Transversal Gates for Highly Asymmetric qLDPC Codes

• URL: http://arxiv.org/abs/2506.15905v1
• Date: Wed, 18 Jun 2025 22:37:21 GMT
• Title: Transversal Gates for Highly Asymmetric qLDPC Codes
• Authors: Heather Leitch, Alastair Kay,
• Abstract summary: Transversal gates are the ideal gates in a fault-tolerant scenario.<n>We show that qLDPC codes with phase gates have a number of logical qubits that grows linearly with $n$.<n>This is critical when addressing the question of what a phase gate truly means when there are many logical qubits in the system.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Transversal gates are the ideal gates in a fault-tolerant scenario; relatively easy to implement, and minimally error propagating. Their availability will maximise fault tolerant thresholds, enabling universal quantum computation in a wider range of noisy hardware. Transversal gates in quantum low density parity check (qLDPC) codes are largely unstudied, with the early results of Burton & Browne suggesting that transversal non-Clifford gates may be impossible. In this paper, we contradict this expectation with constructions for both hypergraph product codes and balanced product codes, although these first examples have weak properties. We find qLDPC codes with transversal phase gates that have a number of logical qubits that grows linearly with $n$, the number of physical qubits. The distance is highly asymmetric; while the distance against bit flip errors also grows (almost) linearly in $n$, the distance against phase flip errors is limited to $O(1)$. Moreover, existing distance rebalancing techniques are one-sided; we show that they only preserve the transversality when rebalancing to increase the asymmetry, not decrease it. We also collate a toolbox of techniques that identify a single transversal gate from which we can individuate a large range of different transversal gates. This is critical when addressing the question of what a transversal phase gate truly means when there are many logical qubits in the system.

Related papers

• Directional Codes: a new family of quantum LDPC codes on hexagonal- and square-grid connectivity hardware [0.0]
  Utility-scale quantum computing requires quantum error correction (QEC) to protect quantum information against noise.<n>Currently, superconducting hardware is a promising candidate for achieving fault tolerance due to its fast gate times and feasible scalability.<n>We construct a new family of qLDPC codes, which outperforms the rotated planar code (RPC)<n>We numerically evaluate the performance of directional codes, encoding four, six and twelve logical qubits.
  arXiv  Detail & Related papers  (2025-07-25T16:57:21Z)
• Accessible Quantum Gates on Classical Stabilizer Codes [0.0]
  We consider $[n,k,d]$-classical stabilizer codes addressing bit-flip errors where $n$, $k$ and $d$ are the numbers of physical and logical qubits, and the code distance respectively.<n>We prove that operations essential for achieving a universal logical gate set necessarily require complex unitary circuits to be implemented.<n>Similar constraints apply not only to classical codes designed to correct phase-flip errors, but also to quantum stabilizer codes tailored to biased noise.
  arXiv  Detail & Related papers  (2025-07-07T18:47:58Z)
• Fault-Tolerant Stabilizer Measurements in Surface Codes with Three-Qubit Gates [1.351813974961217]
  We show that stabilizer measurement circuits for unrotated surface codes can be fault-tolerant using single auxiliary qubits and three-qubit gates.<n>These gates enable lower-depth circuits leading to fewer fault locations and potentially shorter QEC cycle times.
  arXiv  Detail & Related papers  (2025-06-10T17:54:23Z)
• Multi-Target Rydberg Gates via Spatial Blockade Engineering [47.582155477608445]
  Multi-target gates offer the potential to reduce gate depth in syndrome extraction for quantum error correction.<n>We propose single-control-multi-target CZotimes N gates on a single-species neutral-atom platform.<n>We synthesise smooth control pulses for CZZ and CZZZ gates, achieving fidelities of up to 99.55% and 99.24%, respectively.
  arXiv  Detail & Related papers  (2025-04-21T17:59:56Z)
• Efficient fault-tolerant code switching via one-way transversal CNOT gates [0.0]
  We present a code scheme that respects the constraints of FT circuit design by only making use of switching gates. We analyze application of the scheme to low-distance color codes, which are suitable for operation in existing quantum processors. We discuss how the scheme can be implemented with a large degree of parallelization, provided that logical auxiliary qubits can be prepared reliably enough.
  arXiv  Detail & Related papers  (2024-09-20T12:54:47Z)
• Permutation-Invariant Quantum Codes with Transversal Generalized Phase Gates [0.0]
  We demonstrate that non-additive codes can outperform stabilizer codes. We construct permutation-invariant quantum codes that implement a $T$ gate using fewer qubits.
  arXiv  Detail & Related papers  (2023-10-26T17:59:33Z)
• Transversal Injection: A method for direct encoding of ancilla states for non-Clifford gates using stabiliser codes [55.90903601048249]
  We introduce a protocol to potentially reduce this overhead for non-Clifford gates. Preliminary results hint at high quality fidelities at larger distances.
  arXiv  Detail & Related papers  (2022-11-18T06:03:10Z)
• Partitioning qubits in hypergraph product codes to implement logical gates [0.0]
  Transversal gates are the simplest type of fault-tolerant logical gates. We show that gates can be used as the basis for universal quantum computing on LDPC codes.
  arXiv  Detail & Related papers  (2022-04-22T16:45:19Z)
• Experimental Characterization of Fault-Tolerant Circuits in Small-Scale Quantum Processors [67.47400131519277]
  A code's logical gate set may be deemed fault-tolerant for gate sequences larger than 10 gates. Some circuits did not satisfy the fault tolerance criterion. It is most accurate to assess the fault tolerance criterion when the circuits tested are restricted to those that give rise to an output state with a low dimension.
  arXiv  Detail & Related papers  (2021-12-08T01:52:36Z)
• Software mitigation of coherent two-qubit gate errors [55.878249096379804]
  Two-qubit gates are important components of quantum computing. But unwanted interactions between qubits (so-called parasitic gates) can degrade the performance of quantum applications. We present two software methods to mitigate parasitic two-qubit gate errors.
  arXiv  Detail & Related papers  (2021-11-08T17:37:27Z)
• 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)
• Random quantum circuits anti-concentrate in log depth [118.18170052022323]
  We study the number of gates needed for the distribution over measurement outcomes for typical circuit instances to be anti-concentrated. Our definition of anti-concentration is that the expected collision probability is only a constant factor larger than if the distribution were uniform. In both the case where the gates are nearest-neighbor on a 1D ring and the case where gates are long-range, we show $O(n log(n)) gates are also sufficient.
  arXiv  Detail & Related papers  (2020-11-24T18:44:57Z)

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.