Fock state-enhanced expressivity of quantum machine learning models

Gan, Beng Yee; Leykam, Daniel; Angelakis, Dimitris G.

doi:10.1140/epjqt/s40507-022-00135-0

Cited by 13 publications

(5 citation statements)

References 93 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This paper came to our attention after we had released the preprint, and we recognise that the parallel exponential architecture bears resemblance to the Trenary encoding both for the two-qubit case and in the type of growth in Fourier terms, albeit with different scaling strategies. Furthermore, [40] follows a similar example and creates this architecture for an optical setup. resultant wavenumber.…”

Section: Discussionmentioning

confidence: 99%

An exponentially-growing family of universal quantum circuits

Kordzanganeh

Sekatski

Fedichkin

et al. 2023

Mach. Learn.: Sci. Technol.

View full text Add to dashboard Cite

Quantum machine learning has become an area of growing interest but has certain theoretical and hardware-specific limitations. Notably, the problem of vanishing gradients, or barren plateaus, renders the training impossible for circuits with high qubit counts, imposing a limit on the number of qubits that data scientists can use for solving problems. Independently, angle-embedded supervised quantum neural networks were shown to produce truncated Fourier series with a degree directly dependent on two factors: the depth of the encoding and the number of parallel qubits the encoding applied to. The degree of the Fourier series limits the model expressivity. This work introduces two new architectures whose Fourier degrees grow exponentially: the sequential and parallel exponential quantum machine learning architectures. This is done by efficiently using the available Hilbert space when encoding, increasing the expressivity of the quantum encoding. Therefore, the exponential growth allows staying at the low-qubit limit to create highly expressive circuits avoiding barren plateaus. Practically, parallel exponential architecture was shown to outperform the existing linear architectures by reducing their final mean square error value by up to 44.7% in a one-dimensional test problem. Furthermore, the feasibility of this technique was also shown on a trapped ion quantum processing unit.

show abstract

Section: Discussionmentioning

confidence: 99%

An exponentially-growing family of universal quantum circuits

Kordzanganeh

Sekatski

Fedichkin

et al. 2023

Mach. Learn.: Sci. Technol.

View full text Add to dashboard Cite

show abstract

“…We build a VQE algorithm where, taking inspiration from ref. 49, we use a native photonic ansatz. We perform multiclass classification on the well-known IRIS dataset 50 .…”

Section: Photon-native Quantum Computationmentioning

confidence: 99%

A versatile single-photon-based quantum computing platform

Maring,

Fyrillas,

Pont

et al. 2024

Nat. Photon.

View full text Add to dashboard Cite

Quantum computing aims at exploiting quantum phenomena to efficiently perform computations that are unfeasible even for the most powerful classical supercomputers. Among the promising technological approaches, photonic quantum computing offers the advantages of low decoherence, information processing with modest cryogenic requirements, and native integration with classical and quantum networks. So far, quantum computing demonstrations with light have implemented specific tasks with specialized hardware, notably Gaussian boson sampling, which permits the quantum computational advantage to be realized. Here we report a cloud-accessible versatile quantum computing prototype based on single photons. The device comprises a high-efficiency quantum-dot single-photon source feeding a universal linear optical network on a reconfigurable chip for which hardware errors are compensated by a machine-learned transpilation process. Our full software stack allows remote control of the device to perform computations via logic gates or direct photonic operations. For gate-based computation, we benchmark one-, two- and three-qubit gates with state-of-the art fidelities of 99.6 ± 0.1%, 93.8 ± 0.6% and 86 ± 1.2%, respectively. We also implement a variational quantum eigensolver, which we use to calculate the energy levels of the hydrogen molecule with chemical accuracy. For photon native computation, we implement a classifier algorithm using a three-photon-based quantum neural network and report a six-photon boson sampling demonstration on a universal reconfigurable integrated circuit. Finally, we report on a heralded three-photon entanglement generation, a key milestone toward measurement-based quantum computing.

show abstract

“…4). We further consider a data reuploading strategy where an input data point is repeatedly uploaded into the data embedding 15,29,69,70 . In particular, the i th -component of a data point x is encoded as the rotation angle of qubit i in every HEE layer.…”

Section: Sources Of Exponential Concentrationmentioning

confidence: 99%

Exponential concentration in quantum kernel methods

Thanasilp,

Wang,

Cerezo

et al. 2024

Nat Commun

View full text Add to dashboard Cite

Kernel methods in Quantum Machine Learning (QML) have recently gained significant attention as a potential candidate for achieving a quantum advantage in data analysis. Among other attractive properties, when training a kernel-based model one is guaranteed to find the optimal model’s parameters due to the convexity of the training landscape. However, this is based on the assumption that the quantum kernel can be efficiently obtained from quantum hardware. In this work we study the performance of quantum kernel models from the perspective of the resources needed to accurately estimate kernel values. We show that, under certain conditions, values of quantum kernels over different input data can be exponentially concentrated (in the number of qubits) towards some fixed value. Thus on training with a polynomial number of measurements, one ends up with a trivial model where the predictions on unseen inputs are independent of the input data. We identify four sources that can lead to concentration including expressivity of data embedding, global measurements, entanglement and noise. For each source, an associated concentration bound of quantum kernels is analytically derived. Lastly, we show that when dealing with classical data, training a parametrized data embedding with a kernel alignment method is also susceptible to exponential concentration. Our results are verified through numerical simulations for several QML tasks. Altogether, we provide guidelines indicating that certain features should be avoided to ensure the efficient evaluation of quantum kernels and so the performance of quantum kernel methods.

show abstract

Fock state-enhanced expressivity of quantum machine learning models

Cited by 13 publications

References 93 publications

An exponentially-growing family of universal quantum circuits

An exponentially-growing family of universal quantum circuits

A versatile single-photon-based quantum computing platform

Exponential concentration in quantum kernel methods

Contact Info

Product

Resources

About