A Random Matrix Theory of Pauli Tomography

• URL: http://arxiv.org/abs/2506.12010v3
• Date: Mon, 20 Oct 2025 11:10:49 GMT
• Title: A Random Matrix Theory of Pauli Tomography
• Abstract summary: A detailed characterization of the error $Deltahatrho = hatrho-hatrhoprime$ in a QST reconstruction is of clear importance to quantum theory and experiment.<n>We develop a fully random matrix theory (RMT) treatment of state tomography in informationally-complete bases.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum state tomography (QST), the process of reconstructing some unknown quantum state $\hat\rho$ from repeated measurements on copies of said state, is a foundationally important task in the context of quantum computation and simulation. For this reason, a detailed characterization of the error $\Delta\hat\rho = \hat\rho-\hat\rho^\prime$ in a QST reconstruction $\hat\rho^\prime$ is of clear importance to quantum theory and experiment. In this work, we develop a fully random matrix theory (RMT) treatment of state tomography in informationally-complete bases; and in doing so we reveal deep connections between QST errors $\Delta\hat\rho$ and the gaussian unitary ensemble (GUE). By exploiting this connection we prove that wide classes of functions of the spectrum of $\Delta\hat\rho$ can be evaluated by substituting samples of an appropriate GUE for realizations of $\Delta\hat\rho$. This powerful and flexible result enables simple analytic treatments of the mean value and variance of the error as quantified by the trace distance $\|\Delta\hat\rho\|_\mathrm{Tr}$ (which we validate numerically for common tomographic protocols), allows us to derive a bound on the QST sample complexity, and subsequently demonstrate that said bound doesn't change under the most widely-used rephysicalization procedure. These results collectively demonstrate the flexibility, strength, and broad applicability of our approach; and lays the foundation for broader studies of RMT treatments of QST in the future.

Related papers

• The Optimal Rate Function in Covariant Quantum State Tomography [40.87574349486165]
  We characterize quantum tomography protocols by their emphrate function<n>This function governs the exponential rate at which a protocol assigns probability to a particular estimate $$ of the true state $$.<n>For any $$ and $$ we construct a family of protocols whose rate functions converge to the quantum relative entropy $D(|)$.
  arXiv  Detail & Related papers  (2026-06-15T16:47:46Z)
• Parametrized Variational Quantum Tomography [0.0]
  We introduce a parametrized cost function that interpolates between the 1-norm and the infinity norm, thereby unifying VQT and VQT$_infty$ within a single framework.<n>We show that this interplay yields reconstructed states with higher fidelity to the MaxEnt solution than those obtained via VQT$_infty$ while preserving computational tractability.
  arXiv  Detail & Related papers  (2026-04-29T19:35:49Z)
• qSHIFT: An Adaptive Sampling Protocol for Higher-Order Quantum Simulation [0.5635658368100682]
  Quantum simulation is a cornerstone application for quantum computing.<n>Standard methods face a trade-off between circuit depth and accuracy.<n>We introduce qSHIFT, an adaptive sampling protocol that overcomes these limitations.
  arXiv  Detail & Related papers  (2026-04-29T03:47:21Z)
• Phase-space entropy at acquisition reflects downstream learnability [54.4100065023873]
  We propose an acquisition-level scalar $S_mathcal B$ based on instrument-resolved phase space.<n>We show theoretically that (S_mathcal B) correctly identifies the phase-space coherence of periodic sampling.<n>$|S_mathcal B|$ consistently ranks sampling geometries and predicts downstream reconstruction/recognition difficulty emphwithout training.
  arXiv  Detail & Related papers  (2025-12-22T10:03:51Z)
• Performance Guarantees for Quantum Neural Estimation of Entropies [31.955071410400947]
  Quantum neural estimators (QNEs) combine classical neural networks with parametrized quantum circuits.<n>We study formal guarantees for QNEs of measured relative entropies in the form of non-asymptotic error risk bounds.<n>Our theory aims to facilitate principled implementation of QNEs for measured relative entropies.
  arXiv  Detail & Related papers  (2025-11-24T16:36:06Z)
• Measurement protocol for detecting correlated topological insulators in synthetic quantum systems [5.131649203576665]
  Two-dimensional topological insulators, characterized by symmetry-protected anomalous boundary modes, have been generalized to the strongly correlated regime for bosonic and fermionic systems.<n>In this study, we focus on two examples of correlated TI: a bosonic TI protected by $mathbbZ$times U(1)$ symmetry and the fermionic quantum spin Hall insulator protected by time-reversal symmetry.<n>We propose a unified, readily implementable protocol based on measuring the disorder parameter $langleexp(mathrmihatQ_A)rangle for
  arXiv  Detail & Related papers  (2025-11-13T10:18:18Z)
• Exponential Advantage from One More Replica in Estimating Nonlinear Properties of Quantum States [16.185988658474635]
  We prove that estimation of $mathrmtr(rhok O)$ for a broad class of observables $O$ is exponentially hard for any protocol restricted to $(k-1)$-replica joint measurements.<n>Results establish, for the first time, an exponential separation between $(k-1)$- and $k$-replica protocols for any integer $k>2$.
  arXiv  Detail & Related papers  (2025-09-28T17:46:43Z)
• Reconstructing Real-Valued Quantum States [3.089686736734106]
  We introduce a novel readout method for real-valued quantum states that reduces measurement settings required for state vector reconstruction to $O(N_mathrmq)$.<n>We experimentally validate our method up to 10qubits on the latest available IBM quantum processor and demonstrate that it accurately extracts key properties such as entanglement and magic.
  arXiv  Detail & Related papers  (2025-05-09T22:12:54Z)
• Conditional Distribution Quantization in Machine Learning [83.54039134248231]
  Conditional expectation mathbbE(Y mid X) often fails to capture the complexity of multimodal conditional distributions mathcalL(Y mid X)<n>We propose using n-point conditional quantizations--functional mappings of X that are learnable via gradient descent--to approximate mathcalL(Y mid X)
  arXiv  Detail & Related papers  (2025-02-11T00:28:24Z)
• Enhancing Quantum State Reconstruction with Structured Classical Shadows [22.432806329828782]
  We introduce a projected classical shadow (PCS) method with guaranteed performance for QST based on Haar-random projective measurements.<n>PCS extends the standard CS method by incorporating a projection step onto the target subspace.<n>For matrix product operator states, we demonstrate that the PCS method can recover the ground-truth state with $O(n2)$ total state copies.
  arXiv  Detail & Related papers  (2025-01-06T17:09:38Z)
• Sample-Efficient Estimation of Nonlinear Quantum State Functions [5.641998714611475]
  We introduce the quantum state function (QSF) framework by extending the SWAP test via linear combination of unitaries and parameterized quantum circuits.<n>Our framework enables the implementation of arbitrarily normalized degree-$n$ functions of quantum states with precision.<n>We apply QSF for developing quantum algorithms for fundamental tasks, including entropy, fidelity, and eigenvalue estimations.
  arXiv  Detail & Related papers  (2024-12-02T16:40:17Z)
• Variational Quantum Imaginary Time Evolution for Matrix Product State Ansatz with Tests on Transcorrelated Hamiltonians [11.985673663540688]
  The matrix product state (MPS) ansatz offers a promising approach for finding the ground state of molecular Hamiltonians. We enhance the optimization performance of the QCMPS ansatz by employing the variational quantum imaginary time evolution (VarQITE) approach.
  arXiv  Detail & Related papers  (2024-07-15T08:28:52Z)
• The Power of Unentangled Quantum Proofs with Non-negative Amplitudes [55.90795112399611]
  We study the power of unentangled quantum proofs with non-negative amplitudes, a class which we denote $textQMA+(2)$. In particular, we design global protocols for small set expansion, unique games, and PCP verification. We show that QMA(2) is equal to $textQMA+(2)$ provided the gap of the latter is a sufficiently large constant.
  arXiv  Detail & Related papers  (2024-02-29T01:35:46Z)
• On the Convergence and Sample Complexity Analysis of Deep Q-Networks with $\epsilon$-Greedy Exploration [86.71396285956044]
  This paper provides a theoretical understanding of Deep Q-Network (DQN) with the $varepsilon$-greedy exploration in deep reinforcement learning.
  arXiv  Detail & Related papers  (2023-10-24T20:37:02Z)
• Quantum tomography of helicity states for general scattering processes [55.2480439325792]
  Quantum tomography has become an indispensable tool in order to compute the density matrix $rho$ of quantum systems in Physics. We present the theoretical framework for reconstructing the helicity quantum initial state of a general scattering process.
  arXiv  Detail & Related papers  (2023-10-16T21:23:42Z)
• Efficient Quantum Mixed-State Tomography with Unsupervised Tensor Network Machine Learning [13.02007068572165]
  We propose an efficient mixed-state quantum state scheme based on the locally purified state ansatz. We demonstrate the efficiency and robustness of our scheme on various randomly initiated states with different purities. Our work reveals the prospects of applying network state ansatz and the machine learning approaches for efficient QST of many-body states.
  arXiv  Detail & Related papers  (2023-08-14T02:35:23Z)
• Importance sampling for stochastic quantum simulations [68.8204255655161]
  We introduce the qDrift protocol, which builds random product formulas by sampling from the Hamiltonian according to the coefficients. We show that the simulation cost can be reduced while achieving the same accuracy, by considering the individual simulation cost during the sampling stage. Results are confirmed by numerical simulations performed on a lattice nuclear effective field theory.
  arXiv  Detail & Related papers  (2022-12-12T15:06:32Z)
• Posterior Coreset Construction with Kernelized Stein Discrepancy for Model-Based Reinforcement Learning [78.30395044401321]
  We develop a novel model-based approach to reinforcement learning (MBRL) It relaxes the assumptions on the target transition model to belong to a generic family of mixture models. It can achieve up-to 50 percent reduction in wall clock time in some continuous control environments.
  arXiv  Detail & Related papers  (2022-06-02T17:27:49Z)
• Tightening the Dependence on Horizon in the Sample Complexity of Q-Learning [59.71676469100807]
  This work sharpens the sample complexity of synchronous Q-learning to an order of $frac|mathcalS|| (1-gamma)4varepsilon2$ for any $0varepsilon 1$. Our finding unveils the effectiveness of vanilla Q-learning, which matches that of speedy Q-learning without requiring extra computation and storage.
  arXiv  Detail & Related papers  (2021-02-12T14:22:05Z)
• Sampling Overhead Analysis of Quantum Error Mitigation: Uncoded vs. Coded Systems [69.33243249411113]
  We show that Pauli errors incur the lowest sampling overhead among a large class of realistic quantum channels. We conceive a scheme amalgamating QEM with quantum channel coding, and analyse its sampling overhead reduction compared to pure QEM.
  arXiv  Detail & Related papers  (2020-12-15T15:51:27Z)
• Even more efficient quantum computations of chemistry through tensor hypercontraction [0.6234350105794442]
  We describe quantum circuits with only $widetildecal O(N)$ Toffoli complexity that block encode the spectra of quantum chemistry Hamiltonians in a basis of $N$ arbitrary orbitals. This is the lowest complexity that has been shown for quantum computations of chemistry within an arbitrary basis.
  arXiv  Detail & Related papers  (2020-11-06T18:03:29Z)

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.