Light Cone Cancellation for Variational Quantum Eigensolver Ansatz

• URL: http://arxiv.org/abs/2404.19497v2
• Date: Mon, 09 Dec 2024 04:08:11 GMT
• Title: Light Cone Cancellation for Variational Quantum Eigensolver Ansatz
• Authors: Xinjian Yan, Xinwei Lee, Ningyi Xie, Yoshiyuki Saito, Leo Kurosawa, Nobuyoshi Asai, Dongsheng Cai, Hoong Chuin Lau,
• Abstract summary: Variational Quantum Algorithms (VQAs) represent a class of algorithms that utilize a hybrid approach, combining classical and quantum computing techniques. In this study, we apply a method known as Light Cone Cancellation (LCC) to optimize variational circuits. We show that LCC yields higher approximation ratios than those cases without LCC.
• Score: 3.1347083354427707
• License:
• Abstract: Variational Quantum Algorithms (VQAs) represent a class of algorithms that utilize a hybrid approach, combining classical and quantum computing techniques. In this approach, classical computers serve as optimizers that update circuit parameters to find approximate solutions to complex problems. In this study, we apply a method known as Light Cone Cancellation (LCC) to optimize variational circuits, effectively reducing the required number of qubits and gates for circuit simulation. We then evaluate the performance of LCC one of the VQAs -- the Variational Quantum Eigensolver (VQE) -- to address the Max-Cut problem. Compared with the Quantum Approximate Optimization Algorithm (QAOA), VQE offers greater degrees of freedom and promising results at lower circuit depths. By applying LCC to VQE, we can shift the complexity of circuit simulation from the number of qubits to the number of edges in the graph, i.e., from exponential time to polynomial time. This enables us to solve large problems up to 100 vertices, without actually simulating the entire circuit. From our simulation in a 7-qubit and a 27-qubit fake backends, we show that LCC yields higher approximation ratios than those cases without LCC, implying that the effect of noise is reduced when LCC is applied.

Related papers

• Classical optimization with imaginary time block encoding on quantum computers: The MaxCut problem [2.4968861883180447]
  Finding ground state solutions of diagonal Hamiltonians is relevant for both theoretical as well as practical problems of interest in many domains such as finance, physics and computer science. Here we use imaginary time evolution through a new block encoding scheme to obtain the ground state of such problems and apply our method to MaxCut as an illustration.
  arXiv  Detail & Related papers  (2024-11-16T08:17:36Z)
• Optimization by Decoded Quantum Interferometry [43.55132675053983]
  We introduce a quantum algorithm for reducing classical optimization problems to classical decoding problems. We show that DQI achieves a better approximation ratio than any quantum-time classical algorithm known to us.
  arXiv  Detail & Related papers  (2024-08-15T17:47:42Z)
• Nonlinear dynamics as a ground-state solution on quantum computers [39.58317527488534]
  We present variational quantum algorithms (VQAs) that encode both space and time in qubit registers. The spacetime encoding enables us to obtain the entire time evolution from a single ground-state computation.
  arXiv  Detail & Related papers  (2024-03-25T14:06:18Z)
• Towards Optimizations of Quantum Circuit Simulation for Solving Max-Cut Problems with QAOA [1.5047640669285467]
  Quantum approximate optimization algorithm (QAOA) is one of the popular quantum algorithms that are used to solve optimization problems via approximations. However, performing QAOA on virtual quantum computers suffers from a slow simulation speed for solving optimization problems. We propose techniques to accelerate QCS for QAOA using mathematical optimizations to compress quantum operations.
  arXiv  Detail & Related papers  (2023-12-05T06:08:57Z)
• Efficient DCQO Algorithm within the Impulse Regime for Portfolio Optimization [41.94295877935867]
  We propose a faster digital quantum algorithm for portfolio optimization using the digitized-counterdiabatic quantum optimization (DCQO) paradigm. Our approach notably reduces the circuit depth requirement of the algorithm and enhances the solution accuracy, making it suitable for current quantum processors. We experimentally demonstrate the advantages of our protocol using up to 20 qubits on an IonQ trapped-ion quantum computer.
  arXiv  Detail & Related papers  (2023-08-29T17:53:08Z)
• NISQ-compatible approximate quantum algorithm for unconstrained and constrained discrete optimization [0.0]
  We present an approximate gradient-based quantum algorithm for hardware-efficient circuits with amplitude encoding. We show how simple linear constraints can be directly incorporated into the circuit without additional modification of the objective function with penalty terms.
  arXiv  Detail & Related papers  (2023-05-23T16:17:57Z)
• 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)
• Scaling Quantum Approximate Optimization on Near-term Hardware [49.94954584453379]
  We quantify scaling of the expected resource requirements by optimized circuits for hardware architectures with varying levels of connectivity. We show the number of measurements, and hence total time to synthesizing solution, grows exponentially in problem size and problem graph degree. These problems may be alleviated by increasing hardware connectivity or by recently proposed modifications to the QAOA that achieve higher performance with fewer circuit layers.
  arXiv  Detail & Related papers  (2022-01-06T21:02:30Z)
• 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)
• Layer VQE: A Variational Approach for Combinatorial Optimization on Noisy Quantum Computers [5.644434841659249]
  We propose an iterative Layer VQE (L-VQE) approach, inspired by the Variational Quantum Eigensolver (VQE) We show that L-VQE is more robust to finite sampling errors and has a higher chance of finding the solution as compared with standard VQE approaches. Our simulation results show that L-VQE performs well under realistic hardware noise.
  arXiv  Detail & Related papers  (2021-02-10T16:53:22Z)
• 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)

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.