Symmetry-enhanced Counterdiabatic Quantum Algorithm for Qudits

• URL: http://arxiv.org/abs/2410.06710v2
• Date: Fri, 18 Oct 2024 11:37:06 GMT
• Title: Symmetry-enhanced Counterdiabatic Quantum Algorithm for Qudits
• Authors: Alberto Bottarelli, Mikel Garcia de Andoin, Pranav Chandarana, Koushik Paul, Xi Chen, Mikel Sanz, Philipp Hauke,
• Abstract summary: We propose a symmetry-enhanced digitized counterdiabatic quantum algorithm utilizing qudits instead of qubits. First, compression in the circuit depth is achieved by counterdiabatic protocols. Second, information about the problem is compressed by replacing qubits with qudits, allowing for a more efficient representation of the problem.
• Score: 2.8606554662852846
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Qubit-based variational quantum algorithms have undergone rapid development in recent years but still face several challenges. In this context, we propose a symmetry-enhanced digitized counterdiabatic quantum algorithm utilizing qudits instead of qubits. This approach offers three types of compression as compared to with respect to conventional variational circuits. First, compression in the circuit depth is achieved by counterdiabatic protocols. Second, information about the problem is compressed by replacing qubits with qudits, allowing for a more efficient representation of the problem. Lastly, the number of parameters is reduced by employing the symmetries of the system. We illustrate this approach by tackling a graph-based optimization problem Max-3-Cut and a highly-entangled state preparation, the qutrit W state. As our numerical results show, we achieve a better convergence with a lower circuit depth and less measurement overhead in all the cases considered. This work leads to a better design of shallow variational quantum circuits, improving the feasibility of their implementation on near-term qudit devices

Related papers

• Symmetry-preserved cost functions for variational quantum eigensolver [0.0]
  Hybrid quantum-classical variational algorithms are considered ideal for noisy quantum computers. We propose encoding symmetry preservation directly into the cost function, enabling more efficient use of Hardware-Efficient Ans"atze.
  arXiv  Detail & Related papers  (2024-11-25T20:33:47Z)
• High-dimensional counterdiabatic quantum computing [0.0]
  We consider qutrits in the context of quadratic problems, obtaining the qutrit Hamiltonian codifications and the counterdiabatic drivings. Our findings show that the use of qutrits can improve the quality of the solution up to 90 times compared to qubits counterpart.
  arXiv  Detail & Related papers  (2024-10-14T15:29:01Z)
• Quantum State Preparation Circuit Optimization Exploiting Don't Cares [6.158168913938158]
  Quantum state preparation initializes the quantum registers and is essential for running quantum algorithms. Existing methods synthesize an initial circuit and leverage compilers to reduce the circuit's gate count. We introduce a peephole optimization algorithm that identifies such unitaries for replacement in the original circuit.
  arXiv  Detail & Related papers  (2024-09-02T18:40:42Z)
• Bias-field digitized counterdiabatic quantum optimization [39.58317527488534]
  We call this protocol bias-field digitizeddiabatic quantum optimization (BF-DCQO) Our purely quantum approach eliminates the dependency on classical variational quantum algorithms. It achieves scaling improvements in ground state success probabilities, increasing by up to two orders of magnitude.
  arXiv  Detail & Related papers  (2024-05-22T18:11:42Z)
• A two-circuit approach to reducing quantum resources for the quantum lattice Boltzmann method [41.66129197681683]
  Current quantum algorithms for solving CFD problems use a single quantum circuit and, in some cases, lattice-based methods. We introduce the a novel multiple circuits algorithm that makes use of a quantum lattice Boltzmann method (QLBM) The problem is cast as a stream function--vorticity formulation of the 2D Navier-Stokes equations and verified and tested on a 2D lid-driven cavity flow.
  arXiv  Detail & Related papers  (2024-01-20T15:32:01Z)
• Parallel circuit implementation of variational quantum algorithms [0.0]
  We present a method to split quantum circuits of variational quantum algorithms (VQAs) to allow for parallel training and execution. We apply this specifically to optimization problems, where inherent structures from the problem can be identified. We show that not only can our method address larger problems, but that it is also possible to run full VQA models while training parameters using only one slice.
  arXiv  Detail & Related papers  (2023-04-06T12:52:29Z)
• Efficient estimation of trainability for variational quantum circuits [43.028111013960206]
  We find an efficient method to compute the cost function and its variance for a wide class of variational quantum circuits. This method can be used to certify trainability for variational quantum circuits and explore design strategies that can overcome the barren plateau problem.
  arXiv  Detail & Related papers  (2023-02-09T14:05:18Z)
• 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)
• Bayesian Learning of Parameterised Quantum Circuits [0.0]
  We take a probabilistic point of view and reformulate the classical optimisation as an approximation of a Bayesian posterior. We describe a dimension reduction strategy based on a maximum a posteriori point estimate with a Laplace prior. Experiments on the Quantinuum H1-2 computer show that the resulting circuits are faster to execute and less noisy than circuits trained without a gradient.
  arXiv  Detail & Related papers  (2022-06-15T14:20:14Z)
• Quantum algorithms for grid-based variational time evolution [36.136619420474766]
  We propose a variational quantum algorithm for performing quantum dynamics in first quantization. Our simulations exhibit the previously observed numerical instabilities of variational time propagation approaches.
  arXiv  Detail & Related papers  (2022-03-04T19:00:45Z)
• Adiabatic Quantum Graph Matching with Permutation Matrix Constraints [75.88678895180189]
  Matching problems on 3D shapes and images are frequently formulated as quadratic assignment problems (QAPs) with permutation matrix constraints, which are NP-hard. We propose several reformulations of QAPs as unconstrained problems suitable for efficient execution on quantum hardware. The proposed algorithm has the potential to scale to higher dimensions on future quantum computing architectures.
  arXiv  Detail & Related papers  (2021-07-08T17:59:55Z)
• Variational Quantum Optimization with Multi-Basis Encodings [62.72309460291971]
  We introduce a new variational quantum algorithm that benefits from two innovations: multi-basis graph complexity and nonlinear activation functions. Our results in increased optimization performance, two increase in effective landscapes and a reduction in measurement progress.
  arXiv  Detail & Related papers  (2021-06-24T20:16:02Z)
• Space-efficient binary optimization for variational computing [68.8204255655161]
  We show that it is possible to greatly reduce the number of qubits needed for the Traveling Salesman Problem. We also propose encoding schemes which smoothly interpolate between the qubit-efficient and the circuit depth-efficient models.
  arXiv  Detail & Related papers  (2020-09-15T18:17:27Z)
• 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.