Best-approximation error for parametric quantum circuits

• URL: http://arxiv.org/abs/2107.07378v1
• Date: Thu, 15 Jul 2021 15:09:16 GMT
• Title: Best-approximation error for parametric quantum circuits
• Authors: Lena Funcke, Tobias Hartung, Karl Jansen, Stefan K\"uhn, Manuel Schneider, Paolo Stornati
• Abstract summary: In Variational Quantum Simulations, the construction of a suitable parametric quantum circuit is subject to two counteracting effects. The number of parameters should be small for the device noise to be manageable, but also large enough for the circuit to be able to represent the solution. To characterize such circuits, we estimate the best-approximation error using Voronoi diagrams.
• Score: 0.13980986259786224
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In Variational Quantum Simulations, the construction of a suitable parametric quantum circuit is subject to two counteracting effects. The number of parameters should be small for the device noise to be manageable, but also large enough for the circuit to be able to represent the solution. Dimensional expressivity analysis can optimize a candidate circuit considering both aspects. In this article, we will first discuss an inductive construction for such candidate circuits. Furthermore, it is sometimes necessary to choose a circuit with fewer parameters than necessary to represent all relevant states. To characterize such circuits, we estimate the best-approximation error using Voronoi diagrams. Moreover, we discuss a hybrid quantum-classical algorithm to estimate the worst-case best-approximation error, its complexity, and its scaling in state space dimensionality. This allows us to identify some obstacles for variational quantum simulations with local optimizers and underparametrized circuits, and we discuss possible remedies.

Related papers

• Reducing Mid-Circuit Measurements via Probabilistic Circuits [0.13108652488669736]
  Mid-circuit measurements and measurement-controlled gates are supported by an increasing number of quantum hardware platforms. This work presents a static circuit optimization that can substitute some of these measurements with an equivalent circuit with randomized gate applications.
  arXiv  Detail & Related papers  (2024-05-22T15:33:19Z)
• Bayesian Parameterized Quantum Circuit Optimization (BPQCO): A task and hardware-dependent approach [49.89480853499917]
  Variational quantum algorithms (VQA) have emerged as a promising quantum alternative for solving optimization and machine learning problems. In this paper, we experimentally demonstrate the influence of the circuit design on the performance obtained for two classification problems. We also study the degradation of the obtained circuits in the presence of noise when simulating real quantum computers.
  arXiv  Detail & Related papers  (2024-04-17T11:00:12Z)
• FragQC: An Efficient Quantum Error Reduction Technique using Quantum Circuit Fragmentation [4.2754140179767415]
  We present it FragQC, a software tool that cuts a quantum circuit into sub-circuits when its error probability exceeds a certain threshold. We achieve an increase of fidelity by 14.83% compared to direct execution without cutting the circuit, and 8.45% over the state-of-the-art ILP-based method.
  arXiv  Detail & Related papers  (2023-09-30T17:38:31Z)
• Approximate Quantum Compiling for Quantum Simulation: A Tensor Network based approach [1.237454174824584]
  We introduce AQCtensor, a novel algorithm to produce short-depth quantum circuits from Matrix Product States (MPS) Our approach is specifically tailored to the preparation of quantum states generated from the time evolution of quantum many-body Hamiltonians. For simulation problems on 100 qubits, we show that AQCtensor achieves at least an order of magnitude reduction in the depth of the resulting optimized circuit.
  arXiv  Detail & Related papers  (2023-01-20T14:40:29Z)
• End-to-end resource analysis for quantum interior point methods and portfolio optimization [63.4863637315163]
  We provide a complete quantum circuit-level description of the algorithm from problem input to problem output. We report the number of logical qubits and the quantity/depth of non-Clifford T-gates needed to run the algorithm.
  arXiv  Detail & Related papers  (2022-11-22T18:54:48Z)
• Quantum circuit debugging and sensitivity analysis via local inversions [62.997667081978825]
  We present a technique that pinpoints the sections of a quantum circuit that affect the circuit output the most. We demonstrate the practicality and efficacy of the proposed technique by applying it to example algorithmic circuits implemented on IBM quantum machines.
  arXiv  Detail & Related papers  (2022-04-12T19:39:31Z)
• Numerical Simulations of Noisy Quantum Circuits for Computational Chemistry [51.827942608832025]
  Near-term quantum computers can calculate the ground-state properties of small molecules. We show how the structure of the computational ansatz as well as the errors induced by device noise affect the calculation.
  arXiv  Detail & Related papers  (2021-12-31T16:33:10Z)
• Capacity and quantum geometry of parametrized quantum circuits [0.0]
  Parametrized quantum circuits can be effectively implemented on current devices. We evaluate the capacity and trainability of these circuits using the geometric structure of the parameter space. Our results enhance the understanding of parametrized quantum circuits for improving variational quantum algorithms.
  arXiv  Detail & Related papers  (2021-02-02T18:16:57Z)
• Dimensional Expressivity Analysis of Parametric Quantum Circuits [0.0]
  We show how to efficiently implement the expressivity analysis using quantum hardware. We also discuss the effect of symmetries and demonstrate how to incorporate or remove symmetries from the parametrized ansatz.
  arXiv  Detail & Related papers  (2020-11-06T18:59:04Z)
• 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)
• Hardware-Encoding Grid States in a Non-Reciprocal Superconducting Circuit [62.997667081978825]
  We present a circuit design composed of a non-reciprocal device and Josephson junctions whose ground space is doubly degenerate and the ground states are approximate codewords of the Gottesman-Kitaev-Preskill (GKP) code. We find that the circuit is naturally protected against the common noise channels in superconducting circuits, such as charge and flux noise, implying that it can be used for passive quantum error correction.
  arXiv  Detail & Related papers  (2020-02-18T16:45:09Z)

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.