Efficient Approximate Quantum State Tomography with Basis Dependent Neural-Networks.

Alistair W. R. Smith, Johnnie Gray, M. S. Kim

Published Sep 16, 2020• 2 citations

Abstract

We use a meta-learning neural-network approach to predict measurement outcomes of a quantum state in arbitrary local bases and thus carry out an approximate quantum state tomography. Each stage of this procedure can be performed efficiently, allowing it to be used effectively on large systems. We demonstrate this approach on the most recent noisy intermediate-scale IBM Quantum devices, achieving an accurate generative model for a 6-qubit state's measurement outcomes with only 100 random measurement settings as opposed to the 729 settings required for full tomography. This reduction in the required number of measurements scales favourably, with around 200 measurement settings yielding good results for a 10 qubit state that would require 59,049 settings for full quantum state tomography. This reduction in the number of measurement settings coupled with the efficiency of the procedure could allow for estimations of expectation values and state fidelities in practicable times on current quantum devices. For suitable states, this could then help in increasing the speed of other optimization schemes when attempting to produce states on noisy quantum devices at a scale where traditional maximum likelihood based approaches are impractical.

Related papers

Efficient Quantum State Sample Tomography with Basis-Dependent Neural Networks

Alistair W. R. Smith, Johnnie Gray, M. S. Kim

We use a metalearning neural-network approach to analyze 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 to 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 six-qubit state's measurement outcomes with a predictive accuracy (classical fidelity) greater than 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 favorably, with training data in 200 measurement settings, yielding a predictive accuracy greater than 92% for a ten-qubit state where 59 049 settings are typically required for full local measurement-based quantum state tomography.A reduction in the 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.

arXiv:2009.07601PRX QuantumJun 28, 202132 citations

Efficient quantum state tomography with convolutional neural networks

Tobias Schmale, Moritz Reh, Martin Gärttner

Abstract Modern day quantum simulators can prepare a wide variety of quantum states but the accurate estimation of observables from tomographic measurement data often poses a challenge. We tackle this problem by developing a quantum state tomography scheme which relies on approximating the probability distribution over the outcomes of an informationally complete measurement in a variational manifold represented by a convolutional neural network. We show an excellent representability of prototypical ground- and steady states with this ansatz using a number of variational parameters that scales polynomially in system size. This compressed representation allows us to reconstruct states with high classical fidelities outperforming standard methods such as maximum likelihood estimation. Furthermore, it achieves a reduction of the estimation error of observables by up to an order of magnitude compared to their direct estimation from experimental data.

arXiv:2109.13776npj Quantum InformationSep 23, 202276 citations

Quantum state tomography with tensor train cross approximation

Alexander Lidiak, Casey Jameson, Zhen Qin +4 more

It has been recently shown that a state generated by a one-dimensional noisy quantum computer is well approximated by a matrix product operator with a finite bond dimension independent of the number of qubits. We show that full quantum state tomography can be performed for such a state with a minimal number of measurement settings using a method known as tensor train cross approximation. The method works for reconstructing full rank density matrices and only requires measuring local operators, which are routinely performed in state-of-art experimental quantum platforms. Our method requires exponentially fewer state copies than the best known tomography method for unstructured states and local measurements. The fidelity of our reconstructed state can be further improved via supervised machine learning, without demanding more experimental data. Scalable tomography is achieved if the full state can be reconstructed from local reductions.

arXiv:2207.06397Jul 13, 20225 citations

Quantum machine learning for state tomography using classical data

S. Jabeen, Dmytro Kurdydyk, Aadi Palnitkar +3 more

Reconstructing quantum states from measurement data represents a formidable challenge in quantum information science, especially as system sizes grow beyond the reach of traditional tomography methods. While recent studies have explored quantum machine learning (QML) for quantum state tomography (QST), nearly all rely on idealized assumptions, such as direct access to the unknown quantum state as quantum data input, which are incompatible with current hardware constraints. In this work, we present a QML-based tomography protocol that operates entirely on classical measurement data and is fully executable on noisy intermediate-scale quantum (NISQ) devices. Our approach employs a variational quantum circuit trained to reconstruct quantum states based solely on measurement outcomes. We test the method in simulation, achieving high-fidelity reconstructions of diverse quantum states, including GHZ states, spin chain ground states, and states generated by random circuits. The protocol is then validated on quantum hardware from IBM and IonQ. Additionally, we demonstrate accurate tomography is possible using incomplete measurement bases, a crucial step towards scaling up our protocol. Our results in various scenarios illustrate successful state reconstruction with fidelity reaching 90% or higher. To our knowledge, this is the first QML-based tomography scheme that has been implemented on real quantum processors using exclusively classical measurements. This work establishes the feasibility of QML-based tomography on current quantum platforms and offers a scalable pathway for practical quantum state reconstruction.

arXiv:2507.01246Quantum Machine IntelligenceApr 2, 20260 citations

Neural network state estimation for full quantum state tomography

Qian Xu, Shuqi Xu

An efficient state estimation model, neural network estimation (NNE), empowered by machine learning techniques, is presented for full quantum state tomography (FQST). A parameterized function based on neural network is applied to map the measurement outcomes to the estimated quantum states. Parameters are updated with supervised learning procedures. From the computational complexity perspective our algorithm is the most efficient one among existing state estimation algorithms for full quantum state tomography. We perform numerical tests to prove both the accuracy and scalability of our model.

arXiv:1811.06654Nov 16, 201822 citations

Scalable quantum state tomography with artificial neural networks

Tobias Schmale, Moritz Reh, Martin Gärttner

Modern day simulators can prepare a wide variety of states but extracting observables from the resulting quantum data often poses a challenge. We tackle this problem by developing a state tomography scheme which relies on approximating the probability distribution over the outcomes of an informationally complete measurement in a variational manifold represented by a convolutional neural network. We show an excellent representability of prototypical ground- and steady states with this ansatz using a number of variational parameters that scales polynomially in system size. This compressed representation allows us to reconstruct states with high classical fidelities outperforming standard methods such as maximum likelihood estimation. Furthermore, it achieves a reduction of the root mean square errors of observables by up to an order of magnitude compared to their direct estimation from experimental data.

Sep 28, 20210 citations