Related papers: Floquet Codes from Coupled Spin Chains
In the absence of fault tolerant quantum error correction for analog, Hamiltonian quantum computation, error suppression via energy penalties is an effective alternative. We construct families of distance-$2$ stabilizer subsystem codes we…
Conventional fault-tolerant quantum error-correction schemes require a number of extra qubits that grows linearly with the code's maximum stabilizer generator weight. For some common distance-three codes, the recent "flag paradigm" uses…
Stabilizer codes are a simple and successful class of quantum error-correcting codes. Yet this success comes in spite of some harsh limitations on the ability of these codes to fault-tolerantly compute. Here we introduce a new metric for…
We derive the spectral domain properties of two-dimensional (2-D) $(\lambda_1, \lambda_2)$-constacyclic codes over $\mathbb{F}_q$ using the 2-D finite field Fourier transform (FFFT). Based on the spectral nulls of 2-D $(\lambda_1,…
Current 3D tokenizers largely treat representation as spatial compression: compact codes reconstruct surface geometry, but leave component ownership and attachment validity implicit. In open-world assets with intersecting components, noisy…
Time-periodic driving of a quantum system can enable new dynamical topological phases of matter that could not exist in thermal equilibrium. We investigate two related classes of dynamical topological phenomena in 2D systems: Floquet…
A circulant-based spatially-coupled (SC) code is constructed by partitioning the circulants of an underlying block code into a number of components, and then coupling copies of these components together. By connecting (coupling) several SC…
We propose a systematic framework to construct a (d+1)-dimensional stabilizer model from an initial generic d-dimensional abelian symmetry. Our approach builds upon the iterative gauging procedure, developed by one of the authors in [J.…
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 $-$…
Subsystem quantum error-correcting codes typically involve measuring a sequence of non-commuting parity check operators. They can sometimes exhibit greater fault-tolerance than conventional subspace codes, which use commuting checks.…
Topological edge states form at the edges of periodic materials with specific degeneracies in their modal spectra, such as Dirac points, under the action of effects breaking certain symmetries of the system. In particular, in Floquet…
We study the implementation of fault-tolerant logical Clifford gates on stabilizer quantum error correcting codes based on their symmetries. Our approach is to map the stabilizer code to a binary linear code, compute its automorphism group,…
Recent advances in the field of quantum technologies have opened up the road for the realization of small-scale quantum simulators of lattice gauge theories which, among other goals, aim at improving our understanding on the…
This paper investigates the possibility of generating Floquet-time crystals in higher dimensions ($d\geq 2$) through the time-periodic driving of integrable free-fermionic models. The realization leads to rigid time-crystal phases that are…
Superconducting cavities with high quality factors, coupled to a fixed-frequency transmon, provide a state-of-the-art platform for quantum information storage and manipulation. The commonly used selective number-dependent arbitrary phase…
We introduce a morphing procedure that can be used to generate new quantum codes from existing quantum codes. In particular, we morph the 15-qubit Reed-Muller code to obtain a $[\![10,1,2]\!]$ code that is the smallest known stabilizer code…
It is of theoretical and experimental interest to engineer topological phases with very large topological invariants via periodic driving. As advocated by this work, such Floquet engineering can be elegantly achieved by the particle swarm…
Floquet codes are an intriguing generalisation of stabiliser and subsystem codes, which can provide good fault-tolerant characteristics while benefiting from reduced connectivity requirements in hardware. A recent question of interest has…
Designs for quantum error correction depend strongly on the connectivity of the qubits. For solid state qubits, the most straightforward approach is to have connectivity constrained to a planar graph. Practical considerations may also…
Topological phases with a widely tunable number of edge modes have been extensively studied as a typical class of exotic states of matter with potentially important applications. Although several models have been shown to support such…