Compare Papers

Paper 1

Dense packing of the surface code: code deformation procedures and hook-error-avoiding gate scheduling

Kohei Fujiu, Shota Nagayama, Shin Nishio, Hideaki Kawaguchi, Takahiko Satoh

Year

2025

Journal

arXiv preprint

DOI

arXiv:2511.06758

arXiv

2511.06758

The surface code is one of the leading quantum error correction codes for realizing large-scale fault-tolerant quantum computing (FTQC). One major challenge in realizing surface-code-based FTQC is the extremely large number of qubits required. To mitigate this problem, fusing multiple codewords of the surface code into a densely packed configuration has been proposed. It is known that by using dense packing, the number of physical qubits required per logical qubit can be reduced to approximately three-fourths compared to simply placing surface-code patches side by side. Despite its potential, concrete deformation procedures and quantitative error-rate analyses have remained largely unexplored. In this work, we present a detailed code-deformation procedure that transforms multiple standard surface code patches into a densely packed, connected configuration, along with a conceptual microarchitecture to utilize this dense packing. We also propose a CNOT gate-scheduling for stabilizer measurement circuits that suppresses hook errors in the densely packed surface code. We performed circuit-level Monte Carlo noise simulation of densely packed surface codes using this gate scheduling. The numerical results demonstrate that as the code distance of the densely packed surface code increases and the physical error rate decreases, the logical error rate of the densely packed surface code becomes lower than that of the standard surface code. Furthermore, we find that only when employing hook-error-avoiding syndrome extraction can the densely packed surface code achieve a lower logical error rate than the standard surface code, while simultaneously reducing the space overhead.

Open paper

Paper 2

Supersymmetric Quantum Mechanics of Hypergeometric-like Differential Operators

Tianchun Zhou

Year

2023

Journal

arXiv preprint

DOI

arXiv:2307.15948

arXiv

2307.15948

Systematic iterative algorithms of supersymmetric quantum mechanics (SUSYQM) type for solving the eigenequation of principal hypergeometric-like differential operator (HLDO) and for generating the eigenequation of associated HLDO itself as well its solutions are developed, without any input from traditional methods. These are initiated by devising two types of active supersymmetrization transformations and momentum operator maps, which work to transform the same eigenequation of HLDO in its two trivial asymmetric factorizations into two distinct supersymmetrically factorized Schrödinger equations. The rest iteration flows are completely controlled by repeatedly performing intertwining action and incorporating some generalized commutator relations to renormalize the superpartner equation of the eigenequation of present level into that of next level. These algorithms therefore provide a simple SUSYQM answer to the question regarding why there exist simultaneously a series of principal as well as associated eigenfunctions for the same HLDO, which boils down to two basic facts: two distinct types of quantum momentum kinetic energy operators and superpotentials are rooted in this operator; each initial superpotential can proliferate into a hierarchy of descendant ones in a shape-invariant fashion. The two active supersymmetrizations establish the isomorphisms between the nonstandard and standard coordinate representations of the SUSYQM algorithm either for principal HLDO or for its associated one, so these algorithms can be constructed in either coordinate representation with equal efficiency. Due to their relatively high efficiency, algebraic elementariness and logical independence, the iterative SUSYQM algorithms developed in this paper could become the hopefuls for supplanting some traditional methods for solving the eigenvalue problems of principal HLDOs and their associated cousins.

Open paper