Improving application performance with biased distributions of quantum states
arXiv:2107.07642 · doi:10.1103/PhysRevResearch.3.043145
Abstract
We consider the properties of a specific distribution of mixed quantum states of arbitrary dimension that can be biased towards a specific mean purity. In particular, we analyze mixtures of Haar-random pure states with Dirichlet-distributed coefficients. We analytically derive the concentration parameters required to match the mean purity of the Bures and Hilbert--Schmidt distributions in any dimension. Numerical simulations suggest that this value recovers the Hilbert--Schmidt distribution exactly, offering an alternative and intuitive physical interpretation for ensembles of Hilbert--Schmidt-distributed random quantum states. We then demonstrate how substituting these Dirichlet-weighted Haar mixtures in place of the Bures and Hilbert--Schmidt distributions results in measurable performance advantages in machine-learning-based quantum state tomography systems and Bayesian quantum state reconstruction. Finally, we experimentally characterize the distribution of quantum states generated by both a cloud-accessed IBM quantum computer and an in-house source of polarization-entangled photons. In each case, our method can more closely match the underlying distribution than either Bures or Hilbert--Schmidt distributed states for various experimental conditions.
arXiv comment16 pages, 15 figures
References in corpus (41)
- On the volume of the set of mixed entangled states
- Predicting Many Properties of a Quantum System from Very Few Measurements
- Direct estimations of linear and non-linear functionals of a quantum state
- Universal Quantum Estimator
- Induced measures in the space of mixed quantum states
- Optimal, reliable estimation of quantum states
- Quantum discord for general two--qubit states: Analytical progress
- Active learning machine learns to create new quantum experiments
- Maximum Likelihood, Minimum Effort
- On the volume of the set of mixed entangled states II
- Optimal measurements to access classical correlations of two-qubit states
- Bures volume of the set of mixed quantum states
- Statistical properties of random density matrices
- Average fidelity between random quantum states
- A practical and efficient approach for Bayesian quantum state estimation
- A Separability-Entanglement Classifier via Machine Learning
- A Reconfigurable Quantum Local Area Network Over Deployed Fiber
- Practical Bayesian Tomography
- Machine learning assisted quantum state estimation
- Adaptive bandwidth management for entanglement distribution in quantum networks
- Random Bures mixed states and the distribution of their purity
- Quantum entanglement in random physical states
- Entanglement Classification via Neural Network Quantum States
- Machine Learning meets Quantum Foundations: A Brief Survey
- Fully Arbitrary Control of Frequency-Bin Qubits
- On the distinguishability of random quantum states
- Entanglement Swapping of Two Arbitrarily Degraded Entangled States
- Bipartite entanglement of quantum states in a pair basis
- A Bayesian analysis of classical shadows
- 1-bit Matrix Completion: PAC-Bayesian Analysis of a Variational Approximation
- Monte Carlo sampling from the quantum state space. II
- Quantum learning of coherent states
- On the experimental feasibility of quantum state reconstruction via machine learning
- A Bayesian Approach for Noisy Matrix Completion: Optimal Rate under General Sampling Distribution
- Ehrenfest dynamics is purity non-preserving: a necessary ingredient for decoherence
- Pseudo-Bayesian Quantum Tomography with Rank-adaptation
- Quantum state estimation when qubits are lost: A no-data-left-behind approach
- Classification and reconstruction of optical quantum states with deep neural networks
- Thermalization of strongly interacting bosons after spontaneous emissions in optical lattices
- Dirichlet draws are sparse with high probability
- Recovering full coherence in a qubit by measuring half of its environment