Fault-Tolerant Non-Clifford GKP Gates using Polynomial Phase Gates and On-Demand Noise Biasing

• URL: http://arxiv.org/abs/2511.20355v1
• Date: Tue, 25 Nov 2025 14:34:36 GMT
• Title: Fault-Tolerant Non-Clifford GKP Gates using Polynomial Phase Gates and On-Demand Noise Biasing
• Authors: Minh T. P. Nguyen, Mackenzie H. Shaw,
• Abstract summary: We propose a method for on-demand noise biasing based on a standard GKP error correction circuit.<n>We prove that the logical error rate of the $T$ gate can be made arbitrarily small as the quality of the GKP codestates increases.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Gottesman-Kitaev-Preskill (GKP) error correcting code uses a bosonic mode to encode a logical qubit, and has the attractive property that its logical Clifford gates can be implemented using Gaussian unitary gates. In contrast, a direct unitary implementation of the ${T}$ gate using the cubic phase gate has been shown to have logical error floor unless the GKP codestate has a biased noise profile [1]. In this work, we propose a method for on-demand noise biasing based on a standard GKP error correction circuit. This on-demand biasing circuit can be used to bias the GKP codestate before a $T$ gate and return it to a non-biased state afterwards. With the on-demand biasing circuit, we prove that the logical error rate of the $T$ gate can be made arbitrarily small as the quality of the GKP codestates increases. We complement our proof with a numerical investigation of the cubic phase gate subject to a phenomenological noise model, showing that the ${T}$ gate can achieve average gate fidelities above $99\%$ with 12 dB of GKP squeezing without the use of postselection. Moreover, we develop a formalism for finding optimal unitary representations of logical diagonal gates in higher levels of the Clifford hierarchy that is based on a framework of ``polynomial phase stabilizers'' whose exponents are polynomial functions of one of the quadrature operators. This formalism naturally extends to multi-qubit logical gates and even to number-phase bosonic codes, providing a powerful algebraic tool for analyzing non-Clifford gates in bosonic quantum codes. [1] J. Hastrup, M. V. Larsen, J. S. Neergaard-Nielsen, N. C. Menicucci, and U. L. Andersen, Phys. Rev. A 103, 032409 (2021)

Related papers

• Composable logical gate error in approximate quantum error correction: reexamining gate implementations in Gottesman-Kitaev-Preskill codes [0.13764085113103217]
  We introduce a single scalar quantity we call the (composable) logical gate error.<n>It captures both the deviation of the logical action from the desired target gate as well as leakage out of the code space.<n>We show how to bound the composable logical gate error in terms of matrix elements of physical unitaries between (approximate) logical computational basis states.
  arXiv  Detail & Related papers  (2025-09-18T06:27:09Z)
• Leveraging biased noise for more efficient quantum error correction at the circuit-level with two-level qubits [0.0]
  We show that a residual bias up to $etasim$5 can be maintained in CNOT gates under certain conditions.<n>We numerically study the performance of the XZZX surface code and observe that bias-preserving CZ gates are critical for leveraging biased noise.
  arXiv  Detail & Related papers  (2025-05-23T10:35:36Z)
• Logical Gates and Read-Out of Superconducting Gottesman-Kitaev-Preskill Qubits [0.0]
  In superconducting circuits, all the required two-qubit gates can be implemented with a single piece of hardware. We analyze the error-spreading properties of GKP Clifford gates and describe how a modification in the decoder can reduce the gate infidelity by multiple orders of magnitude.
  arXiv  Detail & Related papers  (2024-03-04T19:00:04Z)
• 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)
• Clifford-deformed Surface Codes [43.586723306759254]
  Various realizations of Kitaev's surface code perform surprisingly well for biased Pauli noise. We analyze CDSCs on the $3times 3$ square lattice and find that, depending on the noise bias, their logical error rates can differ by orders of magnitude.
  arXiv  Detail & Related papers  (2022-01-19T19:00:00Z)
• 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)
• 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)
• Engineering fast bias-preserving gates on stabilized cat qubits [64.20602234702581]
  bias-preserving gates can significantly reduce resource overhead for fault-tolerant quantum computing. In this work, we apply a derivative-based leakage suppression technique to overcome non-adiabatic errors.
  arXiv  Detail & Related papers  (2021-05-28T15:20:21Z)
• Low overhead fault-tolerant quantum error correction with the surface-GKP code [60.44022726730614]
  We propose a highly effective use of the surface-GKP code, i.e., the surface code consisting of bosonic GKP qubits instead of bare two-dimensional qubits. We show that a low logical failure rate $p_L 10-7$ can be achieved with moderate hardware requirements.
  arXiv  Detail & Related papers  (2021-03-11T23:07:52Z)
• 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)
• Cubic phase gates are not suitable for non-Clifford operations on GKP states [0.0]
  With the Gottesman-Kitaev-Preskill (GKP) encoding, Clifford gates and error correction can be carried out using simple Gaussian operations. In their original proposal, GKP suggested a particularly simple method of using a single application of the cubic phase gate to perform the logical non-Clifford T-gate. Here we show that this cubic phase gate approach performs extraordinarily poorly, even for arbitrarily large amounts of squeezing in the GKP state.
  arXiv  Detail & Related papers  (2020-09-11T09:45:28Z)
• Cost-optimal single-qubit gate synthesis in the Clifford hierarchy [0.0]
  A synthesis algorithm can be used to approximate any unitary gate up to arbitrary precision. Current procedures do not yet support individual assignment of base gate costs.
  arXiv  Detail & Related papers  (2020-05-12T07:21:12Z)

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.