Measurement-induced non-commutativity in adaptive fermionic linear optics

• URL: http://arxiv.org/abs/2603.24950v1
• Date: Thu, 26 Mar 2026 02:37:23 GMT
• Title: Measurement-induced non-commutativity in adaptive fermionic linear optics
• Abstract summary: We show that quantum circuits for fermions with internal degrees of freedom, equipped with mid-circuit number monitoring and classical feed-forward are efficient.<n>In our architecture, the measurement record routes the selected blocks into a fixed-order Bell-fusion pairing geometry.<n>Results thus establish mid-circuit measurement-induced non-commutativity as a route to sampling hardness for noninteracting fermions.
• Score: 3.437835147462586
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Fermionic linear optics (FLO) with Gaussian resources is efficiently classically simulable. We show that this is no longer the case for such quantum circuits for fermions with internal degrees of freedom, equipped with mid-circuit number monitoring and classical feedforward. In our architecture, the measurement record routes the selected blocks into a fixed-order Bell-fusion pairing geometry. On the level of classical description, this implies realizing a situation in which the permutation sum no longer collapses to a single determinant or Pfaffian. Each post-selected branch expands as a signed sum of path-ordered products of typically non-commuting dressed blocks, and branch amplitudes are matrix elements of the resulting non-commutative trace polynomials. Numerically, we observe Porter-Thomas statistics as the output distribution and a rapid growth of the minimal order-respecting matrix product operator bond dimension. These results thus establish mid-circuit measurement-induced non-commutativity as a route to sampling hardness for noninteracting fermions under reasonable complexity assumptions, without introducing coherent two-body interactions into the FLO evolution.

Related papers

• Immittance formulas for exact blackbox quantization and divergence-free effective models in circuit QED [0.0]
  We provide formulas to construct exact Hamiltonians for superconducting qudits capacitively, inductively, or galvanically coupled to passive linear environments.<n>We extend the black-box quantization framework to multiport, dissipative, and nonreciprocal settings.
  arXiv  Detail & Related papers  (2026-08-26T17:08:02Z)
• Postselection-Free Reconstruction of Monitored SPT Flux-Charge Responses [1.599072005190786]
  A class of monitored topological invariants compares ordinary and symmetry-twisted quantum trajectories with identical records.<n>We replace the twisted quantum experiment by uniformly randomized symmetry eigenstates with known charges, ordinary-boundary monitoring, and an offline twist decoder.
  arXiv  Detail & Related papers  (2026-08-16T01:52:10Z)
• Quantum Turing Patterns [0.0]
  We construct quantum Turing patterns in Lindblad lattice dynamics and establish a rigorous theory of their nonlinear order and quantum fluctuations.<n>For an explicit family of completely positive lattice generators with finite-range couplings, the first-moment equations undergo a supercritical instability at a nonzero wave number.
  arXiv  Detail & Related papers  (2026-07-28T23:05:00Z)
• Hidden Gauge Freedom in Complex-Pole Hierarchical Equations of Motion [0.0]
  We report a previously unknown gauge freedom in complex-pole HEOM.<n>This gauge controls both the eigenspectrum and non-normality of the hierarchy generator.<n>We extend numerically exact simulations of sub-Ohmic dynamics to previously inaccessible coupling strengths.
  arXiv  Detail & Related papers  (2026-07-06T09:08:52Z)
• Linear combination of unitaries with exponential convergence [0.0]
  We present a general method for decomposing non-unitary operators into a linear combination of unitary operators.<n>When implemented in a quantum circuit, the subnormalisation of the resulting block encoding scales with the double logarithm of the inverse error.
  arXiv  Detail & Related papers  (2026-01-25T22:47:21Z)
• Random-Matrix-Induced Simplicity Bias in Over-parameterized Variational Quantum Circuits [72.0643009153473]
  We show that expressive variational ansatze enter a Haar-like universality class in which both observable expectation values and parameter gradients concentrate exponentially with system size.<n>As a consequence, the hypothesis class induced by such circuits collapses with high probability to a narrow family of near-constant functions.<n>We further show that this collapse is not unavoidable: tensor-structured VQCs, including tensor-network-based and tensor-hypernetwork parameterizations, lie outside the Haar-like universality class.
  arXiv  Detail & Related papers  (2026-01-05T08:04:33Z)
• Avoided-crossings, degeneracies and Berry phases in the spectrum of quantum noise through analytic Bloch-Messiah decomposition [49.1574468325115]
  "analytic Bloch-Messiah decomposition" provides approach for characterizing dynamics of quantum optical systems.<n>We show that avoided crossings arise naturally when a single parameter is varied, leading to hypersensitivity of the singular vectors.<n>We highlight the possibility of programming the spectral response of photonic systems through the deliberate design of avoided crossings.
  arXiv  Detail & Related papers  (2025-04-29T13:14:15Z)
• Postselection-free experimental observation of the measurement-induced phase transition in circuits with universal gates [0.0]
  Many-body systems can exhibit a phase transition between entangling and disentangling dynamical phases by tuning the strength of measurements made on the system as it evolves.<n>This phenomenon is called the measurement-induced phase transition (MIPT)<n>We show that the MIPT can be detected without postselection using only a simple classical decoding process.
  arXiv  Detail & Related papers  (2025-02-03T19:00:01Z)
• Generalized Statistics on Lattices [4.779830375897805]
  We develop a universal microscopic method to determine the generalized statistics of Abelian excitations on lattices of arbitrary dimension.<n>We show that each statistical invariant corresponds to an 't Hooft anomaly of a generalized symmetry.<n>This establishes a precise connection between microscopic lattice anomalies and many-body dynamics.
  arXiv  Detail & Related papers  (2024-12-02T19:00:00Z)
• Theory of free fermions dynamics under partial post-selected monitoring [49.1574468325115]
  We derive a partial post-selected Schrdinger"o equation based on a microscopic description of continuous weak measurement. We show that the passage to the monitored universality occurs abruptly at finite partial post-selection. Our approach establishes a way to study MiPTs for arbitrary subsets of quantum trajectories.
  arXiv  Detail & Related papers  (2023-12-21T16:53:42Z)
• Third quantization of open quantum systems: new dissipative symmetries and connections to phase-space and Keldysh field theory formulations [77.34726150561087]
  We reformulate the technique of third quantization in a way that explicitly connects all three methods. We first show that our formulation reveals a fundamental dissipative symmetry present in all quadratic bosonic or fermionic Lindbladians. For bosons, we then show that the Wigner function and the characteristic function can be thought of as ''wavefunctions'' of the density matrix.
  arXiv  Detail & Related papers  (2023-02-27T18:56:40Z)
• Order-invariant two-photon quantum correlations in PT-symmetric interferometers [62.997667081978825]
  Multiphoton correlations in linear photonic quantum networks are governed by matrix permanents. We show that the overall multiphoton behavior of a network from its individual building blocks typically defies intuition. Our results underline new ways in which quantum correlations may be preserved in counterintuitive ways even in small-scale non-Hermitian networks.
  arXiv  Detail & Related papers  (2023-02-23T09:43:49Z)
• Designing Kerr Interactions for Quantum Information Processing via Counterrotating Terms of Asymmetric Josephson-Junction Loops [68.8204255655161]
  static cavity nonlinearities typically limit the performance of bosonic quantum error-correcting codes. Treating the nonlinearity as a perturbation, we derive effective Hamiltonians using the Schrieffer-Wolff transformation. Results show that a cubic interaction allows to increase the effective rates of both linear and nonlinear operations.
  arXiv  Detail & Related papers  (2021-07-14T15:11:05Z)
• Surveying the Multicomponent Scattering Matrix: Unitarity and Symmetries [0.0]
  We derive a robust theoretical procedure, which is fundamental in quantum-transport problems for unitarity preservation. We predict the interplay for the state-vector transfer matrix, together with the large values of its condition number, as a novel complementary tools for a more accurate definition of the threshold for tunnelling channels.
  arXiv  Detail & Related papers  (2020-10-29T20:37:37Z)
• Recovering quantum correlations in optical lattices from interaction quenches [0.0]
  Quantum simulations with ultra-cold atoms in optical lattices open up an exciting path towards understanding strongly interacting quantum systems. Currently a direct measurement of local coherent currents is out of reach. We show how to achieve that by measuring densities that are altered in response to quenches to non-interacting dynamics.
  arXiv  Detail & Related papers  (2020-05-18T18:03:33Z)

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.