Optimal number of parametrized rotations and Hadamard gates in parametrized Clifford circuits with non-repeated parameters

• URL: http://arxiv.org/abs/2407.07846v1
• Date: Wed, 10 Jul 2024 17:08:18 GMT
• Title: Optimal number of parametrized rotations and Hadamard gates in parametrized Clifford circuits with non-repeated parameters
• Authors: Vivien Vandaele, Simon Perdrix, Christophe Vuillot,
• Abstract summary: 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.
• Score: 4.423586186569902
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present an efficient algorithm to reduce the number of non-Clifford gates in quantum circuits and the number of parametrized rotations in parametrized quantum circuits. The method consists in finding rotations that can be merged into a single rotation gate. This approach has already been considered before and is used as a pre-processing procedure in many optimization algorithms, notably for optimizing the number of Hadamard gates or the number of $T$ gates in Clifford$+T$ circuits. Our algorithm has a better complexity than similar methods and is particularly efficient for circuits with a low number of internal Hadamard gates. Furthermore, we show that this approach is optimal for parametrized circuits composed of Clifford gates and parametrized rotations with non-repeated parameters. For the same type of parametrized quantum circuits, we also prove that a previous procedure optimizing the number of Hadamard gates and internal Hadamard gates is optimal. This procedure is notably used in our low-complexity algorithm for optimally reducing the number of parametrized rotations.

Related papers

• Optimal compilation of parametrised quantum circuits [0.0]
  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.
  arXiv  Detail & Related papers  (2024-01-23T16:13:20Z)
• Characterization, synthesis, and optimization of quantum circuits over multiple-control $\textit{Z}$-rotation gates: A systematic study [4.385466953937176]
  We study quantum circuits composed of multiple-control $Z$-rotation (MCZR) gates as primitives. We present a gate-exchange strategy together with a flexible iterative algorithm for effectively optimizing the depth of any MCZR circuit.
  arXiv  Detail & Related papers  (2023-04-18T06:34:18Z)
• 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)
• Iterative Qubit Coupled Cluster using only Clifford circuits [52.77024349608834]
  We draw attention to a variant of the iterative qubit coupled cluster (iQCC) method that only uses Clifford circuits. This method is useful for near-term variational quantum algorithm applications as it generates good initial parameters. It may also be useful beyond the NISQ era to create short-depth Clifford pre-optimized circuits.
  arXiv  Detail & Related papers  (2022-11-18T20:31:10Z)
• 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)
• Faster Born probability estimation via gate merging and frame optimisation [3.9198548406564604]
  Outcome probabilities of any quantum circuit can be estimated using Monte Carlo sampling. We propose two classical sub-routines: circuit gate optimisation and frame optimisation. We numerically demonstrate that our methods provide improved scaling in the negativity overhead for all tested cases of random circuits.
  arXiv  Detail & Related papers  (2022-02-24T14:18:34Z)
• 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)
• 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)
• Improving the Performance of Deep Quantum Optimization Algorithms with Continuous Gate Sets [47.00474212574662]
  Variational quantum algorithms are believed to be promising for solving computationally hard problems. In this paper, we experimentally investigate the circuit-depth-dependent performance of QAOA applied to exact-cover problem instances. Our results demonstrate that the use of continuous gate sets may be a key component in extending the impact of near-term quantum computers.
  arXiv  Detail & Related papers  (2020-05-11T17:20:51Z)

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.