Catalytic Tomography of Ground States

• URL: http://arxiv.org/abs/2512.10247v1
• Date: Thu, 11 Dec 2025 03:07:19 GMT
• Title: Catalytic Tomography of Ground States
• Authors: Chi-Fang Chen, Robbie King,
• Abstract summary: We introduce a protocol for measuring properties of a gapped ground state with essentially no disturbance to the state.<n>For local observables on geometrically local systems, the protocol only requires Hamiltonian evolution on a quasi-local patch of inverse-gap radius.
• Score: 0.6359338352511207
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce a simple protocol for measuring properties of a gapped ground state with essentially no disturbance to the state. The required Hamiltonian evolution time scales inversely with the spectral gap and target precision (up to logarithmic factors), which is optimal. For local observables on geometrically local systems, the protocol only requires Hamiltonian evolution on a quasi-local patch of inverse-gap radius. Our results show that gapped ground states are algorithmically readable from a single copy without a recovery or rewinding procedure, which may drastically reduce tomography overhead in certain quantum simulation tasks.

Related papers

• Optimal Quantum Estimation with Stabilizer-Based Local Measurements [3.9436039611833964]
  We present a sufficient criterion for metrological schemes to saturate the quantum Cram'er-Rao bound (QCRB) using local measurements.<n>A family of graph states is identified as probe states that achieve suboptimal precision scaling.<n>We construct several subspaces of probe states that not only saturate the QCRB with local measurements but also maintain approximately invariant precision scaling.
  arXiv  Detail & Related papers  (2025-08-10T02:51:07Z)
• Quantization Meets Reasoning: Exploring and Mitigating Degradation of Low-Bit LLMs in Mathematical Reasoning [39.56908863102256]
  Low-bit post-training quantization impairs mathematical reasoning up to 69.81% in harder settings.<n>We address two deployment-critical questions with process-level precision.<n>In our settings, as few as 332 curated examples and 3--5 minutes of compute on a single GPU recover 4-bit weight math reasoning toward the full-precision baseline.
  arXiv  Detail & Related papers  (2025-05-16T12:11:40Z)
• Provably Accelerating Ill-Conditioned Low-rank Estimation via Scaled Gradient Descent, Even with Overparameterization [48.65416821017865]
  This chapter introduces a new algorithmic approach, dubbed scaled gradient (ScaledGD) It converges linearly at a constant rate independent of the condition number of the low-rank object. It maintains the low periteration cost of gradient descent for a variety of tasks.
  arXiv  Detail & Related papers  (2023-10-09T21:16:57Z)
• Single-ancilla ground state preparation via Lindbladians [4.328210085579236]
  We design a quantum algorithm for ground state preparation in the early fault tolerant regime. As a Monte Carlo-style quantum algorithm, our method features a Lindbladian where the target state is stationary. Our algorithm can be implemented using just one ancilla qubit and efficiently simulated on a quantum computer.
  arXiv  Detail & Related papers  (2023-08-30T00:11:19Z)
• Quantum state preparation via engineered ancilla resetting [0.0]
  We study a protocol that incorporates periodic quantum resetting to prepare ground states of frustration-free parent Hamiltonians. This protocol uses a steering Hamiltonian that enables local coupling between the system and ancillary degrees of freedom. Our numerical results show that ancilla system entanglement is essential for faster convergence.
  arXiv  Detail & Related papers  (2023-05-15T13:34:07Z)
• Simulating scalar field theories on quantum computers with limited resources [62.997667081978825]
  We present a quantum algorithm for implementing $phi4$ lattice scalar field theory on qubit computers. The algorithm allows efficient $phi4$ state preparation for a large range of input parameters in both the normal and broken symmetry phases.
  arXiv  Detail & Related papers  (2022-10-14T17:28:15Z)
• Quantum state tomography with tensor train cross approximation [84.59270977313619]
  We show that full quantum state tomography can be performed for such a state with a minimal number of measurement settings. Our method requires exponentially fewer state copies than the best known tomography method for unstructured states and local measurements.
  arXiv  Detail & Related papers  (2022-07-13T17:56:28Z)
• From observations to complexity of quantum states via unsupervised learning [0.0]
  We use unsupervised learning with autoencoder neural networks to detect the local complexity of time-evolved states. Our approach is an ideal diagnostics tool for data obtained from (noisy) quantum simulators because it requires only practically accessible local observations.
  arXiv  Detail & Related papers  (2021-02-22T19:44:55Z)
• Highly accurate Gaussian process tomography with geometrical sets of coherent states [1.0499611180329804]
  We propose a strategy for choosing sets of input coherent states that are near-optimal for reconstructing single-mode Gaussian quantum processes. We numerically show that process reconstruction from such input coherent states is nearly as accurate as that from the best possible set of coherent states.
  arXiv  Detail & Related papers  (2020-12-28T10:40:44Z)
• Entanglement purification by counting and locating errors with entangling measurements [62.997667081978825]
  We consider entanglement purification protocols for multiple copies of qubit states. We use high-dimensional auxiliary entangled systems to learn about number and positions of errors in the noisy ensemble.
  arXiv  Detail & Related papers  (2020-11-13T19:02:33Z)
• Activation Relaxation: A Local Dynamical Approximation to Backpropagation in the Brain [62.997667081978825]
  Activation Relaxation (AR) is motivated by constructing the backpropagation gradient as the equilibrium point of a dynamical system. Our algorithm converges rapidly and robustly to the correct backpropagation gradients, requires only a single type of computational unit, and can operate on arbitrary computation graphs.
  arXiv  Detail & Related papers  (2020-09-11T11:56:34Z)

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.