Quantum Error Correction Exploiting Quantum Spatial Distribution and Gauge Symmetry

• URL: http://arxiv.org/abs/2604.25747v1
• Date: Tue, 28 Apr 2026 15:12:14 GMT
• Title: Quantum Error Correction Exploiting Quantum Spatial Distribution and Gauge Symmetry
• Abstract summary: We explore what the integrated use of quantum spatial distribution (QSD) provides for quantum error correction.<n>The exploration employs $3+2$ particles on nested squares proposed in the companion letter (arXiv:2504.07941)<n>We show implementations of the error detection (stabilizer measurement), logical Hadamard and Toffoli gates, and a quantum adder with the required interactions only between nearest-neighbor and next-nearest-neighbor particles.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We explore what the integrated use of quantum spatial distribution (QSD), or more specifically, superposition of both spin and position states of particles, and gauge symmetry (GS) within stabilizer formalism provides for quantum error correction. The exploration employs $3+2$ particles on nested squares proposed in the companion letter (arXiv:2504.07941), where three of them encode Shor's nine-qubit code and the remaining two detect errors in this code through their spin state measurements (unlike the letter's quantum walk model, each particle evolves by gate operations acting exclusively on either its spin or position state). The first result is that the GS offers resilience against three types of noise acting on a particle: arbitrary decoherence of its spin or position state, and dephasing of both states, which partly or completely destroys its QSD. To show that, we formulate a noise model unifying the above noise and prove the correctability of this unified model under our error-correcting scheme. The second result is that QSD provides architectural flexibility allowing us to stack the error-correcting systems both vertically and horizontally. Indeed, we show implementations of the error detection (stabilizer measurement), logical Hadamard and Toffoli gates, and a quantum adder with the required interactions only between nearest-neighbor and next-nearest-neighbor particles.

Related papers

• Probabilistic Error Cancellation for Single-Mode Gottesman-Kitaev-Preskill Codes [45.91504150103373]
  We study a quantum error mitigation method known as probabilistic error cancellation in the context of the Gottesman-Kitaev-Preskill code.<n>We employ the stabilizer subsystem decomposition for GKP codes to obtain an effective logical channel for noisy operations.
  arXiv  Detail & Related papers  (2026-09-15T12:29:45Z)
• Quantum Steering Geometry at High Energy Particle Colliders [0.0]
  We formulate collider observables based on quantum steering ellipsoids (QSEs)<n>A collider spin density matrix defines a two-qubit state, while its QSE gives the geometry of conditional states accessible through local measurements.
  arXiv  Detail & Related papers  (2026-08-30T20:53:58Z)
• Error Correction of Beamsplitter-Generated Entangled GKP States [56.80803785296797]
  A promising bosonic code is the Gottesman-Kitaev-Preskill (GKP) code.<n>We generate entangled states of GKP qubits by interfering two qunaught states, which have a grid structure but carry no logical information, on a beamsplitter.<n>We generate all four Bell states with an average fidelity of 69%, and demonstrate an extension of the entangled state lifetime through the use of quantum error correction.
  arXiv  Detail & Related papers  (2026-05-08T17:01:19Z)
• Measurement-induced phase transitions in quantum inference problems and quantum hidden Markov models [0.0]
  We show a connection between'sharpening' and 'learnability' order parameters and quantum hidden Markov models.<n>We study the Haar-random U(1)-symmetric monitored quantum circuit and tree, mapping each to inference models that we call the planted SSEP and planted XOR.<n>We present an exact solution of the entire phase boundary, which displays re-entrance as does the 2D RBIM.
  arXiv  Detail & Related papers  (2025-04-11T18:00:06Z)
• Quantum error correction via multi-particle discrete-time quantum walk [0.0]
  We propose a scheme of quantum error correction that employs a multi-particle quantum walk defined on nested squares.<n>In this model, each particle moves within its own distinct square through iterations of three discrete-time steps.<n>By exploiting gauge symmetry, our scheme achieves redundant encoding, error correction, and arbitrary operations on the encoded information.
  arXiv  Detail & Related papers  (2025-04-10T17:51:39Z)
• Designing quantum error correction codes for practical spin qudit [0.0]
  We present a quantitative analysis of the performance of a spin-qudit-based error-correctable quantum memory.<n>We claim that electric field fluctuations should also be considered as a noise source.<n>We illustrate an encoding/decoding scheme for a multi-spin-qudit-based error correction code that can simultaneously compensate for both electric and magnetic field perturbations.
  arXiv  Detail & Related papers  (2025-03-15T13:57:06Z)
• Extending Quantum Perceptrons: Rydberg Devices, Multi-Class Classification, and Error Tolerance [67.77677387243135]
  Quantum Neuromorphic Computing (QNC) merges quantum computation with neural computation to create scalable, noise-resilient algorithms for quantum machine learning (QML) At the core of QNC is the quantum perceptron (QP), which leverages the analog dynamics of interacting qubits to enable universal quantum computation.
  arXiv  Detail & Related papers  (2024-11-13T23:56:20Z)
• Realizing fracton order from long-range quantum entanglement in programmable Rydberg atom arrays [45.19832622389592]
  Storing quantum information requires battling quantum decoherence, which results in a loss of information over time. To achieve error-resistant quantum memory, one would like to store the information in a quantum superposition of degenerate states engineered in such a way that local sources of noise cannot change one state into another. We show that this platform also allows to detect and correct certain types of errors en route to the goal of true error-resistant quantum memory.
  arXiv  Detail & Related papers  (2024-07-08T12:46:08Z)
• Parity-controlled gate in a two-dimensional neutral-atom array [0.4473518548010192]
  We propose a parity-controlled gate within a two-dimensional Rydberg atom array.<n>We explore its implementation in three-qubit repetition codes and rotated surface codes featuring $XZZX$ stabilizers.<n>Our study highlights the inherent advantages of the physical mechanisms underlying parity measurement.
  arXiv  Detail & Related papers  (2024-05-29T23:13:57Z)
• Normal quantum channels and Markovian correlated two-qubit quantum errors [77.34726150561087]
  We study general normally'' distributed random unitary transformations. On the one hand, a normal distribution induces a unital quantum channel. On the other hand, the diffusive random walk defines a unital quantum process.
  arXiv  Detail & Related papers  (2023-07-25T15:33:28Z)
• Vulnerability of fault-tolerant topological quantum error correction to quantum deviations in code space [0.0]
  We study the performance of the topological toric code in 2D under the dual influence of noise and quantum deviations.<n>We find two distinct error thresholds that demarcate varying efficacies in error correction.<n>For codes of finite or modest distance $d distances, it is revealed that maintaining the preparation error rate beneath a crossover scale, proportional to $1/log d, allows for the suppression of logical errors.
  arXiv  Detail & Related papers  (2023-01-30T13:12:41Z)
• Witnessing entanglement in trapped-ion quantum error correction under realistic noise [41.94295877935867]
  Quantum Error Correction (QEC) exploits redundancy by encoding logical information into multiple physical qubits. We present a detailed microscopic error model to estimate the average gate infidelity of two-qubit light-shift gates used in trapped-ion platforms. We then apply this realistic error model to quantify the multipartite entanglement generated by circuits that act as QEC building blocks.
  arXiv  Detail & Related papers  (2022-12-14T20:00:36Z)
• Single-shot quantum error correction with the three-dimensional subsystem toric code [77.34726150561087]
  We introduce a new topological quantum code, the three-dimensional subsystem toric code (3D STC) The 3D STC can be realized by measuring geometrically-local parity checks of weight at most three on the cubic lattice with open boundary conditions.
  arXiv  Detail & Related papers  (2021-06-04T17:35:00Z)
• Universal quantum computation and quantum error correction with ultracold atomic mixtures [47.187609203210705]
  We propose a mixture of two ultracold atomic species as a platform for universal quantum computation with long-range entangling gates. One atomic species realizes localized collective spins of tunable length, which form the fundamental unit of information. We discuss a finite-dimensional version of the Gottesman-Kitaev-Preskill code to protect quantum information encoded in the collective spins.
  arXiv  Detail & Related papers  (2020-10-29T20:17:14Z)

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.