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Transformer-based large language models (LLMs) have demonstrated significant potential in addressing logic problems. capitalizing on the great capabilities of LLMs for code-related activities, several frameworks leveraging logical solvers…
Topological color codes are widely acknowledged as promising candidates for fault-tolerant quantum computing. Neither a two-dimensional nor a three-dimensional topology, however, can provide a universal gate set $\{$H, T, CNOT$\}$, with the…
The typical time-independent view of quantum error correction (QEC) codes hides significant freedom in the decomposition into circuits that are executable on hardware. Using the concept of detecting regions, we design time-dynamic QEC…
The construction of topological error correction codes requires the ability to fabricate a lattice of physical qubits embedded on a manifold with a non-trivial topology such that the quantum information is encoded in the global degrees of…
We take initial steps towards a general framework for constructing logical gates in general quantum CSS codes. Viewing CSS codes as cochain complexes, we observe that cohomology invariants naturally give rise to diagonal logical gates. We…
Lattice surgery is a leading approach for implementing fault-tolerant logical operations in surface code quantum computing, but compiling efficient lattice surgery layouts remains challenging. Existing compilers are largely circuit-centric…
Formal control synthesis approaches over stochastic systems have received significant attention in the past few years, in view of their ability to provide provably correct controllers for complex logical specifications in an automated…
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…
The surface code is a promising candidate for fault-tolerant quantum computation and has been implemented in many quantum hardware platforms. In this work, we propose a new non-local unitary circuit to encode a surface code state based on a…
We revisit the Kitaev model for fault tolerant quantum computing on a square lattice with underlying quantum double $D(G)$ symmetry, where $G$ is a finite group. We provide projection operators for its quasiparticles content as irreducible…
We analyse some QR decomposition algorithms, and show that the I/O complexity of the tile based algorithm is asymptotically the same as that of matrix multiplication. This algorithm, we show, performs the best when the tile size is chosen…
Linear codes are widely studied in coding theory as they have nice applications in distributed storage, combinatorics, lattices, cryptography and so on. Constructing linear codes with desirable properties is an interesting research topic.…
Practical large-scale quantum computation requires both efficient error correction and robust implementation of logical operations. Three-dimensional (3D) color codes are a promising candidate for fault-tolerant quantum computation due to…
We introduce homological measurement, a framework for measuring the logical Pauli operators encoded in CSS stabilizer codes. The framework is based on the algebraic description of such codes as chain complexes. Protocols such as lattice…
In this article, we study some parallel processing algorithms for multiplication and modulo operations. We demonstrate that the state transitions that are formed under these algorithms satisfy lattice-linearity, where these algorithms…
As fault-tolerant quantum computers scale, certifying the accuracy of computations performed with encoded logical qubits will soon become classically intractable. This creates a critical need for scalable, device-independent certification…
Many reasoning, planning, and problem-solving tasks share an intrinsic algorithmic nature: correctly simulating each step is a sufficient condition to solve them correctly. We collect pairs of naturalistic and synthetic reasoning tasks to…
Quantum information is fragile and must be protected by a quantum error-correcting code for large-scale practical applications. Recently, highly efficient quantum codes have been discovered which require a high degree of spatial…
The development of quantum codes with good error correction parameters and useful sets of transversal gates is a problem of major interest in quantum error-correction. Abundant prior works have studied transversal gates which are restricted…
We show how to exploit excitable regimes mediated by localized structures (LS) to perform AND, OR, and NOT logical operations providing full logical functionality. Our scheme is general and can be implemented in any physical system…