Full reconstruction of a 14-qubit state within four hours

Abstract

Full quantum state tomography (FQST) plays a unique role in the estimation of the state of a quantum system without \emph{a priori} knowledge or assumptions. Unfortunately, since FQST requires informationally (over)complete measurements, both the number of measurement bases and the computational complexity of data processing suffer an exponential growth with the size of the quantum system. A 14-qubit entangled state has already been experimentally prepared in an ion trap, and the data processing capability for FQST of a 14-qubit state seems to be far away from practical applications. In this paper, the computational capability of FQST is pushed forward to reconstruct a 14-qubit state with a run time of only 3.35 hours using the linear regression estimation (LRE) algorithm, even when informationally overcomplete Pauli measurements are employed. The computational complexity of the LRE algorithm is first reduced from $O(10^{19})$ to $O(10^{15})$ for a 14-qubit state, by dropping all the zero elements, and its computational efficiency is further sped up by fully exploiting the parallelism of the LRE algorithm with parallel Graphic Processing Unit (GPU) programming. Our result can play an important role in quantum information technologies with large quantum systems.

7 pages, 2 figures, comments welcome

References in corpus (9)

• Scalable multi-particle entanglement of trapped ions
• 14-qubit entanglement: creation and coherence
• Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
• Efficient quantum state tomography
• Direct Fidelity Estimation from Few Pauli Measurements
• Entanglement-enhanced measurement of a completely unknown phase
• Permutationally invariant quantum tomography
• Benchmarking quantum control methods on a 12-qubit system
• Optimal two-qubit tomography based on local and global measurements: Maximal robustness against errors as described by condition numbers

Cited by in corpus (42)

• Speedup for quantum optimal control from automatic differentiation based on graphics processing units
• Recursively Adaptive Quantum State Tomography: Theory and Two-qubit Experiment
• Superfast maximum likelihood reconstruction for quantum tomography
• A Quantum Hamiltonian Identification Algorithm: Computational Complexity and Error Analysis
• Machine learning assisted quantum state estimation
• Local-measurement-based quantum state tomography via neural networks
• Simple preparation of Bell and GHZ states using ultrastrong-coupling circuit QED
• Experimental Optimal Verification of Entangled States using Local Measurements
• Eigenstate extraction with neural-network tomography
• Experimental demonstration of cheap and accurate phase estimation
• Quantum gate identification: error analysis, numerical results and optical experiment
• Quantum Hamiltonian Identifiability via a Similarity Transformation Approach and Beyond
• Classical shadow tomography for continuous variables quantum systems
• On the experimental feasibility of quantum state reconstruction via machine learning
• Optimal experiment design for quantum state tomography
• Experimental realization of self-guided quantum process tomography
• Adaptive quantum tomography of high-dimensional bipartite systems
• Quantum State Tomography with Conditional Generative Adversarial Networks
• Classification and reconstruction of optical quantum states with deep neural networks
• Experimental measurement of nonlinear entanglement witness by hyper-entangling two-qubit states
• On the capability of a class of quantum sensors
• Certification of Genuine Multipartite Entanglement with General and Robust Device-independent Witnesses
• Provable quantum state tomography via non-convex methods
• Demonstration of machine-learning-enhanced Bayesian quantum state estimation
• Gradient-descent methods for fast quantum state tomography
• Efficient factored gradient descent algorithm for quantum state tomography
• Quantum Steering on IBMQ
• Quantum tomography of Rydberg atom graphs by configurable ancillas
• Tomography from collective measurements
• A tomographic approach to the sum uncertainty relation and quantum entanglement in continuous variable systems
• On the connection between least squares, regularization, and classical shadows
• Quantum state tomography with disentanglement algorithm
• Mitigation of correlated readout errors without randomized measurements
• Signatures of nonclassical effects in tomograms
• Unorthodox parallelization for Bayesian quantum state estimation
• Hybrid filtering for a class of nonlinear quantum systems subject to classical stochastic disturbances
• Efficient quantum state tomography with auxiliary Hilbert space
• Several recent developments in estimation and robust control of quantum systems
• Tomographic entanglement indicators from NMR experiments
• Classical Communication Enhanced Quantum State Verification
• Sample Optimal and Memory Efficient Quantum State Tomography
• Rigorous Maximum Likelihood Estimation for Quantum States