Noisy Tensor Ring approximation for computing gradients of Variational Quantum Eigensolver for Combinatorial Optimization

• URL: http://arxiv.org/abs/2307.03884v1
• Date: Sat, 8 Jul 2023 03:14:28 GMT
• Title: Noisy Tensor Ring approximation for computing gradients of Variational Quantum Eigensolver for Combinatorial Optimization
• Authors: Dheeraj Peddireddy, Utkarsh Priyam, Vaneet Aggarwal
• Abstract summary: 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.
• Score: 33.12181620473604
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Variational Quantum algorithms, especially Quantum Approximate Optimization and Variational Quantum Eigensolver (VQE) have established their potential to provide computational advantage in the realm of combinatorial optimization. However, these algorithms suffer from classically intractable gradients limiting the scalability. This work addresses the scalability challenge for VQE by proposing a classical gradient computation method which utilizes the parameter shift rule but computes the expected values from the circuits using a tensor ring approximation. The parametrized gates from the circuit transform the tensor ring by contracting the matrix along the free edges of the tensor ring. While the single qubit gates do not alter the ring structure, the state transformations from the two qubit rotations are evaluated by truncating the singular values thereby preserving the structure of the tensor ring and reducing the computational complexity. This variation of the Matrix product state approximation grows linearly in number of qubits and the number of two qubit gates as opposed to the exponential growth in the classical simulations, allowing for a faster evaluation of the gradients on classical simulators.

Related papers

• Tensor networks based quantum optimization algorithm [0.0]
  In optimization, one of the well-known classical algorithms is power iterations. We propose a quantum realiziation to circumvent this pitfall. Our methodology becomes instance agnostic and thus allows one to address black-box optimization within the framework of quantum computing.
  arXiv  Detail & Related papers  (2024-04-23T13:49:11Z)
• Quantum Circuit Optimization with AlphaTensor [47.9303833600197]
  We develop AlphaTensor-Quantum, a method to minimize the number of T gates that are needed to implement a given circuit. Unlike existing methods for T-count optimization, AlphaTensor-Quantum can incorporate domain-specific knowledge about quantum computation and leverage gadgets. Remarkably, it discovers an efficient algorithm akin to Karatsuba's method for multiplication in finite fields.
  arXiv  Detail & Related papers  (2024-02-22T09:20:54Z)
• Parsimonious Optimisation of Parameters in Variational Quantum Circuits [1.303764728768944]
  We propose a novel Quantum-Gradient Sampling that requires the execution of at most two circuits per iteration to update the optimisable parameters. Our proposed method achieves similar convergence rates to classical gradient descent, and empirically outperforms gradient coordinate descent, and SPSA.
  arXiv  Detail & Related papers  (2023-06-20T18:50:18Z)
• Fast Computation of Optimal Transport via Entropy-Regularized Extragradient Methods [75.34939761152587]
  Efficient computation of the optimal transport distance between two distributions serves as an algorithm that empowers various applications. This paper develops a scalable first-order optimization-based method that computes optimal transport to within $varepsilon$ additive accuracy.
  arXiv  Detail & Related papers  (2023-01-30T15:46:39Z)
• Exploring the role of parameters in variational quantum algorithms [59.20947681019466]
  We introduce a quantum-control-inspired method for the characterization of variational quantum circuits using the rank of the dynamical Lie algebra. A promising connection is found between the Lie rank, the accuracy of calculated energies, and the requisite depth to attain target states via a given circuit architecture.
  arXiv  Detail & Related papers  (2022-09-28T20:24:53Z)
• Characterization of variational quantum algorithms using free fermions [0.0]
  We numerically study the interplay between these symmetries and the locality of the target state. We find that the number of iterations to converge to the solution scales linearly with system size.
  arXiv  Detail & Related papers  (2022-06-13T18:11:16Z)
• Twisted hybrid algorithms for combinatorial optimization [68.8204255655161]
  Proposed hybrid algorithms encode a cost function into a problem Hamiltonian and optimize its energy by varying over a set of states with low circuit complexity. We show that for levels $p=2,ldots, 6$, the level $p$ can be reduced by one while roughly maintaining the expected approximation ratio.
  arXiv  Detail & Related papers  (2022-03-01T19:47:16Z)
• Adaptive pruning-based optimization of parameterized quantum circuits [62.997667081978825]
  Variisy hybrid quantum-classical algorithms are powerful tools to maximize the use of Noisy Intermediate Scale Quantum devices. We propose a strategy for such ansatze used in variational quantum algorithms, which we call "Efficient Circuit Training" (PECT) Instead of optimizing all of the ansatz parameters at once, PECT launches a sequence of variational algorithms.
  arXiv  Detail & Related papers  (2020-10-01T18:14:11Z)
• Large gradients via correlation in random parameterized quantum circuits [0.0]
  The presence of exponentially vanishing gradients in cost function landscapes is an obstacle to optimization by gradient descent methods. We prove that reducing the dimensionality of the parameter space can allow one to circumvent the vanishing gradient phenomenon.
  arXiv  Detail & Related papers  (2020-05-25T16:15:53Z)

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.