Anticoherent $k$-planes and coding techniques for a 3-qubit scheme of universal quantum computing

• URL: http://arxiv.org/abs/2509.23464v1
• Date: Sat, 27 Sep 2025 19:26:16 GMT
• Title: Anticoherent $k$-planes and coding techniques for a 3-qubit scheme of universal quantum computing
• Authors: L. Aragón-Muñoz, C. Chryssomalakos, A. G. Flores-Delgado, V. Rascón-Barajas, I. Vázquez Mota,
• Abstract summary: Toponomic quantum computing (TQC) employs rotation sequences of anticoherent $k$-planes to construct noise-tolerant quantum gates.<n>We propose a universal quantum computing scheme for 3-qubit systems (via Hadamard + Toffoli gates) based on coding techniques.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Toponomic quantum computing (TQC) employs rotation sequences of anticoherent $k$-planes to construct noise-tolerant quantum gates. In this work, we demonstrate the implementation of generalized Toffoli gates, using $k$-planes of spin systems with $s \geq k + 1$, and of the Hadamard gate for a 3-qubit system, using a spin $s \!= \! 15$ 8-plane. We propose a universal quantum computing scheme for 3-qubit systems (via Hadamard + Toffoli gates) based on coding techniques. A key advantage of this construction is its inherent robustness against noise: apart from reparametrization invariance, our scheme is characterized by immunity to arbitrarily large deformations of the path in (rotational) parameter space.

Related papers

• Barenco gate implementation using driven two- and three-qubit spin chains [1.9078991171384019]
  We propose a protocol for implementing Barenco-type multi-qubit controlled gates using short driven spin chains.<n>We derive explicit conditions on the coupling strengths and driving parameters, provide closed-form expressions for the time-evolution operators in each relevant subspace, and characterize the quality of the implementation using the operator fidelity.<n> Numerical simulations show that the protocol achieves high fidelities over broad parameter ranges, demonstrating its robustness and suitability for quantum information processing in spin-chain platforms.
  arXiv  Detail & Related papers  (2026-03-02T20:56:24Z)
• A Universal Circuit Set Using the $S_3$ Quantum Double [0.5231056284485742]
  We give an explicit construction of the circuits for creating, moving, and measuring all non-trivial anyons.<n>We encode each physical degree of freedom of $mathcalD(S_3)$ into a novel, quantum, error-correcting code.<n>Our proposal offers a promising path to realize robust universal topological quantum computation in the NISQ era.
  arXiv  Detail & Related papers  (2024-11-14T18:58:41Z)
• Quantum circuit model for discrete-time three-state quantum walks on Cayley graphs [0.0]
  We develop qutrit circuit models for discrete-time three-state quantum walks on Cayley graphs. We numerically simulate these circuits to mimic its performance on noisy quantum computers.
  arXiv  Detail & Related papers  (2024-01-19T20:45:26Z)
• Quantum control landscape for generation of $H$ and $T$ gates in an open qubit with both coherent and environmental drive [57.70351255180495]
  An important problem in quantum computation is generation of single-qubit quantum gates such as Hadamard ($H$) and $pi/8$ ($T$) Here we consider the problem of optimal generation of $H$ and $T$ gates using coherent control and the environment as a resource acting on the qubit via incoherent control.
  arXiv  Detail & Related papers  (2023-09-05T09:05:27Z)
• GRAPE optimization for open quantum systems with time-dependent decoherence rates driven by coherent and incoherent controls [77.34726150561087]
  The GRadient Ascent Pulse Engineering (GRAPE) method is widely used for optimization in quantum control. We adopt GRAPE method for optimizing objective functionals for open quantum systems driven by both coherent and incoherent controls. The efficiency of the algorithm is demonstrated through numerical simulations for the state-to-state transition problem.
  arXiv  Detail & Related papers  (2023-07-17T13:37:18Z)
• Direct pulse-level compilation of arbitrary quantum logic gates on superconducting qutrits [36.30869856057226]
  We demonstrate any arbitrary qubit and qutrit gate can be realized with high-fidelity, which can significantly reduce the length of a gate sequence. We show that optimal control gates are robust to drift for at least three hours and that the same calibration parameters can be used for all implemented gates.
  arXiv  Detail & Related papers  (2023-03-07T22:15:43Z)
• Universal qudit gate synthesis for transmons [44.22241766275732]
  We design a superconducting qudit-based quantum processor. We propose a universal gate set featuring a two-qudit cross-resonance entangling gate. We numerically demonstrate the synthesis of $rm SU(16)$ gates for noisy quantum hardware.
  arXiv  Detail & Related papers  (2022-12-08T18:59:53Z)
• Quantum simulation of $\phi^4$ theories in qudit systems [53.122045119395594]
  We discuss the implementation of quantum algorithms for lattice $Phi4$ theory on circuit quantum electrodynamics (cQED) system. The main advantage of qudit systems is that its multi-level characteristic allows the field interaction to be implemented only with diagonal single-qudit gates.
  arXiv  Detail & Related papers  (2021-08-30T16:30:33Z)
• Realization of arbitrary doubly-controlled quantum phase gates [62.997667081978825]
  We introduce a high-fidelity gate set inspired by a proposal for near-term quantum advantage in optimization problems. By orchestrating coherent, multi-level control over three transmon qutrits, we synthesize a family of deterministic, continuous-angle quantum phase gates acting in the natural three-qubit computational basis.
  arXiv  Detail & Related papers  (2021-08-03T17:49:09Z)
• Hoare meets Heisenberg: A Lightweight Logic for Quantum Programs [0.932065750652415]
  We show that Gottesman's (1998) semantics for Clifford circuits based on the Heisenberg representation gives rise to a lightweight Hoare-like logic.<n>Our applications include (i) certifying whether auxiliary qubits can be safely disposed of, (ii) checking theity of a gate with respect to a given stabilizer code, and (iv) computing post-measurement states.
  arXiv  Detail & Related papers  (2021-01-22T04:07:12Z)
• QUANTIFY: A framework for resource analysis and design verification of quantum circuits [69.43216268165402]
  QUANTIFY is an open-source framework for the quantitative analysis of quantum circuits. It is based on Google Cirq and is developed with Clifford+T circuits in mind. For benchmarking purposes QUANTIFY includes quantum memory and quantum arithmetic circuits.
  arXiv  Detail & Related papers  (2020-07-21T15:36:25Z)
• Simulating nonnative cubic interactions on noisy quantum machines [65.38483184536494]
  We show that quantum processors can be programmed to efficiently simulate dynamics that are not native to the hardware. On noisy devices without error correction, we show that simulation results are significantly improved when the quantum program is compiled using modular gates.
  arXiv  Detail & Related papers  (2020-04-15T05:16:24Z)

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.