Differentiation of Linear Optical Circuits

• URL: http://arxiv.org/abs/2401.07997v3
• Date: Sun, 08 Dec 2024 22:30:30 GMT
• Title: Differentiation of Linear Optical Circuits
• Authors: Giovanni de Felice, Christopher Corlett,
• Abstract summary: This paper develops classical and quantum algorithms for evaluating the analytic gradients of linear optical circuits. We show how to compute the gradients of the expectation values of a special class of non-interacting'' observables arising in full-counting-statistics.
• Score: 0.0
• License:
• Abstract: Linear optical circuits with single-photon sources offer a promising platform for quantum chemistry and machine learning. However, current applications are all based on support vector machines or gradient-free optimization methods. This paper develops classical and quantum algorithms for evaluating the analytic gradients of linear optical circuits with respect to their phase parameters. First, we set up a general framework by characterising the class of observables whose expectation values can be estimated efficiently by sampling from a passive linear optical circuit with finitely many photons. We then show how to compute the gradients of the expectation values of a special class of ``non-interacting'' observables arising in full-counting-statistics. Our differentiation algorithm uses the Halmos dilation and requires evaluating two circuits of twice the size, using one additional photon. Building on the methods of full-counting-statistics, we show how to recover the gradients of arbitrary observables from the gradient of a non-interacting characteristic function. Throughout the paper, we compare the performance of classical and quantum algorithms on the same estimation problems, analysing the sampling complexity of the algorithms and suggesting different cases for which quantum speed-ups could be obtained.

Related papers

• Variational approach to photonic quantum circuits via the parameter shift rule [0.0]
  We derive a formulation of the parameter shift rule for reconfigurable optical linear circuits based on the Boson Sampling paradigm. We also present similar rules for the computations of integrals over the variational parameters. We employ the developed approach to experimentally test variational algorithms with single-photon states processed in a reconfigurable 6-mode universal integrated interferometer.
  arXiv  Detail & Related papers  (2024-10-09T15:06:17Z)
• A Photonic Parameter-shift Rule: Enabling Gradient Computation for Photonic Quantum Computers [0.0]
  We present a method for gradient computation in quantum computation algorithms implemented on linear optical quantum computing platforms. Our method scales linearly with the number of input photons and utilizes the same parameterized photonic circuit with shifted parameters for each evaluation.
  arXiv  Detail & Related papers  (2024-10-03T17:47:38Z)
• Exact gradients for linear optics with single photons [38.74529485263391]
  We derive an analytical formula for the gradients in quantum circuits with respect to phaseshifters via a generalized parameter shift rule. We propose two strategies through which one can reduce the number of shifts in the expression, and hence reduce the overall sample complexity. Numerically, we show that this generalized parameter-shift rule can converge to the minimum of a cost function with fewer parameter update steps than alternative techniques.
  arXiv  Detail & Related papers  (2024-09-24T18:02:06Z)
• Characterizing randomness in parameterized quantum circuits through expressibility and average entanglement [39.58317527488534]
  Quantum Circuits (PQCs) are still not fully understood outside the scope of their principal application. We analyse the generation of random states in PQCs under restrictions on the qubits connectivities. We place a connection between how steep is the increase on the uniformity of the distribution of the generated states and the generation of entanglement.
  arXiv  Detail & Related papers  (2024-05-03T17:32:55Z)
• Noisy Tensor Ring approximation for computing gradients of Variational Quantum Eigensolver for Combinatorial Optimization [33.12181620473604]
  Variational Quantum algorithms have established their potential to provide computational advantage in the realm of optimization. These algorithms suffer from classically intractable gradients limiting the scalability. This work proposes a classical gradient method which utilizes the parameter shift rule but computes the expected values from the circuits using a tensor ring approximation.
  arXiv  Detail & Related papers  (2023-07-08T03:14:28Z)
• Approximating outcome probabilities of linear optical circuits [0.0]
  We propose classical algorithms for approximating outcome probabilities of a linear optical circuit. Our scheme renders an efficient estimation of outcome probabilities with precision depending on the classicality of the circuit. Our study sheds light on the power of linear optics, providing plenty of quantum-inspired algorithms for problems in computational complexity.
  arXiv  Detail & Related papers  (2022-11-14T08:21:51Z)
• Retrieving space-dependent polarization transformations via near-optimal quantum process tomography [55.41644538483948]
  We investigate the application of genetic and machine learning approaches to tomographic problems. We find that the neural network-based scheme provides a significant speed-up, that may be critical in applications requiring a characterization in real-time. We expect these results to lay the groundwork for the optimization of tomographic approaches in more general quantum processes.
  arXiv  Detail & Related papers  (2022-10-27T11:37:14Z)
• Time complexity analysis of quantum algorithms via linear representations for nonlinear ordinary and partial differential equations [31.986350313948435]
  We construct quantum algorithms to compute the solution and/or physical observables of nonlinear ordinary differential equations. We compare the quantum linear systems algorithms based methods and the quantum simulation methods arising from different numerical approximations.
  arXiv  Detail & Related papers  (2022-09-18T05:50:23Z)
• Quantum machine learning with adaptive linear optics [0.0]
  We study supervised learning algorithms in which a quantum device is used to perform a computational subroutine. We design implementations of these quantum subroutines using Boson Sampling architectures in linear optics, supplemented by adaptive measurements.
  arXiv  Detail & Related papers  (2021-02-08T23:56:49Z)
• Rapid characterisation of linear-optical networks via PhaseLift [51.03305009278831]
  Integrated photonics offers great phase-stability and can rely on the large scale manufacturability provided by the semiconductor industry. New devices, based on such optical circuits, hold the promise of faster and energy-efficient computations in machine learning applications. We present a novel technique to reconstruct the transfer matrix of linear optical networks.
  arXiv  Detail & Related papers  (2020-10-01T16:04:22Z)
• Measuring Analytic Gradients of General Quantum Evolution with the Stochastic Parameter Shift Rule [0.0]
  We study the problem of estimating the gradient of the function to be optimized directly from quantum measurements. We derive a mathematically exact formula that provides an algorithm for estimating the gradient of any multi-qubit parametric quantum evolution. Our algorithm continues to work, although with some approximations, even when all the available quantum gates are noisy.
  arXiv  Detail & Related papers  (2020-05-20T18:24:11Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.