The authors show how to map models for scalable quantum computation that have been designed for more conventional static qubits onto into a measurement-based picture; a model of quantum computation that is well suited for qubits that fly through space at the speed of light. The paper shows how to simulate braids between Majorana fermions with photonic qubits to perform the fault-tolerant logic gates of a scalable quantum computer.
The authors show how to map models for scalable quantum computation that have been designed for more conventional static qubits onto into a measurement-based picture; a model of quantum computation that is well suited for qubits that fly through space at the speed of light. The paper shows how to simulate braids between Majorana fermions with photonic qubits to perform the fault-tolerant logic gates of a scalable quantum computer.
Introduction In the standard model of quantum computation [D95], some simple quantum state is prepared and evolved by a partially ordered set of unitary gates, and finally is measured in the computation basis. Up until the late 1990s, transformations that deviate from unitarity were commonly associated with irreversibility, and thus incoherence and harm induced in the quantum data of interest. However, this viewpoint was challenged by three notable results: (1) teleportation [BBC+93], (2) syndrome measurements [S95, S96e], and (3) the fault-tolerant Toffoli and π/8-gate constructions [S96b, BMP+99]. In these schemes, well-designed measurements project the quantum data of interest onto a subspace of the original ambient space for each outcome, up to some known unitary transformation that is either reversible (and harmless) or intended. Subsequently, researchers found many useful error-correction procedures and unitary gates that rely heavily on measurements. Two “measurement models” of quantum computation were proposed in the early 2000s that make extreme use of measurements. In the cluster model [RB01], any quantum computation can be performed by applying a partially time-ordered set of single-qubit measurements on a certain entangled state. The state must be of appropriate size, but is otherwise independent of the computation. The related graph state model [RBB03] uses an initial state that depends on the computation itself. In the seemingly different teleportation-based model [N03, L01a, L04], any quantum computation can be implemented by applying one- or two-qubit nondemolition measurements on an arbitrary initial state, so as to “teleport” each gate in the simulated circuit.
Fault-tolerant quantum computing requires gates which function correctly despite the presence of errors, and are scalable if the error probability-per-gate is below a threshold value. To date, no method has been described for calculating this probability from measurements on a gate. Here we introduce a technique enabling quantitative benchmarking of quantum-logic gates against fault-tolerance thresholds for any architecture. We demonstrate our technique experimentally using a photonic entangling-gate. The relationship between experimental errors and their quantum logic effect is non-trivial: revealing this relationship requires a comprehensive theoretical model of the quantum-logic gate. We show the first such model for any architecture, and find multi-photon emission--a small effect previously regarded as secondary to mode-mismatch--to be the dominant source of logic error. We show that reducing this will move photonic quantum computing to within striking distance of fault-tolerance.
Photonic quantum computing is one of the leading approaches to universal quantum computation. However, large-scale implementation of photonic quantum computing has been hindered by its intrinsic difficulties, such as probabilistic entangling gates for photonic qubits and lack of scalable ways to build photonic circuits. Here, we discuss how to overcome these limitations by taking advantage of two key ideas which have recently emerged. One is a hybrid qubit-continuous variable approach for realizing a deterministic universal gate set for photonic qubits. The other is the time-domain multiplexing technique to perform arbitrarily large-scale quantum computing without changing the configuration of photonic circuits. These ideas together will enable scalable implementation of universal photonic quantum computers in which hardware-efficient error correcting codes can be incorporated. Furthermore, all-optical implementation of such systems can increase the operational bandwidth beyond terahertz in principle, ultimately enabling large-scale fault-tolerant universal quantum computers with ultrahigh operation frequency.
In this thesis, we describe the one-way quantum computer [Formula: see text], a scheme of universal quantum computation that consists entirely of one-qubit measurements on a highly entangled multiparticle state, i.e. the cluster state. We prove the universality of the [Formula: see text], describe the underlying computational model and demonstrate that the [Formula: see text] can be operated fault-tolerantly. In Sec. 2, we show that the [Formula: see text] can be regarded as a simulator of quantum logic networks. In this way, we prove the universality and establish the link to the network model — the common model of quantum computation. We also indicate that the description of the [Formula: see text] as a network simulator is not adequate in every respect. In Sec. 3, we derive the computational model underlying the [Formula: see text], which is very different from the quantum logic network model. The [Formula: see text] has no quantum input, no quantum output and no quantum register, and the unitary gates from some universal set are not the elementary building blocks of [Formula: see text] quantum algorithms. Further, all information that is processed with the [Formula: see text] is the outcomes of one-qubit measurements and thus processing of information exists only at the classical level. The [Formula: see text] is nevertheless quantum-mechanical, as it uses a highly entangled cluster state as the central physical resource. In Sec. 4, we show that there exist nonzero error thresholds for fault-tolerant quantum computation with the [Formula: see text]. Further, we outline the concept of checksums in the context of the [Formula: see text], which may become an element in future practical and adequate methods for fault-tolerant [Formula: see text] computation.
Quantum computers promise to solve computational problems that are inaccessible to classical machines. The reliable execution of large-scale quantum algorithms requires robust operations in the presence of noise. Quantum error correction addresses this challenge by encoding quantum information redundantly across several physical qubits, such that errors can be detected and corrected during a computation. However, no single error-correcting code intrinsically supports an inherently robust, fault-tolerant implementation of all gates needed for universal quantum computing. Moreover, most modern approaches to both quantum error correction and the implementation of universal logical operations on encoded qubits rely on mid-circuit measurements and feed-forward control. These types of operations are technologically demanding, often slow, and prone to high error rates, and they limit the overall success probability of quantum algorithms. In this thesis, we develop fault-tolerant protocols and circuits for quantum error correction and universal logical computation, with an emphasis on implementations compatible with current hardware systems. We first focus on fault-tolerant quantum error correction on small codes. By comparing different protocols, we identify trade-offs between compact circuit constructions and their robustness to noise. We then assess their practical performance by comparing numerical simulations of noisy circuits with experimental data. Beyond the preservation of encoded information, we study how universal logic can be implemented in a fault-tolerant manner on encoded qubits. A central approach considered in this thesis is code switching, in which logical information is transferred between two distinct error-correcting codes that support complementary sets of inherently fault-tolerant logical gates. In combination, these codes give access to a complete universal fault-tolerant logical gate set. In this thesis, we determine conditions that allow us to construct fault-tolerant protocols for code switching. We adapt these protocols to the capabilities of current hardware, thereby enabling the first experimental realization of universal fault-tolerant logic by means of code switching. However, the overall performance of these schemes is limited by slow and noisy mid-circuit measurements. To address this bottleneck, we construct a suite of measurement-free fault-tolerant universal operations that do not require any measurements during the execution of an algorithm. In this framework, error correction and logical operations are implemented coherently as part of the quantum circuit, without mid-circuit measurements or in-sequence classical control. We introduce measurement-free code-switching schemes that can be scaled to arbitrary code distances through concatenation, and which thereby provide, in principle, arbitrarily strong error suppression. We further tailor our approach to the capabilities of current trapped-ion quantum processors. New circuit constructions support the first experimental implementation of a logical quantum algorithm without mid-circuit measurements, demonstrated through Grover's search on three encoded qubits. Together, the results of this thesis expand the toolbox for early fault-tolerant quantum computation. They show how protocols for quantum error correction and universal logical gates can be designed without mid-circuit measurements with realistic hardware constraints in mind, opening new pathways towards universal quantum logic.
Blind quantum computing (BQC) is a computational paradigm that allows a client with limited quantum capabilities to delegate quantum computations to a more powerful server while keeping both the algorithm and data hidden. However, in practice, existing BQC protocols face significant challenges when scaling to large-scale computations due to photon losses, low efficiencies, and high overheads associated with fault-tolerant operations, requiring the client to compile both logical operations and error correction primitives. We use a recently demonstrated hybrid light-matter approach [PRL 132, 150604 (2024); Science 388, 509-513 (2025)] to develop an architecture for scalable fault-tolerant blind quantum computation. By combining high-fidelity local gates on the server's matter qubits with delegated blind rotations using photons, we construct loss-tolerant delegated gates that enable efficient algorithm compilation strategies and a scalable approach for fault-tolerant blind logical algorithms. Our approach improves the error-correction threshold and increases the speed and depth of blind logical circuits. Finally, we outline how this architecture can be implemented on state-of-the-art quantum hardware, including neutral atom arrays and solid-state spin defects. These new capabilities open up new opportunities for deep circuit blind quantum computing.