Quantum state tomography via compressed sensing
arXiv:0909.3304 · doi:10.1103/PhysRevLett.105.150401
Abstract
We establish methods for quantum state tomography based on compressed sensing. These methods are specialized for quantum states that are fairly pure, and they offer a significant performance improvement on large quantum systems. In particular, they are able to reconstruct an unknown density matrix of dimension d and rank r using O(rd log^2 d) measurement settings, compared to standard methods that require d^2 settings. Our methods have several features that make them amenable to experimental implementation: they require only simple Pauli measurements, use fast convex optimization, are stable against noise, and can be applied to states that are only approximately low-rank. The acquired data can be used to certify that the state is indeed close to pure, so no a priori assumptions are needed. We present both theoretical bounds and numerical simulations.
4 pages, 1 figure; v3, v4: presentation improved
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- Estimation and uncertainty quantification for the output from quantum simulators
- Measuring Hamming Distance between Boolean Functions via Entanglement Measure
- Quantum Tomography by Regularized Linear Regression
- Characterizing an Entangled-Photon Source with Classical Detectors and Measurements
- Study of the spin kitten states in a strongly coupled spin-oscillator system
- Fast and simple quantum state estimation
- Minimum Number of Copies in the Measurement of Multi-Photon Entanglement
- Lower Memory Oblivious (Tensor) Subspace Embeddings with Fewer Random Bits: Modewise Methods for Least Squares
- Quantum Assemblage Tomography
- Diagnosing crosstalk in large-scale QPUs using zero-entropy classical shadows
- Convex Optimization Learning of Faithful Euclidean Distance Representations in Nonlinear Dimensionality Reduction
- Beating the Optimal Verification of Entangled States via Collective Strategies
- Sample Optimal and Memory Efficient Quantum State Tomography
- Classification of quantum states of light using random measurements through a multimode fiber
- Rényi entropy of the permutationally invariant part of the ground state across a quantum phase transition
- Matrix Recovery from Rank-One Projection Measurements via Nonconvex Minimization
- Measuring entanglement without local addressing in quantum many-body simulators via spiral quantum state tomography
- Entanglement entropy scaling laws from fluctuations of non-conserved quantities
- Certifying entanglement dimensionality by -reduction moments
- Low-rank matrix recovery via iteratively reweighted least squares minimization
- Ability of entanglement and purity to help to detect systematic experimental errors
- Piecewise Toeplitz Matrices-based Sensing for Rank Minimization
- Selective and efficient quantum state tomography for multi-qubit systems
- Error bound of critical points and KL property of exponent for squared F-norm regularized factorization
- A new inexact iterative hard thresholding algorithm for compressed sensing
- Optimal randomized measurements for a family of non-linear quantum properties
- Rigorous Maximum Likelihood Estimation for Quantum States
- A Robust Compressive Quantum State Tomography Algorithm Using ADMM
- Optimizing Measurements Sequences for Quantum State Verification
- Reducing Complexity of Shadow Process Tomography with Generalized Measurements
- Tensor Train Quantum State Tomography using Compressed Sensing
- Quantum Machine Learning for State Tomography Using Classical Data
- Principles of quantum functional testing
- High-dimensional quantum communication with scalable photonic entanglement in time and frequency
- Physics-Constrained Compressed Sensing for Quantum Sensing in the Data-Starved Regime
- Emergence of Classical Objectivity of Quantum Darwinism in a Photonic Quantum Simulator
- Ptychographic estimation of pure multiqubit states in a quantum device
- A sparse-sampling approach for the fast computation of matrices: application to molecular vibrations
- Reliable optimization of arbitrary functions over quantum measurements
- Estimating the eigenstates of an unknown density operator without damaging it
- Efficient verification and fidelity estimation of discrete bipartite squeezed states
- Detailed Account of Complexity for Implementation of Some Gate-Based Quantum Algorithms
- Maximum-Likelihood Quantum State Tomography by Cover's Method with Non-Asymptotic Analysis
- Multi-weight Matrix Completion with Arbitrary Subspace Prior Information