An Expressive Ansatz for Low-Depth Quantum Approximate Optimisation
- URL: http://arxiv.org/abs/2302.04479v2
- Date: Thu, 15 Feb 2024 07:00:30 GMT
- Title: An Expressive Ansatz for Low-Depth Quantum Approximate Optimisation
- Authors: V. Vijendran, Aritra Das, Dax Enshan Koh, Syed M. Assad, Ping Koy Lam
- Abstract summary: The quantum approximate optimisation algorithm (QAOA) is a hybrid quantum-classical algorithm used to approximately solve optimisation problems.
While QAOA can be implemented on NISQ devices, physical limitations can limit circuit depth and decrease performance.
This work introduces the eXpressive QAOA (XQAOA) that assigns more classical parameters to the ansatz to improve its performance at low depths.
- Score: 0.23999111269325263
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The quantum approximate optimisation algorithm (QAOA) is a hybrid
quantum-classical algorithm used to approximately solve combinatorial
optimisation problems. It involves multiple iterations of a parameterised
ansatz comprising a problem and mixer Hamiltonian, with the parameters being
classically optimised. While QAOA can be implemented on NISQ devices, physical
limitations can limit circuit depth and decrease performance. To address these
limitations, this work introduces the eXpressive QAOA (XQAOA), an
overparameterised variant of QAOA that assigns more classical parameters to the
ansatz to improve its performance at low depths. XQAOA also introduces an
additional Pauli-Y component in the mixer Hamiltonian, allowing the mixer to
implement arbitrary unitary transformations on each qubit. To benchmark the
performance of XQAOA at unit depth, we derive its closed-form expression for
the MaxCut problem and compare it to QAOA, Multi-Angle QAOA (MA-QAOA), a
classical-relaxed algorithm, and the state-of-the-art Goemans-Williamson
algorithm on a set of unweighted regular graphs with 128 and 256 nodes for
degrees ranging from 3 to 10. Our results indicate that at unit depth, XQAOA
has benign loss landscapes, allowing it to consistently outperform QAOA,
MA-QAOA, and the classical-relaxed algorithm on all graph instances and the
Goemans-Williamson algorithm on graph instances with degrees greater than 4.
Small-scale simulations also reveal that unit-depth XQAOA surpasses both QAOA
and MA-QAOA on all tested depths up to five. Additionally, we find an infinite
family of graphs for which XQAOA solves MaxCut exactly and analytically show
that for some graphs in this family, XQAOA achieves a much larger approximation
ratio than QAOA. Overall, XQAOA is a more viable choice for variational quantum
optimisation on NISQ devices, offering competitive performance at low depths.
Related papers
- MG-Net: Learn to Customize QAOA with Circuit Depth Awareness [51.78425545377329]
Quantum Approximate Optimization Algorithm (QAOA) and its variants exhibit immense potential in tackling optimization challenges.
The requisite circuit depth for satisfactory performance is problem-specific and often exceeds the maximum capability of current quantum devices.
We introduce the Mixer Generator Network (MG-Net), a unified deep learning framework adept at dynamically formulating optimal mixer Hamiltonians.
arXiv Detail & Related papers (2024-09-27T12:28:18Z) - Improved Recursive QAOA for Solving MAX-CUT on Bipartite Graphs [4.364124102844566]
We analytically prove the performance limitations of level-1 QAOA in solving the MAX-CUT problem on bipartite graphs.
We show through numerical results that solving the same problem using level-1 Recursive QAOA (RQAOA)
We propose a modified RQAOA that reduces the parameter regime optimized in the QAOA.
arXiv Detail & Related papers (2024-08-23T16:35:47Z) - Hybrid Classical-Quantum Simulation of MaxCut using QAOA-in-QAOA [0.0]
In this work, an implementation of the QAOA2 method for the scalable solution of the MaxCut problem is presented.
The limits of the Goemans-Williamson (GW) algorithm as a purely classical alternative to QAOA are investigated.
Results from large-scale simulations of up to 33 qubits are presented, showing the advantage of QAOA in certain cases and the efficiency of the implementation.
arXiv Detail & Related papers (2024-06-25T09:02:31Z) - Tight Lieb-Robinson Bound for approximation ratio in Quantum Annealing [0.0]
We introduce a new parametrized version of QA enabling a precise 1-local analysis of the algorithm.
We show that a linear-schedule QA with a 1-local analysis achieves an approximation ratio over 0.7020, outperforming any known 1-local algorithms.
arXiv Detail & Related papers (2023-11-21T17:15:21Z) - QAOA-in-QAOA: solving large-scale MaxCut problems on small quantum
machines [81.4597482536073]
Quantum approximate optimization algorithms (QAOAs) utilize the power of quantum machines and inherit the spirit of adiabatic evolution.
We propose QAOA-in-QAOA ($textQAOA2$) to solve arbitrary large-scale MaxCut problems using quantum machines.
Our method can be seamlessly embedded into other advanced strategies to enhance the capability of QAOAs in large-scale optimization problems.
arXiv Detail & Related papers (2022-05-24T03:49:10Z) - 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) - 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) - Quantum Approximate Optimization Algorithm Based Maximum Likelihood
Detection [80.28858481461418]
Recent advances in quantum technologies pave the way for noisy intermediate-scale quantum (NISQ) devices.
Recent advances in quantum technologies pave the way for noisy intermediate-scale quantum (NISQ) devices.
arXiv Detail & Related papers (2021-07-11T10:56:24Z) - Threshold-Based Quantum Optimization [0.0]
Th-QAOA (pronounced Threshold QAOA) is a variation of the Quantum Alternating Operator Ansatz (QAOA)
We focus on a combination with the Grover Mixer operator; the resulting GM-Th-QAOA can be viewed as a generalization of Grover's quantum search algorithm.
arXiv Detail & Related papers (2021-06-25T19:36:49Z) - Empirical performance bounds for quantum approximate optimization [0.27998963147546135]
Quantifying performance bounds provides insight into when QAOA may be viable for solving real-world applications.
We find QAOA exceeds the Goemans-Williamson approximation ratio bound for most graphs.
The resulting data set is presented as a benchmark for establishing empirical bounds on QAOA performance.
arXiv Detail & Related papers (2021-02-12T23:12:09Z) - Hybrid quantum-classical algorithms for approximate graph coloring [65.62256987706128]
We show how to apply the quantum approximate optimization algorithm (RQAOA) to MAX-$k$-CUT, the problem of finding an approximate $k$-vertex coloring of a graph.
We construct an efficient classical simulation algorithm which simulates level-$1$ QAOA and level-$1$ RQAOA for arbitrary graphs.
arXiv Detail & Related papers (2020-11-26T18:22:21Z)
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.