Optimal compilation of parametrised quantum circuits

• URL: http://arxiv.org/abs/2401.12877v2
• Date: Fri, 26 Jan 2024 16:15:10 GMT
• Title: Optimal compilation of parametrised quantum circuits
• Authors: John van de Wetering, Richie Yeung, Tuomas Laakkonen, Aleks Kissinger
• Abstract summary: Parametrised quantum circuits contain phase gates whose phase is determined by a classical algorithm prior to running the circuit on a quantum device. In order for these algorithms to be as efficient as possible it is important that we use the fewest number of parameters. We show that, while the general problem of minimising the number of parameters is NP-hard, when we restrict to circuits that are Clifford apart from parametrised phase gates, we can efficiently find the optimal parameter count.
• Score: 0.0
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: Parametrised quantum circuits contain phase gates whose phase is determined by a classical algorithm prior to running the circuit on a quantum device. Such circuits are used in variational algorithms like QAOA and VQE. In order for these algorithms to be as efficient as possible it is important that we use the fewest number of parameters. We show that, while the general problem of minimising the number of parameters is NP-hard, when we restrict to circuits that are Clifford apart from parametrised phase gates and where each parameter is used just once, we can efficiently find the optimal parameter count. We show that when parameter transformations are required to be sufficiently well-behaved that the only rewrites that reduce parameters correspond to simple 'fusions'. Using this we find that a previous circuit optimisation strategy by some of the authors [Kissinger, van de Wetering. PRA (2019)] finds the optimal number of parameters. Our proof uses the ZX-calculus. We also prove that the standard rewrite rules of the ZX-calculus suffice to prove any equality between parametrised Clifford circuits.

Related papers

• QAdaPrune: Adaptive Parameter Pruning For Training Variational Quantum Circuits [2.3332157823623403]
  emphQAdaPrune is an adaptive parameter pruning algorithm that automatically determines the threshold and then intelligently prunes the redundant and non-performing parameters. We show that the resulting sparse parameter sets yield quantum circuits that perform comparably to the unpruned quantum circuits.
  arXiv  Detail & Related papers  (2024-08-23T19:57:40Z)
• Optimal number of parametrized rotations and Hadamard gates in parametrized Clifford circuits with non-repeated parameters [4.423586186569902]
  We present an efficient algorithm to reduce the number of non-Clifford gates in quantum circuits. We show that this approach is optimal for parametrized circuits composed of Clifford gates and parametrized rotations.
  arXiv  Detail & Related papers  (2024-07-10T17:08:18Z)
• Here comes the SU(N): multivariate quantum gates and gradients [1.7809113449965783]
  Variational quantum algorithms use non-commuting optimization methods to find optimal parameters for a parametrized quantum circuit. Here, we propose a gate which fully parameterizes the special unitary group $mathrm(N) gate. We show that the proposed gate and its optimization satisfy the quantum limit of the unitary group.
  arXiv  Detail & Related papers  (2023-03-20T18:00:04Z)
• Optimizing quantum circuit parameters via SDP [0.0]
  We introduce a new framework for parameterized quantum circuits: round SDP to circuit parameters. Within this, we propose an algorithm that produces approximate solutions for a quantum optimization problem called Quantum Max Cut.
  arXiv  Detail & Related papers  (2022-09-02T02:34:19Z)
• 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)
• Unsupervised strategies for identifying optimal parameters in Quantum Approximate Optimization Algorithm [3.508346077709686]
  We study unsupervised Machine Learning approaches for setting parameters without optimization. We showcase them within Recursive-QAOA up to depth $3$ where the number of QAOA parameters used per iteration is limited to $3$. We obtain similar performances to the case where we extensively optimize the angles, hence saving numerous circuit calls.
  arXiv  Detail & Related papers  (2022-02-18T19:55:42Z)
• Accurate methods for the analysis of strong-drive effects in parametric gates [94.70553167084388]
  We show how to efficiently extract gate parameters using exact numerics and a perturbative analytical approach. We identify optimal regimes of operation for different types of gates including $i$SWAP, controlled-Z, and CNOT.
  arXiv  Detail & Related papers  (2021-07-06T02:02:54Z)
• Reducing the Variance of Gaussian Process Hyperparameter Optimization with Preconditioning [54.01682318834995]
  Preconditioning is a highly effective step for any iterative method involving matrix-vector multiplication. We prove that preconditioning has an additional benefit that has been previously unexplored. It simultaneously can reduce variance at essentially negligible cost.
  arXiv  Detail & Related papers  (2021-07-01T06:43:11Z)
• FLIP: A flexible initializer for arbitrarily-sized parametrized quantum circuits [105.54048699217668]
  We propose a FLexible Initializer for arbitrarily-sized Parametrized quantum circuits. FLIP can be applied to any family of PQCs, and instead of relying on a generic set of initial parameters, it is tailored to learn the structure of successful parameters. We illustrate the advantage of using FLIP in three scenarios: a family of problems with proven barren plateaus, PQC training to solve max-cut problem instances, and PQC training for finding the ground state energies of 1D Fermi-Hubbard models.
  arXiv  Detail & Related papers  (2021-03-15T17:38:33Z)
• 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)
• Machine Learning Optimization of Quantum Circuit Layouts [63.55764634492974]
  We introduce a quantum circuit mapping, QXX, and its machine learning version, QXX-MLP. The latter infers automatically the optimal QXX parameter values such that the layed out circuit has a reduced depth. We present empiric evidence for the feasibility of learning the layout method using approximation.
  arXiv  Detail & Related papers  (2020-07-29T05:26:19Z)

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.