On the Addressability Problem on CSS Codes
J\'er\^ome Guyot, Samuel Jaques

TL;DR
This paper investigates the limitations of implementing logical gates on subsets of qubits in CSS quantum codes, revealing fundamental no-go results for high-rate codes and exploring the role of automorphisms in addressability.
Contribution
It introduces the first systematic study of distance-preserving addressability in quantum codes, establishing impossibility results and analyzing automorphisms for high-rate CSS codes.
Findings
Impossible to implement certain logical gates on subsets in high-rate CSS codes.
Logical qubit permutation is impossible via physical permutation if rate > 1/3 and distance ≥ 3.
No-go results for CNOTs and CZs between high-rate codes under global circuit restrictions.
Abstract
Recent discoveries in asymptotically good quantum codes have intensified research on their application in quantum computation and fault-tolerant operations. This study focuses on the addressability problem within CSS codes: what circuits might implement logical gates on strict subsets of logical qubits? With some notion of fault-tolerance, we show some impossibility results: for CSS codes with non-zero rate, one cannot address a logical H, HP, PH, nor CNOT to any non-empty strict subset of logical qubits using a circuit made only from 1-local Clifford gates. Furthermore, we show that one cannot permute the logical qubits in a code purely by permuting the physical qubits, if the rate of the code is (asymptotically) greater than 1/3 and the distance is at least 3. We can show a similar no-go result for CNOTs and CZs between two such high-rate codes, albeit with a less reasonable…
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Taxonomy
TopicsAdvanced Malware Detection Techniques · Web Application Security Vulnerabilities · Software Testing and Debugging Techniques
