Theory for Equivariant Quantum Neural Networks

Nguyen, Quynh T.; Schatzki, Louis; Paolo, Braccia,; Ragone, Michael; Coles, Patrick J.; Sauvage, Frédéric; Larocca, Martín; Cerezo, M.

doi:10.48550/arxiv.2210.08566

Cited by 12 publications

(15 citation statements)

References 109 publications

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“…[61,62]), and quantum (see e.g. [63][64][65][66]). Equivariant ANNs exploit symmetry in data so that the output samples also preserve this symmetry, such as is the case of E(3) equivariant ANNs (which transform data under translations and rotations, with applications including image processing).…”

Section: Discussionmentioning

confidence: 99%

Symmetric tensor networks for generative modeling and constrained combinatorial optimization

Lopez-Piqueres

Chen

Perdomo-Ortiz³

2023

Mach. Learn.: Sci. Technol.

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Constrained combinatorial optimization problems abound in industry, from portfolio optimization to logistics. One of the major roadblocks in solving these problems is the presence of non-trivial hard constraints which limit the valid search space. In some heuristic solvers, these are typically addressed by introducing certain Lagrange multipliers in the cost function, by relaxing them in some way, or worse yet, by generating many samples and only keeping valid ones, which leads to very expensive and inefficient searches. In this work, we encode arbitrary integer-valued equality constraints of the form A⃗x = ⃗b, directly into U (1) symmetric tensor networks and leverage their applicability as quantum-inspired generative models to assist in the search of solutions to combinatorial optimization problems within the generator-enhanced optimization (GEO) framework of Ref. [1]. This allows us to exploit the generalization capabilities of TN generative models while constraining them so that they only output valid samples. Our constrained TN generative model efficiently captures the constraints by reducing number of parameters and computational costs. We find that at tasks with constraints given by arbitrary equalities, symmetric Matrix Product States outperform their standard unconstrained counterparts at finding novel and better solutions to combinatorial optimization problems.

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Section: Discussionmentioning

confidence: 99%

Symmetric tensor networks for generative modeling and constrained combinatorial optimization

Lopez-Piqueres

Chen

Perdomo-Ortiz³

2023

Mach. Learn.: Sci. Technol.

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“…In the previous section, we have introduced TWI-QRNNs by imposing time warping-invariance in terms of the density matrices produced by the equivalent dissipative QNN. Since the probabilities (18) have the same form as the expectations (5) defining the outputs of QRNNs, the same reasoning applies to SQRNNs ρ AB t . Based on this observation, we define TWI-SQRNNs in a manner analogous to TWI-QRNNs.…”

Section: Twi-sqrnnsmentioning

confidence: 93%

“…Recently, the quantum machine learning (QML) community has also focused on introducing geometric priors into quantum models [11,12,13]. For example, quantum graph neural networks preserve permutations symmetries, making them suitable for learning quantum tasks with a graph structure [14,15,16,17]; whilst quantum convolutional neural networks [18] preserve translations symmetry. As their classical counterparts, symmetry-preserving quantum models have the potential not only of reducing sample complexity, but also to mitigate quantum computing-specific issues such as barren plateaus [19,20].…”

Section: Related Workmentioning

confidence: 99%

Time-Warping Invariant Quantum Recurrent Neural Networks via Quantum-Classical Adaptive Gating

Nikoloska¹,

Simeone²,

Banchi³

et al. 2023

Preprint

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Adaptive gating plays a key role in temporal data processing via classical recurrent neural networks (RNN), as it facilitates retention of past information necessary to predict the future, providing a mechanism that preserves invariance to time warping transformations. This paper builds on quantum recurrent neural networks (QRNNs), a dynamic model with quantum memory, to introduce a novel class of temporal data processing quantum models that preserve invariance to timewarping transformations of the (classical) input-output sequences. The model, referred to as time warping-invariant QRNN (TWI-QRNN), augments a QRNN with a quantum-classical adaptive gating mechanism that chooses whether to apply a parameterized unitary transformation at each time step as a function of the past samples of the input sequence via a classical recurrent model. The TWI-QRNN model class is derived from first principles, and its capacity to successfully implement time-warping transformations is experimentally demonstrated on examples with classical or quantum dynamics.

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“…This issue has given rise to the field of quantum machine learning (QML) [1,2]. QML has seen the proposal of parameterized quantum models, such as quantum neural networks [3][4][5][6], that could efficiently process quantum data. Variational QML, which involves classically training a parameterized quantum model, is indeed a leading candidate for implementing QML in the near term.…”

Section: Introductionmentioning

confidence: 99%

Resource frugal optimizer for quantum machine learning

Moussa¹,

Gordon²,

Baczyk³

et al. 2022

Preprint

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Quantum-enhanced data science, also known as quantum machine learning (QML), is of growing interest as an application of near-term quantum computers. Variational QML algorithms have the potential to solve practical problems on real hardware, particularly when involving quantum data. However, training these algorithms can be challenging and calls for tailored optimization procedures. Specifically, QML applications can require a large shot-count overhead due to the large datasets involved. In this work, we advocate for simultaneous random sampling over both the dataset as well as the measurement operators that define the loss function. We consider a highly general loss function that encompasses many QML applications, and we show how to construct an unbiased estimator of its gradient. This allows us to propose a shot-frugal gradient descent optimizer called Refoqus (REsource Frugal Optimizer for QUantum Stochastic gradient descent). Our numerics indicate that Refoqus can save several orders of magnitude in shot cost, even relative to optimizers that sample over measurement operators alone.

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Theory for Equivariant Quantum Neural Networks

Cited by 12 publications

References 109 publications

Symmetric tensor networks for generative modeling and constrained combinatorial optimization

Symmetric tensor networks for generative modeling and constrained combinatorial optimization

Time-Warping Invariant Quantum Recurrent Neural Networks via Quantum-Classical Adaptive Gating

Resource frugal optimizer for quantum machine learning

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