Abstract
We use a meta-learning neural-network approach to analyse data from a measured quantum state. Once our neural network has been trained it can be used to efficiently sample measurements of the state in measurement bases not contained in the training data. These samples can be used calculate expectation values and other useful quantities. We refer to this process as "state sample tomography". We encode the state's measurement outcome distributions using an efficiently parameterized generative neural network. This allows each stage in the tomography process to be performed efficiently even for large systems. Our scheme is demonstrated on recent IBM Quantum devices, producing a model for a 6-qubit state's measurement outcomes with a predictive accuracy (classical fidelity) > 95% for all test cases using only 100 random measurement settings as opposed to the 729 settings required for standard full tomography using local measurements. This reduction in the required number of measurements scales favourably, with training data in 200 measurement settings yielding a predictive accuracy > 92% for a 10 qubit state where 59,049 settings are typically required for full local measurement-based quantum state tomography. A reduction in number of measurements by a factor, in this case, of almost 600 could allow for estimations of expectation values and state fidelities in practicable times on current quantum devices.
Highlights
There are large practical hurdles to overcome when attempting to perform quantum state tomography (QST) on noisy quantum devices
A basis-dependent RBM (BDRBM) is a composition of two neural networks, a restricted Boltzmann machines (RBM) and a feedforward neural network (FFNN)
In this work we have discussed a method by which machine-learning techniques may be used to perform quantum state sample tomography, a quantum state characterization scheme that we posit is a far more tractable alternative to full QST
Summary
There are large practical hurdles to overcome when attempting to perform quantum state tomography (QST) on noisy quantum devices. Recent examples of these include machine-learning (ML) inspired approaches that attempt to take advantage of the ability of neural networks to efficiently represent and learn complicated probability distributions These approaches have been shown to perform quantum state tomography very effectively for systems of small to intermediate size, requiring fewer measurements and being more computationally efficient than standard MLE-based techniques [18]. The approach exploits the efficiency in training and sampling from RBMs (as in Torlai’s approach) while learning measurement distributions, not the state directly, to avoid needing optimization over complex parameters and reducing the required number of measurement settings This allows samples to be taken efficiently in arbitrary local bases (not just the computational), giving access to all the quantities that can be calculated from these while avoiding sums over exponentially many terms. As we only attempt to predict measurement outcomes, our method works in exactly the same manner for both pure and mixed states, the purity being reflected in the distributions used for training (and can be recovered with the sampling method in Ref. [29])
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
