nflag qubits, this thesis develops new fault-tolerant error correction protocols that are applicable \nto arbitrary distance codes. Various code families are shown to satisfy the requirements \nof flag fault-tolerant error correction. We also provide circuits using a constant number of \nqubits for these codes. It is shown that the proposed flag fault-tolerant method uses fewer \nqubits than previous fault-tolerant error correction protocols. \n \nIt is often the case that the noise afflicting a quantum device cannot be fully characterized. \nFurther, even with some knowledge of the noise, it can be very challenging to use \nanalytic decoding methods to improve the performance of a fault-tolerant scheme. This \nthesis presents decoding schemes using several state of the art machine learning techniques \nwith a focus on fault-tolerant quantum error correction in regimes that are relevant to near \nterm experiments. It is shown that even in low noise rate regimes and with no knowledge \nof the noise, noise can be further suppressed for small distance codes. Limitations of machine \nlearning decoders as well as the classical resources required to perform active error \ncorrection are discussed. \n \nIn many cases, gate times can be much shorter than typical measurement times of \nquantum states. Further, classical decoding of the syndrome information used in quantum \nerror correction to compute recovery operators can also be much slower than gate times. \nFor these reasons, schemes where error correction can be implemented in a frame (known \nas the Pauli frame) have been developed to avoid active error correction. In this thesis, we \ngeneralize previous Pauli frame schemes and show how Clifford frame error correction can \nbe implemented with minimal overhead. Clifford frame error correction is necessary if the \nlogical component of recovery operators were chosen from the Clifford group, but could \nalso be used in randomized benchmarking schemes.