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Recent progress in studies of holographic dualities, originally motivated by insights from string theory, has led to a confluence with concepts and techniques from quantum information theory. A particularly successful approach has involved…
Quantum error correction is an essential ingredient for reliable quantum computation for theoretically provable quantum speedup. Topological color codes, one of the quantum error correction codes, have an advantage against the surface codes…
A major difficulty in quantum computation is the ability to implement fault tolerant computations, protecting information against undesired interactions with the environment. Stabiliser codes were introduced as a means to protect…
Fault tolerance is a prerequisite for scalable quantum computing. Architectures based on 2D topological codes are effective for near-term implementations of fault tolerance. To obtain high performance with these architectures, we require a…
Recent work on approximate quantum error correction (QEC) has opened up the possibility of constructing subspace codes that protect information with high fidelity in scenarios where perfect error correction is impossible. Motivated by this,…
We generalize the Pastawski-Yoshida-Harlow-Preskill (HaPPY) holographic quantum error-correcting code to provide a toy model for bulk gauge fields or linearized gravitons. The key new elements are the introduction of degrees of freedom on…
In this paper, we utilize a concatenation scheme to construct new families of quantum error correction codes achieving the quantum Gilbert-Varshamov (GV) bound asymptotically. We concatenate alternant codes with any linear code achieving…
We develop a novel holographic framework to study dynamical phases in random quantum circuits with a global symmetry $G$. Viewing the circuit as a tensor network, we decompose it into two parts: a symmetric layer, which defines an emergent…
Finding optimal correction of errors in generic stabilizer codes is a computationally hard problem, even for simple noise models. While this task can be simplified for codes with some structure, such as topological stabilizer codes,…
Quantum error correction is a fundamental primitive of fault-tolerant quantum computing. But in order for error correction to proceed, one must first prepare the codespace of the underlying error-correcting code. A popular method for…
Bosonic codes utilize the infinite-dimensional Hilbert space of harmonic oscillators to encode quantum information, offering a hardware-efficient approach to quantum error correction. Designing these codes requires precise geometric…
This paper computationally obtains optimal bounded-weight, binary, error-correcting codes for a variety of distance bounds and dimensions. We compare the sizes of our codes to the sizes of optimal constant-weight, binary, error-correcting…
We construct explicitly two infinite families of genuine nonadditive 1-error correcting quantum codes and prove that their coding subspaces are 50% larger than those of the optimal stabilizer codes of the same parameters via the linear…
We propose and analyze a hierarchical quantum error correction (QEC) scheme that concatenates hypergraph product (HGP) codes with rotated surface codes, which is compatible with quantum computers with only nearest-neighbor interactions. The…
We develop a previously proposed gauge-invariant method to integrate out infinite tower of Kaluza-Klein (KK) modes of vector and axialvector mesons in a class of models of holographic QCD (HQCD). The HQCD is reduced by our method to the…
We introduce a novel type of quantum error correcting code, called the spinor code, based on spaces defined by total spin. The code is a nonstabilizer code, and is also a nonlinear quantum error correcting code, meaning that quantum…
Preparing arbitrary logical states is a central primitive for universal fault-tolerant quantum computation and the cost of encoded-state preparation contributes directly to the overall resource overhead. This makes the synthesis of…
We calculate quantum corrections to holographic entanglement entropy in the proposed duality between $T\bar{T}$-deformed holographic 2D CFTs and gravity in AdS$_{3}$ with a finite cutoff. We first establish the dictionary between the two…
Motivated by the ability to consistently apply the Ryu-Takayanagi prescription for general convex surfaces and the relationship between entanglement and geometry in tensor networks, we introduce a novel, covariant bulk object - the…
We describe a family of quantum error-correcting codes which generalize both the quantum hypergraph-product (QHP) codes by Tillich and Z\'emor, and all families of toric codes on $m$-dimensional hypercubic lattices. Similar to the latter,…