scholarly journals Quantum annealing initialization of the quantum approximate optimization algorithm

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 491
Author(s):  
Stefan H. Sack ◽  
Maksym Serbyn
Keyword(s):  
Optimization Algorithm ◽  
Quantum Algorithm ◽  
External Parameter ◽  
Quantum Annealing ◽  
Time Step ◽  
Quantum Devices ◽  
Approximate Optimization ◽  
Optimal Value ◽  
Random Initialization ◽  
Near Term

The quantum approximate optimization algorithm (QAOA) is a prospective near-term quantum algorithm due to its modest circuit depth and promising benchmarks. However, an external parameter optimization required in QAOA could become a performance bottleneck. This motivates studies of the optimization landscape and search for heuristic ways of parameter initialization. In this work we visualize the optimization landscape of the QAOA applied to the MaxCut problem on random graphs, demonstrating that random initialization of the QAOA is prone to converging to local minima with sub-optimal performance. We introduce the initialization of QAOA parameters based on the Trotterized quantum annealing (TQA) protocol, parameterized by the Trotter time step. We find that the TQA initialization allows to circumvent the issue of false minima for a broad range of time steps, yielding the same performance as the best result out of an exponentially scaling number of random initializations. Moreover, we demonstrate that the optimal value of the time step coincides with the point of proliferation of Trotter errors in quantum annealing. Our results suggest practical ways of initializing QAOA protocols on near-term quantum devices and reveals new connections between QAOA and quantum annealing.

scholarly journals On the universality of the quantum approximate optimization algorithm

2020 ◽  
Vol 19 (9) ◽  
Author(s):  
M. E. S. Morales ◽  
J. D. Biamonte ◽  
Z. Zimborás
Keyword(s):  
Optimization Algorithm ◽  
Quantum Circuit ◽  
Original Form ◽  
Complete Proof ◽  
One Dimensional ◽  
Approximate Optimization ◽  
Near Term ◽  
Set Up ◽  
The Cost ◽  
Universal Gate

Abstract The quantum approximate optimization algorithm (QAOA) is considered to be one of the most promising approaches towards using near-term quantum computers for practical application. In its original form, the algorithm applies two different Hamiltonians, called the mixer and the cost Hamiltonian, in alternation with the goal being to approach the ground state of the cost Hamiltonian. Recently, it has been suggested that one might use such a set-up as a parametric quantum circuit with possibly some other goal than reaching ground states. From this perspective, a recent work (Lloyd, arXiv:1812.11075) argued that for one-dimensional local cost Hamiltonians, composed of nearest neighbour ZZ terms, this set-up is quantum computationally universal and provides a universal gate set, i.e. all unitaries can be reached up to arbitrary precision. In the present paper, we complement this work by giving a complete proof and the precise conditions under which such a one-dimensional QAOA might produce a universal gate set. We further generalize this type of gate-set universality for certain cost Hamiltonians with ZZ and ZZZ terms arranged according to the adjacency structure of certain graphs and hypergraphs.

scholarly journals Quantum Approximate Optimization Algorithm: Performance, Mechanism, and Implementation on Near-Term Devices

2020 ◽  
Vol 10 (2) ◽  
Author(s):  
Leo Zhou ◽  
Sheng-Tao Wang ◽  
Soonwon Choi ◽  
Hannes Pichler ◽  
Mikhail D. Lukin
Keyword(s):  
Optimization Algorithm ◽  
Algorithm Performance ◽  
Approximate Optimization ◽  
Near Term

scholarly journals Classical variational simulation of the Quantum Approximate Optimization Algorithm

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Matija Medvidović ◽  
Giuseppe Carleo
Keyword(s):  
Optimization Algorithm ◽  
Large Scale ◽  
Quantum Algorithms ◽  
Practical Interest ◽  
Approximate Optimization ◽  
Near Term ◽  
Classical Computing ◽  
The Many ◽  
Computational Resources ◽  
Parameter Values

AbstractA key open question in quantum computing is whether quantum algorithms can potentially offer a significant advantage over classical algorithms for tasks of practical interest. Understanding the limits of classical computing in simulating quantum systems is an important component of addressing this question. We introduce a method to simulate layered quantum circuits consisting of parametrized gates, an architecture behind many variational quantum algorithms suitable for near-term quantum computers. A neural-network parametrization of the many-qubit wavefunction is used, focusing on states relevant for the Quantum Approximate Optimization Algorithm (QAOA). For the largest circuits simulated, we reach 54 qubits at 4 QAOA layers, approximately implementing 324 RZZ gates and 216 RX gates without requiring large-scale computational resources. For larger systems, our approach can be used to provide accurate QAOA simulations at previously unexplored parameter values and to benchmark the next generation of experiments in the Noisy Intermediate-Scale Quantum (NISQ) era.

scholarly journals F-Divergences and Cost Function Locality in Generative Modelling with Quantum Circuits

Entropy ◽  
2021 ◽  
Vol 23 (10) ◽  
pp. 1281
Author(s):  
Chiara Leadbeater ◽  
Louis Sharrock ◽  
Brian Coyle ◽  
Marcello Benedetti
Keyword(s):  
Fault Tolerant ◽  
Quantum Algorithm ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Quantum Devices ◽  
Leibler Divergence ◽  
Variation Distance ◽  
Near Term ◽  
Generative Modelling

Generative modelling is an important unsupervised task in machine learning. In this work, we study a hybrid quantum-classical approach to this task, based on the use of a quantum circuit born machine. In particular, we consider training a quantum circuit born machine using f-divergences. We first discuss the adversarial framework for generative modelling, which enables the estimation of any f-divergence in the near term. Based on this capability, we introduce two heuristics which demonstrably improve the training of the born machine. The first is based on f-divergence switching during training. The second introduces locality to the divergence, a strategy which has proved important in similar applications in terms of mitigating barren plateaus. Finally, we discuss the long-term implications of quantum devices for computing f-divergences, including algorithms which provide quadratic speedups to their estimation. In particular, we generalise existing algorithms for estimating the Kullback–Leibler divergence and the total variation distance to obtain a fault-tolerant quantum algorithm for estimating another f-divergence, namely, the Pearson divergence.

scholarly journals Optimal Protocols in Quantum Annealing and Quantum Approximate Optimization Algorithm Problems

2021 ◽  
Vol 126 (7) ◽  
Author(s):  
Lucas T. Brady ◽  
Christopher L. Baldwin ◽  
Aniruddha Bapat ◽  
Yaroslav Kharkov ◽  
Alexey V. Gorshkov
Keyword(s):  
Optimization Algorithm ◽  
Quantum Annealing ◽  
Approximate Optimization

scholarly journals Near-term quantum algorithms for linear systems of equations with regression loss functions

2021 ◽  
Vol 23 (11) ◽  
pp. 113021
Author(s):  
Hsin-Yuan Huang ◽  
Kishor Bharti ◽  
Patrick Rebentrost
Keyword(s):  
Linear Systems ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Systems Of Equations ◽  
Quantum Devices ◽  
Near Term ◽  
Variational Algorithms ◽  
Core Idea ◽  
Classical Combination ◽  
Linear Systems Of Equations

Abstract Solving linear systems of equations is essential for many problems in science and technology, including problems in machine learning. Existing quantum algorithms have demonstrated the potential for large speedups, but the required quantum resources are not immediately available on near-term quantum devices. In this work, we study near-term quantum algorithms for linear systems of equations, with a focus on the two-norm and Tikhonov regression settings. We investigate the use of variational algorithms and analyze their optimization landscapes. There exist types of linear systems for which variational algorithms designed to avoid barren plateaus, such as properly-initialized imaginary time evolution and adiabatic-inspired optimization, suffer from a different plateau problem. To circumvent this issue, we design near-term algorithms based on a core idea: the classical combination of variational quantum states (CQS). We exhibit several provable guarantees for these algorithms, supported by the representation of the linear system on a so-called ansatz tree. The CQS approach and the ansatz tree also admit the systematic application of heuristic approaches, including a gradient-based search. We have conducted numerical experiments solving linear systems as large as 2300 × 2300 by considering cases where we can simulate the quantum algorithm efficiently on a classical computer. Our methods may provide benefits for solving linear systems within the reach of near-term quantum devices.

scholarly journals Lower bounds on circuit depth of the quantum approximate optimization algorithm

2021 ◽  
Vol 20 (2) ◽  
Author(s):  
Rebekah Herrman ◽  
James Ostrowski ◽  
Travis S. Humble ◽  
George Siopsis
Keyword(s):  
Lower Bounds ◽  
Optimization Algorithm ◽  
Approximate Optimization ◽  
Circuit Depth

scholarly journals A bat optimization algorithm with moderate orientation and perturbation of trend

2021 ◽  
Vol 15 ◽  
pp. 174830262110084
Author(s):  
Jingsen Liu ◽  
Hongyuan Ji ◽  
Qingqing Liu ◽  
Yu Li
Keyword(s):  
Local Search ◽  
Optimization Algorithm ◽  
Random Perturbation ◽  
Bat Algorithm ◽  
Local Extremum ◽  
Global Search ◽  
Deep Mining ◽  
Nonlinear Variation ◽  
Optimal Value ◽  
Search Stage

In order to improve the convergence speed and optimization accuracy of the bat algorithm, a bat optimization algorithm with moderate optimal orientation and random perturbation of trend is proposed. The algorithm introduces the nonlinear variation factor into the velocity update formula of the global search stage to maintain a high diversity of bat populations, thereby enhanced the global exploration ability of the algorithm. At the same time, in the local search stage, the position update equation is changed, and a strategy that towards optimal value modestly is used to improve the ability of the algorithm to local search for deep mining. Finally, the adaptive decreasing random perturbation is performed on each bat individual that have been updated in position at each generation, which can improve the ability of the algorithm to jump out of the local extremum, and to balance the early global search extensiveness and the later local search accuracy. The simulating results show that the improved algorithm has a faster optimization speed and higher optimization accuracy.

scholarly journals Classifying data using near-term quantum devices

2018 ◽  
Vol 16 (08) ◽  
pp. 1840001
Author(s):  
Johannes Bausch
Keyword(s):  
Neural Network ◽  
Classification Task ◽  
Training Procedure ◽  
Quantum Annealing ◽  
Quantum Neural Network ◽  
Training Scheme ◽  
Trained Classifier ◽  
Coupling Strengths ◽  
Quantum Simulator ◽  
Near Term

The goal of this work is to define a notion of a “quantum neural network” to classify data, which exploits the low-energy spectrum of a local Hamiltonian. As a concrete application, we build a binary classifier, train it on some actual data and then test its performance on a simple classification task. More specifically, we use Microsoft’s quantum simulator, LIQ[Formula: see text][Formula: see text], to construct local Hamiltonians that can encode trained classifier functions in their ground space, and which can be probed by measuring the overlap with test states corresponding to the data to be classified. To obtain such a classifier Hamiltonian, we further propose a training scheme based on quantum annealing which is completely closed-off to the environment and which does not depend on external measurements until the very end, avoiding unnecessary decoherence during the annealing procedure. For a network of size [Formula: see text], the trained network can be stored as a list of [Formula: see text] coupling strengths. We address the question of which interactions are most suitable for a given classification task, and develop a qubit-saving optimization for the training procedure on a simulated annealing device. Furthermore, a small neural network to classify colors into red versus blue is trained and tested, and benchmarked against the annealing parameters.

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