Fault-tolerant logical measurements via homological measurement

• URL: http://arxiv.org/abs/2410.02753v2
• Date: Mon, 18 Nov 2024 22:08:54 GMT
• Title: Fault-tolerant logical measurements via homological measurement
• Authors: Benjamin Ide, Manoj G. Gowda, Priya J. Nadkarni, Guillaume Dauphinais,
• Abstract summary: homological measurement is a framework for measuring the logical Pauli operators encoded in CSS stabilizer codes. We develop a specific protocol for fault-tolerant measurement of arbitrary logical Pauli operators of general qLDPC codes.
• Score: 0.14999444543328289
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce homological measurement, a framework for measuring the logical Pauli operators encoded in CSS stabilizer codes. The framework is based on the algebraic description of such codes as chain complexes. Protocols such as lattice surgery some of its recent generalizations are shown to be special cases of homological measurement. Using this framework, we develop a specific protocol called edge expanded homological measurement for fault-tolerant measurement of arbitrary logical Pauli operators of general qLDPC codes, requiring a number of ancillary qubits growing only linearly with the weight of the logical operator measured, and guaranteed that the distance of the code is preserved. We further benchmark our protocol numerically in a photonic architecture based on GKP qubits, showing that the logical error rate of various codes are on par with other methods requiring more ancilla qubits.

Related papers

• QGPU: Parallel logic in quantum LDPC codes [1.9960650656921184]
  Quantum low-density parity-check codes are a resource-efficient alternative to surface codes.<n>Key challenge is that logical qubits do not necessarily map to disjoint sets of physical qubits.<n>We introduce clustered-cyclic codes, a quantum low-density parity-check code family with finite-size instances.
  arXiv  Detail & Related papers  (2026-03-05T17:26:00Z)
• Single-Shot and Few-Shot Decoding via Stabilizer Redundancy in Bivariate Bicycle Codes [5.685589351789461]
  We prove that $g(z)$ dictates the code's stabilizer redundancy and the structure of the classical emphsyndrome codes required for single-shot decoding.<n>Within the coprime BB ansatz, high quantum rate imposes an upper bound on syndrome distance, limiting single-shot performance.
  arXiv  Detail & Related papers  (2026-01-03T09:49:58Z)
• Planar Fault-Tolerant Quantum Computation with Low Overhead [5.232949916418351]
  We introduce code craft, a framework for designing fault-tolerant logical operations on planar BB codes.<n>We show that logical operations, including controlled-NOT gates, state transfers, and Pauli measurements, can be efficiently implemented within this framework.
  arXiv  Detail & Related papers  (2025-06-22T15:07:03Z)
• Parallel Logical Measurements via Quantum Code Surgery [42.95092131256421]
  Quantum code surgery is a flexible and low overhead technique for performing logical measurements on quantum error-correcting codes. We present a code surgery scheme, applicable to any Calderbank-Shor-Steane quantum low-density parity check (LDPC) code, that fault-tolerantly measures many logical Pauli operators in parallel.
  arXiv  Detail & Related papers  (2025-03-06T22:05:52Z)
• Emergent unitary designs for encoded qubits from coherent errors and syndrome measurements [1.8854166566682866]
  We propose an efficient approach to generate unitary designs for encoded qubits in surface codes. We numerically show that the ensemble of logical unitaries converges to a unitary design in the thermodynamic limit. Our results provide a practical way to realize unitary designs on encoded qubits.
  arXiv  Detail & Related papers  (2024-12-05T18:36:14Z)
• Chasing shadows with Gottesman-Kitaev-Preskill codes [0.3277163122167433]
  We consider the task of performing shadow tomography of a logical subsystem defined via the Gottesman-Kitaev-Preskill (GKP) error correcting code.<n>Our protocol does not require the input state to be a code state but is implemented by appropriate twirling of the measurement channel.
  arXiv  Detail & Related papers  (2024-10-31T22:16:06Z)
• 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)
• Improved QLDPC Surgery: Logical Measurements and Bridging Codes [0.568907503750523]
  We introduce the gauge-fixed QLDPC surgery scheme, an improved logical measurement scheme based on the construction of Cohen et al.(Sci.Adv.8, eabn1717). Our scheme leverages expansion properties of the Tanner graph to substantially reduce the space overhead of QLDPC surgery. In certain cases, we only require $Theta(w)$ ancilla qubits to fault-tolerantly measure a weight $w$ logical operator.
  arXiv  Detail & Related papers  (2024-07-25T20:55:24Z)
• Low-Overhead Transversal Fault Tolerance for Universal Quantum Computation [36.3664581543528]
  We show that logical operations can be performed fault-tolerantly with only a constant number of extraction rounds.<n>Our work sheds new light on the theory of quantum fault tolerance and has the potential to reduce the space-time cost of practical fault-tolerant quantum computation by over an order of magnitude.
  arXiv  Detail & Related papers  (2024-06-25T15:43:25Z)
• Toward a 2D Local Implementation of Quantum LDPC Codes [1.1936126505067601]
  Geometric locality is an important theoretical and practical factor for quantum low-density parity-check (qLDPC) codes. We present an error correction protocol built on a bilayer architecture that aims to reduce operational overheads when restricted to 2D local gates.
  arXiv  Detail & Related papers  (2024-04-26T19:48:07Z)
• Toward Constructing a Continuous Logical Operator for Error-Corrected Quantum Sensing [0.0]
  Operations on logical qubits are only performed through universal gate sets consisting of finite-sized gates such as Clifford+T. The Eastin-Knill theorem prevents a continuous signal from being both fault tolerant to local errors and transverse. A protocol to design continuous logical z-rotations is proposed and applied to the Steane Code.
  arXiv  Detail & Related papers  (2023-04-30T18:22:34Z)
• Homological Quantum Rotor Codes: Logical Qubits from Torsion [51.9157257936691]
  homological quantum rotor codes allow one to encode both logical rotors and logical qudits in the same block of code. We show that the $0$-$pi$-qubit as well as Kitaev's current-mirror qubit are indeed small examples of such codes.
  arXiv  Detail & Related papers  (2023-03-24T00:29:15Z)
• Homomorphic Logical Measurements [0.0]
  We use the theory of covering spaces to construct homomorphic measurement protocols for arbitrary $X$- or $Z$-type logical Pauli operators. For any Calderbank-Shor-Steane (CSS) code with the appropriate ancilla code, one can avoid repetitive measurements or complicated ancilla state preparation procedures.
  arXiv  Detail & Related papers  (2022-11-07T15:30:55Z)
• Logical blocks for fault-tolerant topological quantum computation [55.41644538483948]
  We present a framework for universal fault-tolerant logic motivated by the need for platform-independent logical gate definitions. We explore novel schemes for universal logic that improve resource overheads. Motivated by the favorable logical error rates for boundaryless computation, we introduce a novel computational scheme.
  arXiv  Detail & Related papers  (2021-12-22T19:00:03Z)
• Quantum error correction with higher Gottesman-Kitaev-Preskill codes: minimal measurements and linear optics [0.0]
  We propose two schemes to obtain Gottesman-Kitaev-Preskill (GKP) error syndromes by means of linear optical operations, homodyne measurements and GKP ancillae. For a concatenation of GKP codes with a stabilizer code only $2n$ measurements are needed in order to obtain the complete syndrome information.
  arXiv  Detail & Related papers  (2021-10-11T14:35:07Z)
• 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)
• Performance of teleportation-based error correction circuits for bosonic codes with noisy measurements [58.720142291102135]
  We analyze the error-correction capabilities of rotation-symmetric codes using a teleportation-based error-correction circuit. We find that with the currently achievable measurement efficiencies in microwave optics, bosonic rotation codes undergo a substantial decrease in their break-even potential.
  arXiv  Detail & Related papers  (2021-08-02T16:12:13Z)
• Cellular automaton decoders for topological quantum codes with noisy measurements and beyond [68.8204255655161]
  We propose an error correction procedure based on a cellular automaton, the sweep rule, which is applicable to a broad range of codes beyond topological quantum codes. For simplicity, we focus on the three-dimensional (3D) toric code on the rhombic dodecahedral lattice with boundaries and prove that the resulting local decoder has a non-zero error threshold. We find that this error correction procedure is remarkably robust against measurement errors and is also essentially insensitive to the details of the lattice and noise model.
  arXiv  Detail & Related papers  (2020-04-15T18:00:01Z)

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.