Purification-based quantum error mitigation of pair-correlated electron simulations
Authors: O'Brien Thomas , Anselmetti Gian-Luca , Gkritsis Fotios , Elfving Vincent , Polla Stefano , Huggins William , Oumarou Oumarou , Kechedzhi Kostyantyn , Abanin Dmitry , Acharya Rajeev , Aleiner Igor , Allen Richard , Andersen Trond , Anderson Kyle , Ansmann Markus , Arute Frank , Arya Kunal , Asfaw Abraham , Atalaya Juan , Bacon Dave , Bardin Joseph , Bengtsson Andreas , Boixo Sergio , Bortoli Gina , Bourassa Alexandre , Bovaird Jenna , Brill Leon , Broughton Michael , Buckley Bob , Buell David , Burger Tim , Burkett Brian , Bushnell Nicholas , Campero Juan , Chen Yu , Chen Zijun , Chiaro Ben , Chik Desmond , Cogan Josh , Collins Roberto , Conner Paul , Courtney William , Crook Alexander , Curtin Ben , Debroy Dripto , Barba Alexander Del Toro , Demura Sean , Drozdov Ilya , Dunsworth Andrew , Eppens Daniel , Erickson Catherine , Faoro Lara , Farhi Edward , Fatemi Reza , Ferreira Vinicius , Burgos Leslie Flores , Forati Ebrahim , Fowler Austin , Foxen Brooks , Giang William , Gidney Craig , Gilboa Dar , Giustina Marissa , Gosula Raja , Dau Alejandro Grajales , Gross Jonathan , Habegger Steve , Hamilton Michael , Hansen Monica , Harrigan Matthew , Harrington Sean , Heu Paula , Hilton Jeremy , Hoffmann Markus , Hong Sabrina , Huang Trent , Huff Ashley , Ioffe L. B. , Isakov Sergei , Iveland Justin , Jeffrey E. , Jiang Zhang , Jones Cody , Juhas Pavol , Kafri Dvir , Kelly Julian , Khattar Tanuj , Khezri Mostafa , Kieferova Marika , Kim Seon , Klimov Paul , Klots Andrey , Korotkov Alexander , Kostritsa Fedor , Kreikebaum John Mark , Landhuis David , Laptev Pavel , Lau Kim-Ming , Laws Lily , Lee Joonho , Lee Kenny , Lester Brian , Lill Alexander , Liu Wayne , Livingston William , Locharla Aditya , Lucero Erik , Malone Fionn , Mandra Salvatore , Martin Orion , Martin Steven , McClean Jarrod , McCourt Trevor , McEwen Matthew , Megrant Anthony , Mi Xiao , Miao Kevin , Mieszala Amanda , Mohseni Masoud , Montazeri Shirin , Morvan Alexis , Movassagh Ramis , Mruczkiewicz Wojciech , Naaman Ofer , Neeley Matthew , Neill Charles , Nersisyan Ani , Neven Hartmut , Newman Michael , Ng Jiun How , Nguyen Anthony , Nguyen Murray , Niu Murphy , Omonije Seun , Opremcak Alex , Petukhov Andre , Potter Rebecca , Pryadko Leonid , Quintana Chris , Rocque Charles , Roushan Pedram , Saei Negar , Sank Daniel , Sankaragomathi Kannan , Satzinger Kevin , Schurkus Henry , Shearn Michael , Shorter Aaron , Shutty Noah , Vladimir Shvarts , Skruzny Jindra , Smelyanskiy Vadim , Smith W. Clarke , Somma Rolando , Sterling George , Strain Doug , Szalay Marco , Thor Douglas , Torres Alfredo , Vidal Guifre , Villalonga Benjamin , Heidweiller Catherine Vollgraff , White Theodore , Woo Bryan , Xing Cheng , Yao Z. Jamie , Yeh Ping , Yoo Juhwan , Young Grayson , Zalcman Adam , Zhang Yaxing , Zhu Ningfeng , Zobrist Nicholas , Gogolin Christian , Babbush Ryan , Rubin Nicholas 
Published: November 2022

Abstract
An important measure of the development of quantum computing platforms has been the simulation of increasingly complex physical systems [1–3]. Prior to fault-tolerant quantum computing, robust error mitigation strategies are necessary to continue this growth [4–11]. Here, we study physical simulation within the seniority-zero electron pairing subspace, which affords both a computational stepping stone to a fully correlated model [12–17], and an opportunity to validate recently introduced “purification-based” error-mitigation strategies [8–10]. We compare the performance of error mitigation based on doubling quantum resources in time (echo verification [10]) or in space (virtual distillation [8, 9]), on up to 20 qubits of a superconducting qubit quantum processor. We observe a reduction of error by one to two orders of magnitude below less sophisticated techniques (e.g. post-selection); the gain from error mitigation is seen to increase with the system size. Employing these error mitigation strategies enables the implementation of the largest variational algorithm for a correlated chemistry system to-date. Extrapolating performance from these results allows us to estimate minimum requirements for a beyond-classical simulation of electronic structure. We find that, despite the impressive gains from purification-based error mitigation, significant hardware improvements will be required for classically intractable variational chemistry simulations.