Quantum information processing (QIP) relies on delicate superposition states that are sensitive to interactions with environment. The quantum gates are imperfect and the use of quantum error correction coding (QECC) is essential to enable the fault-tolerant computing and to deal with quantum errors. The most critical gate, CNOT-gate, has been implemented as a probabilistic device by using integrated optics. CNOT-gates from linear optics provide only probabilistic outcomes and as such are not suitable for large-scale computation. In this paper, we show that arbitrary set of universal quantum gates and gates from Clifford group, needed in QECC, can be implemented based on cavity quantum electrodynamics (CQED). We further show that encoders/decoders for quantum LDPC codes can be implemented based on Hadamard and CNOT gates using CQED. Finally, we perform simulations and evaluate performance of several classes of quantum LDPC codes suitable for implementation in CQED technology.
Quantum information processing (QIP) relies on delicate superposition states that are sensitive to interactions with environment. The quantum gates are imperfect and the use of quantum error correction coding (QECC) is essential to enable the fault-tolerant computing and to deal with quantum errors. The most critical gate, CNOT-gate, has been implemented as a probabilistic device by using integrated optics. CNOT-gates from linear optics provide only probabilistic outcomes and as such are not suitable for large-scale computation. In this paper, we show that arbitrary set of universal quantum gates and gates from Clifford group, needed in QECC, can be implemented based on cavity quantum electrodynamics (CQED). We further show that encoders/decoders for quantum LDPC codes can be implemented based on Hadamard and CNOT gates using CQED. Finally, we perform simulations and evaluate performance of several classes of quantum LDPC codes suitable for implementation in CQED technology.
Quantum information processing (QIP) relies on delicate superposition states that are sensitive to interactions with environment, resulting in errors. Moreover, the quantum gates are imperfect so that the use of quantum error correction coding (QECC) is essential to enable the fault-tolerant computing. The QECC is also important in quantum communication and teleportation applications. The most critical gate, i.e., the CNOT gate, has been implemented recently as a probabilistic device by using integrated optics. CNOT gates from linear optics provide only probabilistic outcomes and, as such, are not suitable for any meaningful quantum computation (on the order of thousand qubits and above). In this paper, we show that arbitrary set of universal quantum gates and gates from Clifford group, which are needed in QECC, can be implemented based on cavity quantum electrodynamics (CQED). Moreover, in CQED technology, the use of the controlled-Zgate instead of the CNOT gate is more appropriate. We then show that encoders/decoders for quantum low-density parity-check (LDPC) codes can be implemented based on Hadamard and controlled-Zgates only using CQED. We also discuss quantum dual-containing and entanglement-assisted codes and show that they can be related to combinatorial objects known as balanced incomplete block designs (BIBDs). In particular, a special class of BIBDs-Steiner triple systems (STSs)-yields to low-complexity quantum LDPC codes. Finally, we perform simulations and evaluate the performance of several classes of large-girth quantum LDPC codes suitable for implementation in CQED technology against that of lower girth entanglement-assisted codes and dual-containing quantum codes.
We propose encoder and decoder architectures for quantum low-density parity-check (LDPC) codes suitable for all-optical implementation, based on controlled-not (CNOT) and Hadamard gates only. Given the fact that the CNOT gate can be implemented using directional couplers, and Hadamard gate by using pi-hybrid, the proposed encoders/decoders architectures are suitable for implementation in integrated optics. In addition, we propose several quantum LDPC codes based on balanced incomplete block designs.
I propose encoder and decoder architectures for entanglement-assisted (EA) quantum low-density parity-check (LDPC) codes suitable for all-optical implementation. I show that two basic gates needed for EA quantum error correction, namely, controlled-NOT (CNOT) and Hadamard gates can be implemented based on Mach-Zehnder interferometer. In addition, I show that EA quantum LDPC codes from balanced incomplete block designs of unitary index require only one entanglement qubit to be shared between source and destination.
Quantum low-density parity check (qLDPC) codes are among the leading candidates to realize error-corrected quantum memories with low qubit overhead. Potentially high encoding rates and large distance relative to their block size make them appealing for practical suppression of noise in near-term quantum computers. In addition to increased qubit-connectivity requirements compared to more conventional topological quantum error correcting codes, qLDPC codes remain notoriously hard to compute with. In this work, we introduce a construction to implement all Clifford quantum gate operations on the recently introduced lift-connected surface (LCS) codes (Old et al. 2024). These codes can be implemented in a 3D-local architecture and achieve asymptotic scaling [[n,O(n1/3),O(n1/3)]]. In particular, LCS codes realize favorable instances with small numbers of qubits: For the [[15,3,3]] LCS code, we provide deterministic fault-tolerant (FT) circuits of the logical gate set {Hi,Hi,CiXj}i,j∈(0,1,2) based on flag qubits. By adding a procedure for FT magic state preparation, we show quantitatively how to realize an FT universal gate set in d=3 LCS codes. Numerical simulations indicate that our gate constructions can attain pseudothresholds in the range pth≈4.8⋅10−3−1.2⋅10−2 for circuit-level noise. The schemes use a moderate number of qubits and are therefore feasible for near-term experiments, facilitating progress for fault-tolerant error corrected logic in high-rate qLPDC codes.
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 error correction (QEC) is a cornerstone of quantum computing, enabling reliable information processing in the presence of noise. Sparse stabilizer codes -- referred to generally as quantum low-density parity-check (QLDPC) codes -- have risen to the forefront of QEC research in recent years. This can be attributed to several key factors. First, classical LDPC codes admit low-complexity belief propagation iterative decoding and near-capacity performance, which contributed to the early interest in QLDPC codes. Then, the result promising constant overhead fault tolerance using QLDPC codes led to the search for code families that go beyond the long-holding n scaling barrier of minimum distance for codelength n. This resulted in recent breakthroughs in the construction of QLDPC codes, which, combined with efficient decoding algorithms and the development of fault-tolerant protocols operating on QLDPC-encoded quantum information, provide a promising pathway to low-overhead, fault-tolerant quantum computation. However, despite their potential, challenges remain, particularly in constructing and decoding finite-length codes that account for, or efficiently leverage, specific characteristics of quantum hardware, such as connectivity, topology, native gate sets, and noise models. This article provides an in-depth examination of QLDPC codes and their iterative decoders, catering to an information theory audience with no or limited background in quantum mechanics. We discuss the theoretical underpinnings, explore unique characteristics of quantum channels, and delineate key code constructions and decoding algorithms, ultimately highlighting the impact and future prospects of QLDPC codes in quantum information science.