Quantum computers have the potential to solve certain problems exponentially faster than classical computers. However, realizing this potential in practice is a major challenge, as it requires precise control over large-scale quantum systems operating at extremely low error rates. Quantum error correction (QEC) provides a path to achieving such error rates, but its substantial resource overhead poses a significant practical barrier. In addition, identifying which computational problems offer a provable quantum advantage—and which remain fundamentally intractable—remains an open question. This thesis presents progress towards addressing both of these challenges. The first part of this thesis describes advances that substantially reduce the resource overhead of QEC. We begin by presenting realizations of logical circuits in dynamically reconfigurable arrays of neutral atoms. By jointly decoding the logical qubits, we reduce the cost of implementing such transversal Clifford circuits by a factor proportional to the code distance. We then develop new theories of fault tolerance to extend these savings to universal quantum computation with magic state inputs. Finally, we introduce techniques for fast correlated decoding, enabling practical implementations of these improvements in experimental hardware. Collectively, these advances accelerate progress toward large-scale computation and reduce the cost of QEC by over an order of magnitude. The second part of the thesis explores the relative power of quantum and classical computation in combinatorial optimization, a class of problems that is ubiquitous in science and engineering and foundational to the theory of computational complexity. We experimentally implement the optimized quantum adiabatic algorithm (QAA) in neutral atom arrays and observe evidence of a superlinear speedup over classical simulated annealing on certain hard problem instances. To interpret these results, we develop a theoretical framework to compare the performance of QAA with a broad class of classical Markov chain Monte Carlo algorithms. We identify conditions under which a quantum quadratic speedup is achievable and propose modifications to the QAA to reliably realize this advantage. Together, these contributions advance both the practical implementation and theoretical understanding of quantum algorithms.
Quantum computers have the potential to solve certain problems exponentially faster than classical computers. However, realizing this potential in practice is a major challenge, as it requires precise control over large-scale quantum systems operating at extremely low error rates. Quantum error correction (QEC) provides a path to achieving such error rates, but its substantial resource overhead poses a significant practical barrier. In addition, identifying which computational problems offer a provable quantum advantage—and which remain fundamentally intractable—remains an open question. This thesis presents progress towards addressing both of these challenges. The first part of this thesis describes advances that substantially reduce the resource overhead of QEC. We begin by presenting realizations of logical circuits in dynamically reconfigurable arrays of neutral atoms. By jointly decoding the logical qubits, we reduce the cost of implementing such transversal Clifford circuits by a factor proportional to the code distance. We then develop new theories of fault tolerance to extend these savings to universal quantum computation with magic state inputs. Finally, we introduce techniques for fast correlated decoding, enabling practical implementations of these improvements in experimental hardware. Collectively, these advances accelerate progress toward large-scale computation and reduce the cost of QEC by over an order of magnitude. The second part of the thesis explores the relative power of quantum and classical computation in combinatorial optimization, a class of problems that is ubiquitous in science and engineering and foundational to the theory of computational complexity. We experimentally implement the optimized quantum adiabatic algorithm (QAA) in neutral atom arrays and observe evidence of a superlinear speedup over classical simulated annealing on certain hard problem instances. To interpret these results, we develop a theoretical framework to compare the performance of QAA with a broad class of classical Markov chain Monte Carlo algorithms. We identify conditions under which a quantum quadratic speedup is achievable and propose modifications to the QAA to reliably realize this advantage. Together, these contributions advance both the practical implementation and theoretical understanding of quantum algorithms.
Quantum error correction (QEC) [1,2] is essential for the realization of large-scale quantum computers [3,4]. However, due to the complexity of operating on the encoded ‘logical’ qubits [5,6], understanding the physical principles for building fault-tolerant quantum devices and combining them into efficient architectures is an outstanding scientific challenge. Here we utilize reconfigurable arrays of up to 448 neutral atoms to implement the key elements of a universal, fault-tolerant quantum processing architecture and experimentally explore their underlying working mechanisms. We first employ surface codes to study how repeated QEC suppresses errors [6,7], demonstrating 2.14(13)x below-threshold performance in a four-round characterization circuit by leveraging atom loss detection and machine learning decoding [8,9]. We then investigate logical entanglement using transversal gates and lattice surgery [10–12], and extend it to universal logic through transversal teleportation with 3D [[15,1,3]] codes [13,14], enabling arbitrary-angle synthesis with polylogarithmic overhead [5,15]. Finally, we develop mid-circuit qubit re-use [16], increasing experimental cycle rates by two orders of magnitude and enabling deep-circuit protocols with dozens of logical qubits and hundreds of logical teleportations [17–20] with [[7,1,3]] and high-rate [[16,6,4]] codes while maintaining constant internal entropy. Our experiments reveal key principles for efficient architecture design, involving the interplay between quantum logic & entropy removal, judiciously using physical entanglement in logic gates & magic state generation, and leveraging teleportations for universality & physical qubit reset. These results establish foundations for scalable, universal error-corrected processing and its practical implementation with neutral atom systems.
Quantum computers open new scientific avenues, from exploring complex quantum mechanical systems to new computational paradigms, but face the fundamental challenge of decoherence. Remarkably, decoherence can be prevented by creating highly entangled states of physical qubits that encode an error-corrected “logical” qubit. This thesis will describe the development of quantum computing with reconfigurable arrays of neutral atoms and their use for quantum processing with logical qubits. Quantum processing in this approach is based on the coherent transport of atoms shuttled by optical tweezers, enabling any-to-any connectivity, high-fidelity programmable logic, and mid-circuit processing within a zoned architecture. Logical qubit processing is greatly facilitated by parallel control and transversal operations, and is used for experiments ranging from entangling logical qubits to their use for precise simulation of quantum scrambling. Core physical mechanisms for achieving deep-circuit, universal algorithms with logical qubits are identified, and these are leveraged into new techniques that greatly reduce overheads for large-scale computation. Finally, applications of quantum processors will be explored via analog and gate-based quantum simulations. These results, alongside other recent advances, herald a transition to error-corrected quantum processing, establishing foundations that can enable future large-scale quantum computers and their useful applications.
Quantum error correction (QEC) represents the cornerstone technology for realizing fault-tolerant quantum computing, addressing the fundamental challenge of quantum state decoherence in noisy intermediate-scale quantum (NISQ) devices. This comprehensive review examines recent advances in QEC implementations from 2020-2024, spanning theoretical foundations to practical hardware demonstrations. We analyze the evolution from pioneering stabilizer codes to modern topological approaches, with particular emphasis on surface codes and low-density parity-check (LDPC) codes that have demonstrated below-threshold error correction in superconducting and trapped-ion systems. The paper provides a comparative analysis of classical and machine learning-based decoder algorithms, evaluating their performance through complexity analysis and threshold comparisons in real-time error correction scenarios. Through examination of breakthrough experiments by Google, IBM, Quantinuum, and emerging platforms, we assess the current state of fault-tolerant quantum computing and identify critical engineering challenges including correlated noise models, cryogenic control systems, and scalable logical gate implementations. Our quantitative analysis reveals that while significant progress has been made toward practical fault-tolerance thresholds, achieving the resource efficiency and reliability required for large-scale quantum computation remains challenging. We provide detailed resource estimates for key applications including Shor's algorithm and optimization problems, along with analysis of industry roadmaps toward thousand-logical-qubit systems. This review serves as a comprehensive guide for researchers and engineers working toward the next generation of fault-tolerant quantum computers, with particular focus on information-theoretic perspectives relevant to quantum information entropy and syndrome processing.
Quantum error correction (QEC) represents the cornerstone technology for realizing fault-tolerant quantum computing, addressing the fundamental challenge of quantum state decoherence in noisy intermediate-scale quantum (NISQ) devices. This comprehensive review examines recent advances in QEC implementations from 2020-2024, spanning theoretical foundations to practical hardware demonstrations. We analyze the evolution from pioneering stabilizer codes to modern topological approaches, with particular emphasis on surface codes and low-density parity-check (LDPC) codes that have demonstrated below-threshold error correction in superconducting and trapped-ion systems. The paper provides a comparative analysis of classical and machine learning-based decoder algorithms, evaluating their performance through complexity analysis and threshold comparisons in real-time error correction scenarios. Through examination of breakthrough experiments by Google, IBM, Quantinuum, and emerging platforms, we assess the current state of fault-tolerant quantum computing and identify critical engineering challenges including correlated noise models, cryogenic control systems, and scalable logical gate implementations. Our quantitative analysis reveals that while significant progress has been made toward practical fault-tolerance thresholds, achieving the resource efficiency and reliability required for large-scale quantum computation remains challenging. We provide detailed resource estimates for key applications including Shor's algorithm and optimization problems, along with analysis of industry roadmaps toward thousand-logical-qubit systems. This review serves as a comprehensive guide for researchers and engineers working toward the next generation of fault-tolerant quantum computers, with particular focus on information-theoretic perspectives relevant to quantum information entropy and syndrome processing.
Quantum computation promises to revolutionize information processing by exploiting superposition and entanglement, enabling applications such as quantum simulation, combinatorial optimization, and secure quantum communication. Beyond individual processors, the quantum internet aims to connect quantum nodes through entanglement distribution, enabling distributed computation. However, quantum states are fragile: environmental interactions, imperfect gate operations, and measurement errors can quickly degrade encoded information. Reliable quantum computation therefore requires carefully designed quantum error-correcting codes and fault-tolerant protocols. Unlike classical redundancy schemes, quantum error correction must preserve delicate phase relationships and relies on indirect error detection through syndrome extraction with ancillary qubits, enabling error identification without collapsing encoded states. Topological codes, in particular, emerged early as the preferred choice for many architectures due to their planar structure, local interactions, and natural support for fault-tolerant logical operations. Color codes, for instance, allow transversal implementation of all Clifford gates, whereas non-Clifford operations require magic-state injection. More recent constructions, including quantum low-density parity-check codes, offer higher encoding rates and reduced resource overhead, but require long-range qubit connectivity and more complex protocols. Despite experimental progress, several challenges remain. Many platforms exhibit biased noise, motivating codes that exploit channel asymmetry. Real-time decoding remains a critical bottleneck, as fault-tolerant computation requires low-latency processing of rapidly generated syndrome data. Fault-tolerant logical state initialization also remains resource-intensive and scales poorly with code distance. Addressing these challenges, this thesis develops a unified framework spanning theory and experiment. It provides precise performance analysis of quantum error-correcting codes in the low physical error-rate regime, introduces codes tailored to biased noise, develops fast low-complexity decoding algorithms for real-time operation, and presents modular and efficient protocols for fault-tolerant state preparation of CSS codes. The latter is demonstrated experimentally through the preparation of a logical zero state of the Golay code on the Quantinuum H2 trapped-ion quantum computer.
Quantum computing is positioned to be a transformative technology to key areas of scientific interest such as quantum chemistry, material science, and cryptography. At a hardware level, recent years have seen broad progress in a variety of qubit modalities, however, error rates are still orders of magnitude higher than what is necessary for large-scale quantum programs. This gap in error rates motivates the use of quantum error correction (QEC) and the realization of fault-tolerant quantum computing (FTQC), yet today, although the theory of FTQC is promising, effectively connecting it to real devices poses significant challenges. In this dissertation we study opportunities for more efficient and scalable FTQC architectures through the co-design of quantum hardware and software. We first look at how unique hardware capabilities in quantum computers made from 2D arrays of optically trapped atoms can improve QEC performance. For computation, we study how longer-range interactions between atoms can enable a novel embedding of QEC blocks on physical qubits that improves logical-level connectivity. For memory, we study how mid-circuit movement of atoms can effectively implement higher encoding rate QEC codes, creating a qubit-efficient memory system. We next consider the performance impact of real-time classical systems in FTQC architectures, and explore the use of speculation to improve large-scale decoding systems. Finally, we study how software systems can be used to improve QEC designs. We consider the problem of QEC circuit optimization, and study an automated approach based on iterative optimization of performance-reducing subcircuits.