Generative machine learning with tensor networks: Benchmarks on near-term quantum computers

Wall, Michael L.; Abernathy, M. R.; Quiroz, Gregory

doi:10.1103/physrevresearch.3.023010

Cited by 24 publications

(33 citation statements)

References 60 publications

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“…Investigations of the fidelity of TTN models compiled to currently available quantum hardware and their resilience to noise, analogous to Ref. [49] for the case of generative matrix product state models, can be performed. Alternative training strategies, e.g.…”

Section: Discussionmentioning

confidence: 99%

“…< l a t e x i t s h a 1 _ b a s e 6 4 = " objects appearing in the TN description are not required to correspond to physically realizable quantum states, some proposals deal with truly quantum data structures, and some have tested TN-based approaches on NISQ hardware [30,49,55]. In the present work, we compare models with a tree tensor network (TTN) structure for classification that are constrained to be true quantum data structures with those that are unconstrained, using metrics of performance and interpretability.…”

Section: Quantum Embeddingmentioning

confidence: 99%

“…Our process is formal because it does not account for the limited connectivity and native gate sets of present-day quantum computers, nor does it optimize the number or type of operations to account for realistic machine noise. We expect that similar techniques to those applied to matrix product state generative models [49], in which the inherent freedom of the TN structure is utilized to aid in compiling to quantum hardware and greedy heuristics are used to compile isometries into native operations on target hardware, can be utilized for TTN models for classification. This stage of quantum compilation enables optimal classical optimization strategies to be utilized to "precondition" a quantum model, defining a model architecture and initial guesses at parameters for the gate set and topology of a given device.…”

Section: Compilation For a Quantum Computermentioning

confidence: 99%

“…Alternatively, variational schemes which measure a distance functional between a family of unitaries with optimizable parameters and the isometry, similar to those developed in Ref. [49] for matrix product state models, can be employed, which can remove the requirement to specify the state of the decoupled qubits. Such methods can be devised to operate in a hardware-aware fashion where the unitary ansatz is built from allowed gates for a given hardware.…”

Section: Compilation For a Quantum Computermentioning

confidence: 99%

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Tree tensor network classifiers for machine learning: from quantum-inspired to quantum-assisted

Wall,

D'Aguanno

2021

Preprint

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We describe a quantum-assisted machine learning (QAML) method in which multivariate data is encoded into quantum states in a Hilbert space whose dimension is exponentially large in the length of the data vector. Learning in this space occurs through applying a low-depth quantum circuit with a tree tensor network (TTN) topology, which acts as an unsupervised feature extractor to identify the most relevant quantum states in a data-driven fashion, analogous to coarse-graining strategies used in renormalization group methodologies from statistical physics. This unsupervised feature extractor then feeds a supervised linear classifier together with a set of truth labels for the data type, and encodes the output in a small-dimensional quantum register. In contrast to previous work on quantum-inspired TTN classifiers, in which the embedding map and class decision weights did not map the data to well-defined quantum states, we present an approach that can be implemented on gate-based quantum computing devices. In particular, we identify an embedding map with accuracy similar to the recently defined exponential machines (Novikov et al., arXiv:1605.03795), but which produces valid quantum state embeddings of classical data vectors, and utilize manifoldbased gradient optimization schemes to produce isometric operations mapping quantum states to a register of qubits defining a class decision. We detail methods for efficiently obtaining one-point and two-point correlation functions of the vectors defining the decision boundary of the quantum model, which can be used for model interpretability, as well as methods for obtaining classification decisions from partial data vectors. Further, we show that the use of isometric tensors can significantly aid in the human interpretability of the correlation functions extracted from the decision weights, and may produce models that are less susceptible to adversarial perturbations. We demonstrate our methodologies in applications utilizing the MNIST handwritten digit dataset and a multivariate timeseries dataset of human activity recognition.

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Section: Discussionmentioning

confidence: 99%

Section: Quantum Embeddingmentioning

confidence: 99%

Section: Compilation For a Quantum Computermentioning

confidence: 99%

Section: Compilation For a Quantum Computermentioning

confidence: 99%

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Tree tensor network classifiers for machine learning: from quantum-inspired to quantum-assisted

Wall,

D'Aguanno

2021

Preprint

Self Cite

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“…A final quantum operation on the ancilla qubits encodes the class label into a subset of those qubits, which can then be read out by measurement in the computational basis. We detail a process in which the tensors in the network architecture are classically optimized using optimization techniques on manifolds inspired by canonical TN algorithms, the tensors of the optimized classical model are compiled into quantum operations using greedy compilation heuristics [34,35], and then the resulting model parameters can be fine-tuned based on results obtained from inferencing the quantum model. In contrast to many other variational quantum circuit approaches, in which a fixed-depth sequence of native gates is optimized over its parameters, our approach only defines the topology of quantum operations between qubits, and allows for an automatic determination of the circuit structure and depth by interfacing with quantum data.…”

Section: Introductionmentioning

confidence: 99%

A tensor network discriminator architecture for classification of quantum data on quantum computers

Wall,

Titum,

Quiroz

et al. 2022

Preprint

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We demonstrate the use of matrix product state (MPS) models for discriminating quantum data on quantum computers using holographic algorithms, focusing on the problem of classifying a translationally invariant quantum state based on L qubits of quantum data extracted from it. We detail a process in which data from single-shot experimental measurements are used to optimize an isometric tensor network, the isometric tensors are compiled into unitary quantum operations using greedy compilation heuristics, parameter optimization on the resulting quantum circuit model removes the post-selection requirements of the isometric tensor model, and the resulting quantum model is inferenced on either product state (single-shot measurement) or entangled quantum data. We demonstrate our training and inference architecture on a synthetic dataset of six-site single-shot measurements from the bulk of a one-dimensional transverse field Ising model (TFIM) deep in its antiferromagnetic and paramagnetic phases. We find that increasing the bond dimension of the tensor network model, amounting to adding more ancilla qubits to the circuit representation, improves both the average number of correct classifications across the dataset and the single-shot probability of correct classification. We experimentally evaluate models on Quantinuum's H1-2 trapped ion quantum computer using entangled input data modeled as translationally invariant, bond dimension 4 MPSs across the known quantum phase transition of the TFIM. Using linear regression on the experimental data near the transition point, we find predictions for the critical transverse field of h = 0.962 and 0.994 for tensor network discriminators of bond dimension χ = 2 and χ = 4, respectively. These predictions compare favorably with the known transition location of h = 1 despite training on data far from the transition point. Our techniques identify families of shortdepth variational quantum circuits in a data-driven and hardware-aware fashion and robust classical techniques to precondition the model parameters, and can be adapted beyond machine learning to myriad applications of tensor networks on quantum computers, such as quantum simulation and error correction.

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Systematic literature review: Quantum machine learning and its applications

Peral-García,

Cruz-Benito,

García-Peñalvo

2024

Computer Science Review

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Generative machine learning with tensor networks: Benchmarks on near-term quantum computers

Cited by 24 publications

References 60 publications

Tree tensor network classifiers for machine learning: from quantum-inspired to quantum-assisted

Tree tensor network classifiers for machine learning: from quantum-inspired to quantum-assisted

A tensor network discriminator architecture for classification of quantum data on quantum computers

Systematic literature review: Quantum machine learning and its applications

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