On the Addressability Problem on CSS Codes

• URL: http://arxiv.org/abs/2502.13889v1
• Date: Wed, 19 Feb 2025 17:18:52 GMT
• Title: On the Addressability Problem on CSS Codes
• Authors: Jérôme Guyot, Samuel Jaques,
• Abstract summary: We show that CSS codes with non-zero rate cannot address a logical H, HP, PH, nor CNOT to any non-empty strict subset of logical qubits. We can show a similar no-go result for CNOTs and CZs between two such high-rate codes. This work pioneers the study of distance-preserving addressability in quantum codes, mainly by considering automorphisms of the code.
• Score: 0.6445605125467574
• License:
• 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. We can show a similar no-go result for CNOTs and CZs between two such high-rate codes, albeit with a less reasonable restriction to circuits that we call ``global'' (though recent addressable CCZ gates use global circuits). This work pioneers the study of distance-preserving addressability in quantum codes, mainly by considering automorphisms of the code. This perspective offers new insights and potential directions for future research. We argue that studying this trade off between addressability and efficiency of the codes is essential to understand better how to do efficient quantum computation.

Related papers

• Realizing Lattice Surgery on Two Distance-Three Repetition Codes with Superconducting Qubits [31.25958618453706]
  We demonstrate lattice surgery between two distance-three repetition-code qubits by splitting a single distance-three surface-code qubit. We achieve an improvement in the value of the decoded $ZZ$ logical two-qubit observable compared to a similar non-encoded circuit.
  arXiv  Detail & Related papers  (2025-01-08T16:49:27Z)
• Experimental Demonstration of Logical Magic State Distillation [62.77974948443222]
  We present the experimental realization of magic state distillation with logical qubits on a neutral-atom quantum computer. Our approach makes use of a dynamically reconfigurable architecture to encode and perform quantum operations on many logical qubits in parallel.
  arXiv  Detail & Related papers  (2024-12-19T18:38:46Z)
• Geometric structure and transversal logic of quantum Reed-Muller codes [51.11215560140181]
  In this paper, we aim to characterize the gates of quantum Reed-Muller (RM) codes by exploiting the well-studied properties of their classical counterparts. A set of stabilizer generators for a RM code can be described via $X$ and $Z$ operators acting on subcubes of particular dimensions.
  arXiv  Detail & Related papers  (2024-10-10T04:07:24Z)
• Many-hypercube codes: High-rate quantum error-correcting codes for high-performance fault-tolerant quantum computing [0.0]
  We propose high-rate small-size quantum error-detecting codes as a new family of high-rate quantum codes. Their simple structure allows for a geometrical interpretation using hypercubes corresponding to logical qubits. We achieve high error thresholds even in a circuit-level noise model.
  arXiv  Detail & Related papers  (2024-03-24T07:46:26Z)
• Experimental fault-tolerant code switching [1.9088985324817254]
  We present the first experimental implementation of fault-tolerant code switching between two codes. We construct logical circuits and prepare 12 different logical states which are not accessible in a fault-tolerant way within a single code. Our results experimentally open up a new route towards deterministic control over logical qubits with low auxiliary qubit overhead.
  arXiv  Detail & Related papers  (2024-03-20T16:40:57Z)
• Discovery of Optimal Quantum Error Correcting Codes via Reinforcement Learning [0.0]
  The recently introduced Quantum Lego framework provides a powerful method for generating complex quantum error correcting codes. We gamify this process and unlock a new avenue for code design and discovery using reinforcement learning (RL) We train on two such properties, maximizing the code distance, and minimizing the probability of logical error under biased Pauli noise.
  arXiv  Detail & Related papers  (2023-05-10T18:00:03Z)
• Hierarchical memories: Simulating quantum LDPC codes with local gates [0.05156484100374058]
  Constant-rate low-density parity-check (LDPC) codes are promising candidates for constructing efficient fault-tolerant quantum memories. We construct a new family of hierarchical codes, that encode a number of logical qubits K = Omega(N/log(N)2. Under conservative assumptions, we find that the hierarchical code outperforms the basic encoding where all logical qubits are encoded in the surface code.
  arXiv  Detail & Related papers  (2023-03-08T18:48:12Z)
• Quantum computation on a 19-qubit wide 2d nearest neighbour qubit array [59.24209911146749]
  This paper explores the relationship between the width of a qubit lattice constrained in one dimension and physical thresholds. We engineer an error bias at the lowest level of encoding using the surface code. We then address this bias at a higher level of encoding using a lattice-surgery surface code bus.
  arXiv  Detail & Related papers  (2022-12-03T06:16:07Z)
• A Quantum Algorithm for Computing All Diagnoses of a Switching Circuit [73.70667578066775]
  Faults are by nature while most man-made systems, and especially computers, work deterministically. This paper provides such a connecting via quantum information theory which is an intuitive approach as quantum physics obeys probability laws.
  arXiv  Detail & Related papers  (2022-09-08T17:55:30Z)
• Finding the disjointness of stabilizer codes is NP-complete [77.34726150561087]
  We show that the problem of calculating the $c-disjointness, or even approximating it to within a constant multiplicative factor, is NP-complete. We provide bounds on the disjointness for various code families, including the CSS codes,$d codes and hypergraph codes. Our results indicate that finding fault-tolerant logical gates for generic quantum error-correcting codes is a computationally challenging task.
  arXiv  Detail & Related papers  (2021-08-10T15:00:20Z)
• Fault-tolerant Coding for Quantum Communication [71.206200318454]
  encode and decode circuits to reliably send messages over many uses of a noisy channel. For every quantum channel $T$ and every $eps>0$ there exists a threshold $p(epsilon,T)$ for the gate error probability below which rates larger than $C-epsilon$ are fault-tolerantly achievable. Our results are relevant in communication over large distances, and also on-chip, where distant parts of a quantum computer might need to communicate under higher levels of noise.
  arXiv  Detail & Related papers  (2020-09-15T15:10:50Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.