Corpus ID: 233231389

Fast quantum state reconstruction via accelerated non-convex programming

  title={Fast quantum state reconstruction via accelerated non-convex programming},
  author={Junhyung Lyle Kim and George Kollias and Amir Kalev and Ken Xuan Wei and Anastasios Kyrillidis},
We propose a new quantum state reconstruction method that combines ideas from compressed sensing, non-convex optimization, and acceleration methods. The algorithm, called Momentum-Inspired Factored Gradient Descent (MiFGD), extends the applicability of quantum tomography for larger systems. Despite being a non-convex method, MiFGD converges provably to the true density matrix at a linear rate, in the absence of experimental and statistical noise, and under common assumptions. With this… Expand


Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization
It is shown that if a certain restricted isometry property holds for the linear transformation defining the constraints, the minimum-rank solution can be recovered by solving a convex optimization problem, namely, the minimization of the nuclear norm over the given affine space. Expand
Neural-network quantum state tomography
It is demonstrated that machine learning allows one to reconstruct traditionally challenging many-body quantities—such as the entanglement entropy—from simple, experimentally accessible measurements, and can benefit existing and future generations of devices. Expand
Experimental quantum compressed sensing for a seven-qubit system
This work presents an experimental implementation of compressed tomography of a seven-qubit system—a topological colour code prepared in a trapped ion architecture and argues that low-rank estimates are appropriate in general since statistical noise enables reliable reconstruction of only the leading eigenvectors. Expand
Superfast maximum likelihood reconstruction for quantum tomography
Conventional methods for computing maximum-likelihood estimators (MLE) often converge slowly in practical situations, leading to a search for simplifying methods that rely on additional assumptionsExpand
Predicting many properties of a quantum system from very few measurements
An efficient method for constructing an approximate classical description of a quantum state using very few measurements of the state is proposed, called a ‘classical shadow’, which can be used to predict many different properties. Expand
Machine-Learning Quantum States in the NISQ Era
The theory of the restricted Boltzmann machine is discussed in detail and its practical use for state reconstruction is demonstrated, starting from a classical thermal distribution of Ising spins, then moving systematically through increasingly complex pure and mixed quantum states. Expand
QuCumber: wavefunction reconstruction with neural networks
An open-source software package called QuCumber is presented that uses machine learning to reconstruct a quantum state consistent with a set of projective measurements and uses a restricted Boltzmann machine to efficiently represent the quantum wavefunction for a large number of qubits. Expand
Low-rank Solutions of Linear Matrix Equations via Procrustes Flow
The algorithm, which is called Procrustes Flow, starts from an initial estimate obtained by a thresholding scheme followed by gradient descent on a non-convex objective and converges to the unknown matrix at a geometric rate. Expand
Recovering Low-Rank Matrices From Few Coefficients in Any Basis
  • D. Gross
  • Computer Science, Mathematics
  • IEEE Transactions on Information Theory
  • 2011
It is shown that an unknown matrix of rank can be efficiently reconstructed from only randomly sampled expansion coefficients with respect to any given matrix basis, which quantifies the “degree of incoherence” between the unknown matrix and the basis. Expand
Universal low-rank matrix recovery from Pauli measurements
It is shown that almost all sets of O(rd log^6 d) Pauli measurements satisfy the rank-r restricted isometry property (RIP), which implies that M can be recovered from a fixed ("universal") set ofPauli measurements, using nuclear-norm minimization (e.g., the matrix Lasso), with nearly-optimal bounds on the error. Expand