From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz.
TLDR
The essence of this extension, the quantum alternating operator ansatz, is the consideration of general parameterized families of unitaries rather than only those corresponding to the time evolution under a fixed local Hamiltonian for a time specified by the parameter.Abstract:
The next few years will be exciting as prototype universal quantum processors emerge, enabling implementation of a wider variety of algorithms. Of particular interest are quantum heuristics, which require experimentation on quantum hardware for their evaluation, and which have the potential to significantly expand the breadth of quantum computing applications. A leading candidate is Farhi et al.'s Quantum Approximate Optimization Algorithm, which alternates between applying a cost-function-based Hamiltonian and a mixing Hamiltonian. Here, we extend this framework to allow alternation between more general families of operators. The essence of this extension, the Quantum Alternating Operator Ansatz, is the consideration of general parametrized families of unitaries rather than only those corresponding to the time-evolution under a fixed local Hamiltonian for a time specified by the parameter. This ansatz supports the representation of a larger, and potentially more useful, set of states than the original formulation, with potential long-term impact on a broad array of application areas. For cases that call for mixing only within a desired subspace, refocusing on unitaries rather than Hamiltonians enables more efficiently implementable mixers than was possible in the original framework. Such mixers are particularly useful for optimization problems with hard constraints that must always be satisfied, defining a feasible subspace, and soft constraints whose violation we wish to minimize. More efficient implementation enables earlier experimental exploration of an alternating operator approach to a wide variety of approximate optimization, exact optimization, and sampling problems. Here, we introduce the Quantum Alternating Operator Ansatz, lay out design criteria for mixing operators, detail mappings for eight problems, and provide brief descriptions of mappings for diverse problems.read more
Citations
More filters
Journal ArticleDOI
Variational Quantum Algorithms
Marco Cerezo,Marco Cerezo,Andrew Arrasmith,Andrew Arrasmith,Ryan Babbush,Simon C. Benjamin,Suguru Endo,Keisuke Fujii,Jarrod R. McClean,Kosuke Mitarai,Kosuke Mitarai,Xiao Yuan,Xiao Yuan,Lukasz Cincio,Lukasz Cincio,Patrick J. Coles,Patrick J. Coles +16 more
TL;DR: An overview of the field of Variational Quantum Algorithms is presented and strategies to overcome their challenges as well as the exciting prospects for using them as a means to obtain quantum advantage are discussed.
Journal ArticleDOI
Quantum approximate optimization of non-planar graph problems on a planar superconducting processor
Matthew P. Harrigan,Kevin J. Sung,Kevin J. Sung,Matthew Neeley,Kevin J. Satzinger,Frank Arute,Kunal Arya,Juan Atalaya,Joseph C. Bardin,Joseph C. Bardin,Rami Barends,Sergio Boixo,Michael Broughton,Bob B. Buckley,David A. Buell,B. Burkett,Nicholas Bushnell,Yu Chen,Zijun Chen,Ben Chiaro,Ben Chiaro,Roberto Collins,William Courtney,Sean Demura,Andrew Dunsworth,Daniel Eppens,Austin G. Fowler,Brooks Foxen,Craig Gidney,Marissa Giustina,R. Graff,Steve Habegger,Alan Ho,Sabrina Hong,Trent Huang,Lev Ioffe,Sergei V. Isakov,Evan Jeffrey,Zhang Jiang,Cody Jones,Dvir Kafri,Kostyantyn Kechedzhi,Julian Kelly,Seon Kim,Paul V. Klimov,Alexander N. Korotkov,Alexander N. Korotkov,Fedor Kostritsa,David Landhuis,Pavel Laptev,Mike Lindmark,Martin Leib,Orion Martin,John M. Martinis,John M. Martinis,Jarrod R. McClean,Matt McEwen,Matt McEwen,Anthony Megrant,Xiao Mi,Masoud Mohseni,Wojciech Mruczkiewicz,Josh Mutus,Ofer Naaman,Charles Neill,Florian Neukart,Murphy Yuezhen Niu,Thomas E. O'Brien,Bryan O'Gorman,Bryan O'Gorman,Eric Ostby,Andre Petukhov,Harald Putterman,Chris Quintana,Pedram Roushan,Nicholas C. Rubin,Daniel Sank,Andrea Skolik,Andrea Skolik,Vadim Smelyanskiy,Doug Strain,Michael Streif,Michael Streif,Marco Szalay,Amit Vainsencher,Theodore White,Z. Jamie Yao,Ping Yeh,Adam Zalcman,Leo Zhou,Leo Zhou,Hartmut Neven,Dave Bacon,E. Lucero,Edward Farhi,Ryan Babbush +95 more
TL;DR: The application of the Google Sycamore superconducting qubit quantum processor to combinatorial optimization problems with the quantum approximate optimization algorithm (QAOA) is demonstrated and an approximation ratio is obtained that is independent of problem size and for the first time, that performance increases with circuit depth.
Journal ArticleDOI
Noisy intermediate-scale quantum algorithms
TL;DR: In this article , the authors discuss what is possible in this ''noisy intermediate scale'' quantum (NISQ) era, including simulation of many-body physics and chemistry, combinatorial optimization, and machine learning.
Posted Content
Noise-Induced Barren Plateaus in Variational Quantum Algorithms
Samson Wang,Enrico Fontana,Marco Cerezo,Kunal Sharma,Akira Sone,Lukasz Cincio,Patrick J. Coles +6 more
TL;DR: This work rigorously proves a serious limitation for noisy VQAs, in that the noise causes the training landscape to have a barren plateau, and proves that the gradient vanishes exponentially in the number of qubits n if the depth of the ansatz grows linearly with n.
Posted Content
Unsupervised Machine Learning on a Hybrid Quantum Computer
Johannes Otterbach,Riccardo Manenti,Nasser Alidoust,A. Bestwick,Maxwell Block,Benjamin Bloom,Shane Caldwell,Nicolas Didier,E. Schuyler Fried,Sabrina Hong,Peter J. Karalekas,Osborn Christopher Butler,Alexander Papageorge,Eric Peterson,Guenevere E. D. K. Prawiroatmodjo,Nicholas C. Rubin,Colm A. Ryan,Diego Scarabelli,Michael Scheer,Eyob A. Sete,Prasahnt Sivarajah,Robert S. Smith,Alexa Staley,Nikolas Tezak,William J. Zeng,A. Hudson,Blake R. Johnson,Matthew Reagor,M. P. da Silva,Chad Rigetti +29 more
TL;DR: This paper uses the quantum approximate optimization algorithm in conjunction with a gradient-free Bayesian optimization to train the quantum machine, and finds evidence that classical optimization can be used to train around both coherent and incoherent imperfections.
References
More filters
Journal ArticleDOI
Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming
TL;DR: This algorithm gives the first substantial progress in approximating MAX CUT in nearly twenty years, and represents the first use of semidefinite programming in the design of approximation algorithms.
Journal ArticleDOI
Some optimal inapproximability results
TL;DR: It is proved optimal, up to an arbitrary ε > 0, inapproximability results for Max-E k-Sat for k ≥ 3, maximizing the number of satisfied linear equations in an over-determined system of linear equations modulo a prime p and Set Splitting.
Journal ArticleDOI
Optimization, approximation, and complexity classes
TL;DR: It follows that such a complete problem has a polynomial-time approximation scheme iff the whole class does, and that a number of common optimization problems are complete for MAX SNP under a kind of careful transformation that preserves approximability.
Book ChapterDOI
Complexity of machine scheduling problems
TL;DR: In this paper, the authors survey and extend the results on the complexity of machine scheduling problems and give a classification of scheduling problems on single, different and identical machines and study the influence of various parameters on their complexity.
Posted Content
A Quantum Approximate Optimization Algorithm
TL;DR: A quantum algorithm that produces approximate solutions for combinatorial optimization problems that depends on a positive integer p and the quality of the approximation improves as p is increased, and is studied as applied to MaxCut on regular graphs.