Related papers: Untangling Surface Codes: Bridging Braids and Latt…
We devise a new realization of the surface code on a rectangular lattice of qubits utilizing single-qubit and nearest-neighbor two-qubit Pauli measurements and three auxiliary qubits per plaquette. This realization gains substantial…
Quantum code surgery is a promising technique to perform fault-tolerant computation on quantum low-density parity-check codes. Recent developments have significantly reduced the space overhead of surgery. However, generic surgery operations…
Braiding defects in topological stabiliser codes has been widely studied as a promising approach to fault-tolerant quantum computing. Here, we explore the potential and limitations of such schemes in codes of all spatial dimensions. We…
The surface code is one of the most successful approaches to topological quantum error-correction. It boasts the smallest known syndrome extraction circuits and correspondingly largest thresholds. Defect-based logical encodings of a new…
Demonstrating subthreshold scaling of a surface-code quantum memory on hardware whose native connectivity does not match the code remains a central challenge. We address this on IBM heavy-hex superconducting processors by co-designing the…
Defect-adaptive surface-code methods have substantially advanced the construction of valid logical patches on imperfect hardware, but fault-tolerant computation also requires executable logical oper ations on the resulting irregular…
A remarkable characteristic of quantum computing is the potential for reliable computation despite faulty qubits. This can be achieved through quantum error correction, which is typically implemented by repeatedly applying static syndrome…
Topological gauge theories in four dimensions which admit surface operators provide a natural framework for realizing homological knot invariants. Every such theory leads to an action of the braid group on branes on the corresponding moduli…
Whether it is at the fabrication stage or during the course of the quantum computation, e.g. because of high-energy events like cosmic rays, the qubits constituting an error correcting code may be rendered inoperable. Such defects may…
The surface code is a many-body quantum system, and simulating it in generic conditions is computationally hard. While the surface code is believed to have a high threshold, the numerical simulations used to establish this threshold are…
Fault-tolerant quantum computation using two-dimensional topological quantum error correcting codes can benefit from multi-qubit long-range operations. By using simple commutation rules, a quantum circuit can be transpiled into a sequence…
Surface codes$\unicode{x2014}$leading candidates for quantum error correction (QEC)$\unicode{x2014}$and entanglement phases$\unicode{x2014}$a key notion for many-body quantum dynamics$\unicode{x2014}$have heretofore been unrelated. Here, we…
The logical S gate implemented via twist defect braiding in the surface code is one of the major sources of overhead in fault-tolerant quantum computing, since an S-gate correction is required in every logical T-gate teleportation. Existing…
The first generations of quantum computers will execute fault-tolerant quantum circuits, and it is very likely that such circuits will use surface quantum error correcting codes. To the best of our knowledge, no complete design automation…
Surface code is an error-correcting method that can be applied to the implementation of a usable quantum computer. At present, a promising candidate for a usable quantum computer is based on superconductor-specifically transmon. Because…
Surface and color codes are two forms of topological quantum error correction in two spatial dimensions with complementary properties. Surface codes have lower-depth error detection circuits and well-developed decoders to interpret and…
This is a comprehensive review on fault-tolerant topological quantum computation with the surface codes. The basic concepts and useful tools underlying fault-tolerant quantum computation, such as universal quantum computation, stabilizer…
The surface code is a promising platform for a quantum memory, but its threshold under coherent errors remains incompletely understood. We study maximum-likelihood decoding of the square-lattice surface code in the presence of single-qubit…
This thesis is a study of quantum error-correction codes from an algebraic perspective. We concern ourselves not only with quantum codes but also protocols to perform logical quantum computation using such codes. We derive new methods of…
The surface code is a powerful quantum error correcting code that can be defined on a 2-D square lattice of qubits with only nearest neighbor interactions. Syndrome and data qubits form a checkerboard pattern. Information about errors is…