scholarly journals Weak Decoupling, Polynomial Folds and Approximate Optimization over the Sphere

2017 ◽  
Author(s):  
Vijay Bhattiprolu ◽  
Mrinalkanti Ghosh ◽  
Venkatesan Guruswami ◽  
Euiwoong Lee ◽  
Madhur Tulsiani
Keyword(s):  
Approximate Optimization

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 Quantum approximate optimization with Gaussian boson sampling

2018 ◽  
Vol 98 (1) ◽  
Author(s):  
Juan Miguel Arrazola ◽  
Thomas R. Bromley ◽  
Patrick Rebentrost
Keyword(s):  
Approximate Optimization ◽  
Boson Sampling

scholarly journals Modeling and mitigation of cross-talk effects in readout noise with applications to the Quantum Approximate Optimization Algorithm

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 464
Author(s):  
Filip B. Maciejewski ◽  
Flavio Baccari ◽  
Zoltán Zimborás ◽  
Michał Oszmaniec
Keyword(s):  
Cross Talk ◽  
Optimization Algorithm ◽  
Probability Distributions ◽  
System Size ◽  
Measurement Noise ◽  
Noise Model ◽  
Noise Mitigation ◽  
Energy Estimation ◽  
Approximate Optimization ◽  
Readout Noise

Measurement noise is one of the main sources of errors in currently available quantum devices based on superconducting qubits. At the same time, the complexity of its characterization and mitigation often exhibits exponential scaling with the system size. In this work, we introduce a correlated measurement noise model that can be efficiently described and characterized, and which admits effective noise-mitigation on the level of marginal probability distributions. Noise mitigation can be performed up to some error for which we derive upper bounds. Characterization of the model is done efficiently using Diagonal Detector Overlapping Tomography – a generalization of the recently introduced Quantum Overlapping Tomography to the problem of reconstruction of readout noise with restricted locality. The procedure allows to characterize k-local measurement cross-talk on N-qubit device using O(k2klog(N)) circuits containing random combinations of X and identity gates. We perform experiments on 15 (23) qubits using IBM's (Rigetti's) devices to test both the noise model and the error-mitigation scheme, and obtain an average reduction of errors by a factor >22 (>5.5) compared to no mitigation. Interestingly, we find that correlations in the measurement noise do not correspond to the physical layout of the device. Furthermore, we study numerically the effects of readout noise on the performance of the Quantum Approximate Optimization Algorithm (QAOA). We observe in simulations that for numerous objective Hamiltonians, including random MAX-2-SAT instances and the Sherrington-Kirkpatrick model, the noise-mitigation improves the quality of the optimization. Finally, we provide arguments why in the course of QAOA optimization the estimates of the local energy (or cost) terms often behave like uncorrelated variables, which greatly reduces sampling complexity of the energy estimation compared to the pessimistic error analysis. We also show that similar effects are expected for Haar-random quantum states and states generated by shallow-depth random circuits.

scholarly journals Classical symmetries and the Quantum Approximate Optimization Algorithm

2021 ◽  
Vol 20 (11) ◽  
Author(s):  
Ruslan Shaydulin ◽  
Stuart Hadfield ◽  
Tad Hogg ◽  
Ilya Safro
Keyword(s):  
Optimization Algorithm ◽  
Approximate Optimization ◽  
Classical Symmetries

Improved Trust Region Model Management for Approximate Optimization

1998 ◽  
Author(s):  
Brett A. Wujek ◽  
John E. Renaud
Keyword(s):  
Design Optimization ◽  
Multidisciplinary Design Optimization ◽  
Low Cost ◽  
Approximation Error ◽  
Trust Region ◽  
Model Management ◽  
Multidisciplinary Design ◽  
Test Problems ◽  
Approximation Techniques ◽  
Approximate Optimization

Abstract Approximations play an important role in multidisciplinary design optimization (MDO) by offering system behavior information at a relatively low cost. Most approximate optimization strategies are sequential in which an optimization of an approximate problem subject to design variable move limits is iteratively repeated until convergence. The move limits are imposed to restrict the optimization to regions of the design space in which the approximations provide meaningful information. In order to insure convergence of the sequence of approximate optimizations to a Karush Kuhn Tucker solution a move limit management strategy is required. In this paper, issues of move-limit management are reviewed and a new adaptive strategy for move limit management is developed. With its basis in the provably convergent trust region methodology, the TRAM (Trust region Ratio Approximation Method) strategy utilizes available gradient information and employs a backtracking process using various two-point approximation techniques to provide a flexible move-limit adjustment factor. The new strategy is successfully implemented in application to a suite of multidisciplinary design optimization test problems. These implementation studies highlight the ability of the TRAM strategy to control the amount of approximation error and efficiently manage the convergence to a Karush Kuhn Tucker solution.

Sign in / Sign up

Export Citation Format

Share Document