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We introduce new algorithms and provide example constructions of stabilizer models for the gapped boundaries, domain walls, and $0D$ defects of Abelian composite-dimensional twisted quantum doubles. Using the physically intuitive concept of…
In order to build a large scale quantum computer, one must be able to correct errors extremely fast. We design a fast decoding algorithm for topological codes to correct for Pauli errors and erasure and combination of both errors and…
Quantum decoherence-the loss of quantum coherence due to interactions with an environment-plays a central role in quantum transport, and controlling this ubiquitous yet inevitable phenomenon is essential for practical quantum technologies.…
In this paper, we address the problem of state communication in finite-level quantum systems through noise-affected channels. Our approach is based on a self-consistent theory of decoding inner products associated with the code and error…
The concept of multiple particle interference is discussed, using insights provided by the classical theory of error correcting codes. This leads to a discussion of error correction in a quantum communication channel or a quantum computer.…
Quantum error-correcting codes aim to protect information in quantum systems to enable fault-tolerant quantum computations. The most prevalent method, stabilizer codes, has been well developed for many varieties of systems, however, largely…
The robustness of quantum memory against physical noises is measured by two methods: the exact and approximate quantum error correction (QEC) conditions for error recoverability, and the decoder-dependent error threshold which assesses if…
The surface code is a promising candidate for fault-tolerant quantum computation, achieving a high threshold error rate with nearest-neighbor gates in two spatial dimensions. Here, through a series of numerical simulations, we investigate…
Quantum information protocols are inevitably affected by decoherence which is associated with the leakage of quantum information into an environment. In this paper we address the possibility of recovering the quantum information from an…
Quantum information theory and strongly correlated electron systems share a common theme of macroscopic quantum entanglement. In both topological error correction codes and theories of quantum materials (spin liquid, heavy fermion and…
In this paper we investigate the role of local information in the decoding of the repetition and surface error correction codes for the protection of quantum states. Our key result is an improvement in resource efficiency when local…
We investigate the stability of logical information in quantum stabilizer codes subject to coherent unitary errors. Beginning with a logical state, we apply a random unitary error channel and subsequently measure stabilizer checks,…
We study the phase transition from two different topological phases to the ferromagnetic phase by focusing on points of the phase transition. To this end, we present a detailed mapping from such models to the Ising model in a transverse…
Reliable processing of quantum information for developing quantum technologies requires precise control of out-of-equilibrium many-bodysystems. This is a highly challenging task as the fragility of quantum states to external perturbations…
The strongly correlated systems we use to realise quantum error-correcting codes may give rise to high-weight, problematic errors. Encouragingly, we can expect local quantum error-correcting codes with no string-like logical operators $-$…
This work explores a deformation of the Kitaev toric code that induces a phase transition out of the topologically ordered phase. By placing the model on a cylinder, the bulk global 1-form symmetries separate into distinct boundary…
Quantum information needs to be protected by quantum error-correcting codes due to imperfect physical devices and operations. One would like to have an efficient and high-performance decoding procedure for the class of quantum stabilizer…
Decoding stabilizer codes such as the surface and toric codes involves evaluating free-energy differences in a disordered statistical mechanics model, in which the randomness comes from the observed pattern of error syndromes. We study the…
We show that a subset of the basis for the irreducible representations of a tensor-product SU(2) rotation forms a covariant approximate quantum error-correcting code with transversal U(1) logical gates. Generalizing previous work on…
The competition between non-commuting projective measurements in discrete quantum circuits can give rise to entanglement transitions. It separates a regime where initially stored quantum information survives the time evolution from a regime…