Characterizing the many-body localization transition through correlations

Benjamin Villalonga, Bryan K. Clark

Closed, interacting, quantum systems have the potential to transition to a many-body localized (MBL) phase under the presence of sufficiently strong disorder, hence breaking ergodicity and failing to thermalize. In this work we study the distribution of correlations throughout the ergodic-MBL phase diagram. We find the typical correlations in the MBL phase decay as a stretched exponential with range $r$ eventually crossing over to an exponential decay deep in the MBL phase. At the transition, the stretched exponential goes as $e^{-A\sqrt{r}}$, a decay that is reminiscent of the random singlet phase. While the standard deviation of the $\log(QMI)$ has a range dependence, the $\log(QMI)$ converges to a range-invariant distribution on all other moments (i.e., the skewness and higher) at the transition. The universal nature of these distributions provides distinct phenomenology of the transition different from both the ergodic and MBL phenomenologies. In addition to the typical correlations, we study the extreme correlations in the system, finding that the probability of strong long-range correlations is maximal at the transition, suggesting the proliferation of resonances there. Finally, we analyze the probability that a single bit of information is shared across two halves of a system, finding that this probability is non-zero deep in the MBL phase but vanishes at moderate disorder well above the transition.

Efficient approximation of experimental Gaussian boson sampling

Benjamin Villalonga, Murphy Yuezhen Niu, Li Li, Hartmut Neven, John C. Platt, Vadim N. Smelyanskiy, Sergio Boixo

Two recent landmark experiments have performed Gaussian boson sampling (GBS) with a non-programmable linear interferometer and threshold detectors on up to 144 output modes (see Refs.~\onlinecite{zhong_quantum_2020,zhong2021phase}). Here we give classical sampling algorithms with better total variation distance and Kullback-Leibler divergence than these experiments and a computational cost quadratic in the number of modes. Our method samples from a distribution that approximates the single-mode and two-mode ideal marginals of the given Gaussian boson sampler, which are calculated efficiently. One implementation sets the parameters of a Boltzmann machine from the calculated marginals using a mean field solution. This is a 2nd order approximation, with the uniform and thermal approximations corresponding to the 0th and 1st order, respectively. The $k$th order approximation reproduces Ursell functions (also known as connected correlations) up to order $k$ with a cost exponential in $k$ and high precision, while the experiment exhibits higher order Ursell functions with lower precision. This methodology, like other polynomial approximations introduced previously, does not apply to random circuit sampling because the $k$th order approximation would simply result in the uniform distribution, in contrast to GBS.

A flexible high-performance simulator for verifying and benchmarking quantum circuits implemented on real hardware

Benjamin Villalonga, Sergio Boixo, Bron Nelson, Christopher Henze, Eleanor Rieffel, Rupak Biswas, Salvatore Mandrà

Here we present qFlex, a flexible tensor network based quantum circuit simulator. qFlex can compute both exact amplitudes, essential for the verification of the quantum hardware, as well as low fidelity amplitudes, in order to mimic sampling from Noisy Intermediate-Scale Quantum (NISQ) devices. In this work, we focus on random quantum circuits (RQCs) in the range of sizes expected for supremacy experiments. Fidelity $f$ simulations are performed at a cost that is $1/f$ lower than perfect fidelity ones. We also present a technique to eliminate the overhead introduced by rejection sampling in most tensor network approaches. We benchmark the simulation of square lattices and Google's Bristlecone QPU. Our analysis is supported by extensive simulations on NASA HPC clusters Pleiades and Electra. For our most computationally demanding simulation, the two clusters combined reached a peak of 20 PFLOPS (single precision), i.e., $64\%$ of their maximum achievable performance, which represents the largest numerical computation in terms of sustained FLOPs and number of nodes utilized ever run on NASA HPC clusters. Finally, we introduce a novel multithreaded, cache-efficient tensor index permutation algorithm of general application.

Lower bounding the MaxCut of high girth 3-regular graphs using the QAOA

Edward Farhi, Sam Gutmann, Daniel Ranard, Benjamin Villalonga

We study MaxCut on 3-regular graphs of minimum girth $g$ for various $g$'s. We obtain new lower bounds on the maximum cut achievable in such graphs by analyzing the Quantum Approximate Optimization Algorithm (QAOA). For $g \geq 16$, at depth $p \geq 7$, the QAOA improves on previously known lower bounds. Our bounds are established through classical numerical analysis of the QAOA's expected performance. This analysis does not produce the actual cuts but establishes their existence. When implemented on a quantum computer, the QAOA provides an efficient algorithm for finding such cuts, using a constant-depth quantum circuit. To our knowledge, this gives an exponential speedup over the best known classical algorithm guaranteed to achieve cuts of this size on graphs of this girth. We also apply the QAOA to the Maximum Independent Set problem on the same class of graphs.

Eigenstates hybridize on all length scales at the many-body localization transition

Benjamin Villalonga, Bryan K. Clark

An interacting quantum system can transition from an ergodic to a many-body localized (MBL) phase under the presence of sufficiently large disorder. Both phases are radically different in their dynamical properties, which are characterized by highly excited eigenstates of the Hamiltonian. Each eigenstate can be characterized by the set of quantum numbers over the set of (local, in the MBL phase) integrals of motion of the system. In this work we study the evolution of the eigenstates of the disordered Heisenberg model as the disorder strength, $W$, is varied adiabatically. We focus on the probability that two `colliding' eigenstates hybridize as a function of both the range $R$ at which they differ as well as the strength of their hybridization. We find, in the MBL phase, that the probability of a colliding eigenstate hybridizing strongly at range $R$ decays as $Pr(R)\propto \exp [-R/η]$, with a length scale $η(W) = 1 / (B \log(W / W_c) )$ which diverges at the critical disorder strength $W_c$. This leads to range-invariance at the transition, suggesting the formation of resonating cat states at all ranges. This range invariance does not survive to the ergodic phase, where hybridization is exponentially more likely at large range, a fact that can be understood with simple combinatorial arguments. In fact, compensating for these combinatorial effects allows us to define an additional correlation length $ξ$ in the MBL phase which is in excellent agreement with previous works and which takes the critical value $1 / \log(2)$ at the transition, found in previous works to destabilize the MBL phase. Finally, we show that deep in the MBL phase hybridization is dominated by two-level collisions of eigenstates close in energy.

Efficient near-optimal decoding of the surface code through ensembling

Noah Shutty, Michael Newman, Benjamin Villalonga

We introduce harmonization, an ensembling method that combines several "noisy" decoders to generate highly accurate decoding predictions. Harmonized ensembles of MWPM-based decoders achieve lower logical error rates than their individual counterparts on repetition and surface code benchmarks, approaching maximum-likelihood accuracy at large ensemble sizes. We can use the degree of consensus among the ensemble as a confidence measure for a layered decoding scheme, in which a small ensemble flags high-risk cases to be checked by a larger, more accurate ensemble. This layered scheme can realize the accuracy improvements of large ensembles with a relatively small constant factor of computational overhead. We conclude that harmonization provides a viable path towards highly accurate real-time decoding.

Exploring one particle orbitals in large Many-Body Localized systems

Benjamin Villalonga, Xiongjie Yu, David J. Luitz, Bryan K. Clark

Strong disorder in interacting quantum systems can give rise to the phenomenon of Many-Body Localization (MBL), which defies thermalization due to the formation of an extensive number of quasi local integrals of motion. The one particle operator content of these integrals of motion is related to the one particle orbitals of the one particle density matrix and shows a strong signature across the MBL transition as recently pointed out by Bera et al. [Phys. Rev. Lett. 115, 046603 (2015); Ann. Phys. 529, 1600356 (2017)]. We study the properties of the one particle orbitals of many-body eigenstates of an MBL system in one dimension. Using shift-and-invert MPS (SIMPS), a matrix product state method to target highly excited many-body eigenstates introduced in [Phys. Rev. Lett. 118, 017201 (2017)], we are able to obtain accurate results for large systems of sizes up to L = 64. We find that the one particle orbitals drawn from eigenstates at different energy densities have high overlap and their occupations are correlated with the energy of the eigenstates. Moreover, the standard deviation of the inverse participation ratio of these orbitals is maximal at the nose of the mobility edge. Also, the one particle orbitals decay exponentially in real space, with a correlation length that increases at low disorder. In addition, we find a 1/f distribution of the coupling constants of a certain range of the number operators of the OPOs, which is related to their exponential decay.

Numerical evidence for many-body localization in two and three dimensions

Eli Chertkov, Benjamin Villalonga, Bryan K. Clark

Disorder and interactions can lead to the breakdown of statistical mechanics in certain quantum systems, a phenomenon known as many-body localization (MBL). Much of the phenomenology of MBL emerges from the existence of $\ell$-bits, a set of conserved quantities that are quasilocal and binary (i.e., possess only $\pm 1$ eigenvalues). While MBL and $\ell$-bits are known to exist in one-dimensional systems, their existence in dimensions greater than one is a key open question. To tackle this question, we develop an algorithm that can find approximate binary $\ell$-bits in arbitrary dimensions by adaptively generating a basis of operators in which to represent the $\ell$-bit. We use the algorithm to study four models: the one-, two-, and three-dimensional disordered Heisenberg models and the two-dimensional disordered hard-core Bose-Hubbard model. For all four of the models studied, our algorithm finds high-quality $\ell$-bits at large disorder strength and rapid qualitative changes in the distributions of $\ell$-bits in particular ranges of disorder strengths, suggesting the existence of MBL transitions. These transitions in the one-dimensional Heisenberg model and two-dimensional Bose-Hubbard model coincide well with past estimates of the critical disorder strengths in these models which further validates the evidence of MBL phenomenology in the other two and three-dimensional models we examine. In addition to finding MBL behavior in higher dimensions, our algorithm can be used to probe MBL in various geometries and dimensionality.

Tensor networks for quantum computing

Aleksandr Berezutskii, Minzhao Liu, Atithi Acharya, Roman Ellerbrock, Johnnie Gray, Reza Haghshenas, Zichang He, Abid Khan, Viacheslav Kuzmin, Dmitry Lyakh, Danylo Lykov, Salvatore Mandrà, Christopher Mansell, Alexey Melnikov, Artem Melnikov, Vladimir Mironov, Dmitry Morozov, Florian Neukart, Alberto Nocera, Michael A. Perlin, Michael Perelshtein, Matthew Steinberg, Ruslan Shaydulin, Benjamin Villalonga, Markus Pflitsch, Marco Pistoia, Valerii Vinokur, Yuri Alexeev

In the rapidly evolving field of quantum computing, tensor networks serve as an important tool due to their multifaceted utility. In this paper, we review the diverse applications of tensor networks and show that they are an important instrument for quantum computing. Specifically, we summarize the application of tensor networks in various domains of quantum computing, including simulation of quantum computation, quantum circuit synthesis, quantum error correction and mitigation, and quantum machine learning. Finally, we provide an outlook on the opportunities and the challenges of the tensor-network techniques.

Bose-Hubbard models with photon pairing in circuit-QED

Benjamin Villalonga Correa, Andreas Kurcz, Juan jose Garcia-Ripoll

In this work we study a family of bosonic lattice models that combine an on-site repulsion term with a nearest-neighbor pairing term, $\sum_{< i,j>} a^\dagger_i a^\dagger_j + \mathrm{H.c.}$ Like the original Bose-Hubbard model, the nearest-neighbor term is responsible for the mobility of bosons and it competes with the local interaction, inducing two-mode squeezing. However, unlike a trivial hopping, the counter-rotating terms form pairing cannot be studied with a simple mean-field theory and does not present a quantum phase transition in phase space. Instead, we show that there is a cross-over from a pure insulator to long-range correlations that start up as soon as the two-mode squeezing is switched on. We also show how this model can be naturally implemented using coupled microwave resonators and superconducting qubits.

Noise-resilient Edge Modes on a Chain of Superconducting Qubits

Xiao Mi, Michael Sonner, Murphy Yuezhen Niu, Kenneth W. Lee, Brooks Foxen, Rajeev Acharya, Igor Aleiner, Trond I. Andersen, Frank Arute, Kunal Arya, Abraham Asfaw, Juan Atalaya, Ryan Babbush, Dave Bacon, Joseph C. Bardin, Joao Basso, Andreas Bengtsson, Gina Bortoli, Alexandre Bourassa, Leon Brill, Michael Broughton, Bob B. Buckley, David A. Buell, Brian Burkett, Nicholas Bushnell, Zijun Chen, Benjamin Chiaro, Roberto Collins, Paul Conner, William Courtney, Alexander L. Crook, Dripto M. Debroy, Sean Demura, Andrew Dunsworth, Daniel Eppens, Catherine Erickson, Lara Faoro, Edward Farhi, Reza Fatemi, Leslie Flores, Ebrahim Forati, Austin G. Fowler, William Giang, Craig Gidney, Dar Gilboa, Marissa Giustina, Alejandro Grajales Dau, Jonathan A. Gross, Steve Habegger, Matthew P. Harrigan, Jeremy Hilton, Markus Hoffmann, Sabrina Hong, Trent Huang, Ashley Huff, William J. Huggins, Lev B. Ioffe, Sergei V. Isakov, Justin Iveland, Evan Jeffrey, Zhang Jiang, Cody Jones, Dvir Kafri, Kostyantyn Kechedzhi, Tanuj Khattar, Seon Kim, Alexei Kitaev, Paul V. Klimov, Andrey R. Klots, Alexander N. Korotkov, Fedor Kostritsa, J. M. Kreikebaum, David Landhuis, Pavel Laptev, Kim-Ming Lau, Joonho Lee, Lily Laws, Wayne Liu, Aditya Locharla, Erik Lucero, Orion Martin, Jarrod R. McClean, Matt McEwen, Bernardo Meurer Costa, Kevin C. Miao, Masoud Mohseni, Shirin Montazeri, Alexis Morvan, Emily Mount, Wojciech Mruczkiewicz, Ofer Naaman, Matthew Neeley, Charles Neill, Michael Newman, Thomas E. O'Brien, Alex Opremcak, Andre Petukhov, Rebecca Potter, Chris Quintana, Nicholas C. Rubin, Negar Saei, Daniel Sank, Kannan Sankaragomathi, Kevin J. Satzinger, Christopher Schuster, Michael J. Shearn, Vladimir Shvarts, Doug Strain, Yuan Su, Marco Szalay, Guifre Vidal, Benjamin Villalonga, Catherine Vollgraff-Heidweiller, Theodore White, Z. Jamie Yao, Ping Yeh, Juhwan Yoo, Adam Zalcman, Yaxing Zhang, Ningfeng Zhu, Hartmut Neven, Sergio Boixo, Anthony Megrant, Yu Chen, Julian Kelly, Vadim Smelyanskiy, Dmitry A. Abanin, Pedram Roushan

Measurement-induced entanglement and teleportation on a noisy quantum processor

Jesse C. Hoke, Matteo Ippoliti, Eliott Rosenberg, Dmitry Abanin, Rajeev Acharya, Trond I. Andersen, Markus Ansmann, Frank Arute, Kunal Arya, Abraham Asfaw, Juan Atalaya, Joseph C. Bardin, Andreas Bengtsson, Gina Bortoli, Alexandre Bourassa, Jenna Bovaird, Leon Brill, Michael Broughton, Bob B. Buckley, David A. Buell, Tim Burger, Brian Burkett, Nicholas Bushnell, Zijun Chen, Ben Chiaro, Desmond Chik, Josh Cogan, Roberto Collins, Paul Conner, William Courtney, Alexander L. Crook, Ben Curtin, Alejandro Grajales Dau, Dripto M. Debroy, Alexander Del Toro Barba, Sean Demura, Augustin Di Paolo, Ilya K. Drozdov, Andrew Dunsworth, Daniel Eppens, Catherine Erickson, Edward Farhi, Reza Fatemi, Vinicius S. Ferreira, Leslie Flores Burgos, Ebrahim Forati, Austin G. Fowler, Brooks Foxen, William Giang, Craig Gidney, Dar Gilboa, Marissa Giustina, Raja Gosula, Jonathan A. Gross, Steve Habegger, Michael C. Hamilton, Monica Hansen, Matthew P. Harrigan, Sean D. Harrington, Paula Heu, Markus R. Hoffmann, Sabrina Hong, Trent Huang, Ashley Huff, William J. Huggins, Sergei V. Isakov, Justin Iveland, Evan Jeffrey, Cody Jones, Pavol Juhas, Dvir Kafri, Kostyantyn Kechedzhi, Tanuj Khattar, Mostafa Khezri, Mária Kieferová, Seon Kim, Alexei Kitaev, Paul V. Klimov, Andrey R. Klots, Alexander N. Korotkov, Fedor Kostritsa, John Mark Kreikebaum, David Landhuis, Pavel Laptev, Kim-Ming Lau, Lily Laws, Joonho Lee, Kenny W. Lee, Yuri D. Lensky, Brian J. Lester, Alexander T. Lill, Wayne Liu, Aditya Locharla, Orion Martin, Jarrod R. McClean, Matt McEwen, Kevin C. Miao, Amanda Mieszala, Shirin Montazeri, Alexis Morvan, Ramis Movassagh, Wojciech Mruczkiewicz, Matthew Neeley, Charles Neill, Ani Nersisyan, Michael Newman, Jiun H. Ng, Anthony Nguyen, Murray Nguyen, Murphy Yuezhen Niu, Tom E. O'Brien, Seun Omonije, Alex Opremcak, Andre Petukhov, Rebecca Potter, Leonid P. Pryadko, Chris Quintana, Charles Rocque, Nicholas C. Rubin, Negar Saei, Daniel Sank, Kannan Sankaragomathi, Kevin J. Satzinger, Henry F. Schurkus, Christopher Schuster, Michael J. Shearn, Aaron Shorter, Noah Shutty, Vlad Shvarts, Jindra Skruzny, W. Clarke Smith, Rolando D. Somma, George Sterling, Douglas Strain, Marco Szalay, Alfredo Torres, Guifre Vidal, Benjamin Villalonga, Catherine Vollgraff Heidweiller, Ted White, Bryan W. K. Woo, Cheng Xing, Z. Jamie. Yao, Ping Yeh, Juhwan Yoo, Grayson Young, Adam Zalcman, Yaxing Zhang, Ningfeng Zhu, Nicholas Zobrist, Harmut Neven, Ryan Babbush, Dave Bacon, Sergio Boixo, Jeremy Hilton, Erik Lucero, Anthony Megrant, Julian Kelly, Yu Chen, Vadim Smelyanskiy, Xiao Mi, Vedika Khemani, Pedram Roushan

Observation of Time-Crystalline Eigenstate Order on a Quantum Processor

Xiao Mi, Matteo Ippoliti, Chris Quintana, Ami Greene, Zijun Chen, Jonathan Gross, Frank Arute, Kunal Arya, Juan Atalaya, Ryan Babbush, Joseph C. Bardin, Joao Basso, Andreas Bengtsson, Alexander Bilmes, Alexandre Bourassa, Leon Brill, Michael Broughton, Bob B. Buckley, David A. Buell, Brian Burkett, Nicholas Bushnell, Benjamin Chiaro, Roberto Collins, William Courtney, Dripto Debroy, Sean Demura, Alan R. Derk, Andrew Dunsworth, Daniel Eppens, Catherine Erickson, Edward Farhi, Austin G. Fowler, Brooks Foxen, Craig Gidney, Marissa Giustina, Matthew P. Harrigan, Sean D. Harrington, Jeremy Hilton, Alan Ho, Sabrina Hong, Trent Huang, Ashley Huff, William J. Huggins, L. B. Ioffe, Sergei V. Isakov, Justin Iveland, Evan Jeffrey, Zhang Jiang, Cody Jones, Dvir Kafri, Tanuj Khattar, Seon Kim, Alexei Kitaev, Paul V. Klimov, Alexander N. Korotkov, Fedor Kostritsa, David Landhuis, Pavel Laptev, Joonho Lee, Kenny Lee, Aditya Locharla, Erik Lucero, Orion Martin, Jarrod R. McClean, Trevor McCourt, Matt McEwen, Kevin C. Miao, Masoud Mohseni, Shirin Montazeri, Wojciech Mruczkiewicz, Ofer Naaman, Matthew Neeley, Charles Neill, Michael Newman, Murphy Yuezhen Niu, Thomas E. O\' Brien, Alex Opremcak, Eric Ostby, Balint Pato, Andre Petukhov, Nicholas C. Rubin, Daniel Sank, Kevin J. Satzinger, Vladimir Shvarts, Yuan Su, Doug Strain, Marco Szalay, Matthew D. Trevithick, Benjamin Villalonga, Theodore White, Z. Jamie Yao, Ping Yeh, Juhwan Yoo, Adam Zalcman, Hartmut Neven, Sergio Boixo, Vadim Smelyanskiy, Anthony Megrant, Julian Kelly, Yu Chen, S. L. Sondhi, Roderich Moessner, Kostyantyn Kechedzhi, Vedika Khemani, Pedram Roushan

Quantum many-body systems display rich phase structure in their low-temperature equilibrium states. However, much of nature is not in thermal equilibrium. Remarkably, it was recently predicted that out-of-equilibrium systems can exhibit novel dynamical phases that may otherwise be forbidden by equilibrium thermodynamics, a paradigmatic example being the discrete time crystal (DTC). Concretely, dynamical phases can be defined in periodically driven many-body localized systems via the concept of eigenstate order. In eigenstate-ordered phases, the entire many-body spectrum exhibits quantum correlations and long-range order, with characteristic signatures in late-time dynamics from all initial states. It is, however, challenging to experimentally distinguish such stable phases from transient phenomena, wherein few select states can mask typical behavior. Here we implement a continuous family of tunable CPHASE gates on an array of superconducting qubits to experimentally observe an eigenstate-ordered DTC. We demonstrate the characteristic spatiotemporal response of a DTC for generic initial states. Our work employs a time-reversal protocol that discriminates external decoherence from intrinsic thermalization, and leverages quantum typicality to circumvent the exponential cost of densely sampling the eigenspectrum. In addition, we locate the phase transition out of the DTC with an experimental finite-size analysis. These results establish a scalable approach to study non-equilibrium phases of matter on current quantum processors.

Quantum error correction below the surface code threshold

Rajeev Acharya, Laleh Aghababaie-Beni, Igor Aleiner, Trond I. Andersen, Markus Ansmann, Frank Arute, Kunal Arya, Abraham Asfaw, Nikita Astrakhantsev, Juan Atalaya, Ryan Babbush, Dave Bacon, Brian Ballard, Joseph C. Bardin, Johannes Bausch, Andreas Bengtsson, Alexander Bilmes, Sam Blackwell, Sergio Boixo, Gina Bortoli, Alexandre Bourassa, Jenna Bovaird, Leon Brill, Michael Broughton, David A. Browne, Brett Buchea, Bob B. Buckley, David A. Buell, Tim Burger, Brian Burkett, Nicholas Bushnell, Anthony Cabrera, Juan Campero, Hung-Shen Chang, Yu Chen, Zijun Chen, Ben Chiaro, Desmond Chik, Charina Chou, Jahan Claes, Agnetta Y. Cleland, Josh Cogan, Roberto Collins, Paul Conner, William Courtney, Alexander L. Crook, Ben Curtin, Sayan Das, Alex Davies, Laura De Lorenzo, Dripto M. Debroy, Sean Demura, Michel Devoret, Agustin Di Paolo, Paul Donohoe, Ilya Drozdov, Andrew Dunsworth, Clint Earle, Thomas Edlich, Alec Eickbusch, Aviv Moshe Elbag, Mahmoud Elzouka, Catherine Erickson, Lara Faoro, Edward Farhi, Vinicius S. Ferreira, Leslie Flores Burgos, Ebrahim Forati, Austin G. Fowler, Brooks Foxen, Suhas Ganjam, Gonzalo Garcia, Robert Gasca, Élie Genois, William Giang, Craig Gidney, Dar Gilboa, Raja Gosula, Alejandro Grajales Dau, Dietrich Graumann, Alex Greene, Jonathan A. Gross, Steve Habegger, John Hall, Michael C. Hamilton, Monica Hansen, Matthew P. Harrigan, Sean D. Harrington, Francisco J. H. Heras, Stephen Heslin, Paula Heu, Oscar Higgott, Gordon Hill, Jeremy Hilton, George Holland, Sabrina Hong, Hsin-Yuan Huang, Ashley Huff, William J. Huggins, Lev B. Ioffe, Sergei V. Isakov, Justin Iveland, Evan Jeffrey, Zhang Jiang, Cody Jones, Stephen Jordan, Chaitali Joshi, Pavol Juhas, Dvir Kafri, Hui Kang, Amir H. Karamlou, Kostyantyn Kechedzhi, Julian Kelly, Trupti Khaire, Tanuj Khattar, Mostafa Khezri, Seon Kim, Paul V. Klimov, Andrey R. Klots, Bryce Kobrin, Pushmeet Kohli, Alexander N. Korotkov, Fedor Kostritsa, Robin Kothari, Borislav Kozlovskii, John Mark Kreikebaum, Vladislav D. Kurilovich, Nathan Lacroix, David Landhuis, Tiano Lange-Dei, Brandon W. Langley, Pavel Laptev, Kim-Ming Lau, Loïck Le Guevel, Justin Ledford, Kenny Lee, Yuri D. Lensky, Shannon Leon, Brian J. Lester, Wing Yan Li, Yin Li, Alexander T. Lill, Wayne Liu, William P. Livingston, Aditya Locharla, Erik Lucero, Daniel Lundahl, Aaron Lunt, Sid Madhuk, Fionn D. Malone, Ashley Maloney, Salvatore Mandrá, Leigh S. Martin, Steven Martin, Orion Martin, Cameron Maxfield, Jarrod R. McClean, Matt McEwen, Seneca Meeks, Anthony Megrant, Xiao Mi, Kevin C. Miao, Amanda Mieszala, Reza Molavi, Sebastian Molina, Shirin Montazeri, Alexis Morvan, Ramis Movassagh, Wojciech Mruczkiewicz, Ofer Naaman, Matthew Neeley, Charles Neill, Ani Nersisyan, Hartmut Neven, Michael Newman, Jiun How Ng, Anthony Nguyen, Murray Nguyen, Chia-Hung Ni, Thomas E. O'Brien, William D. Oliver, Alex Opremcak, Kristoffer Ottosson, Andre Petukhov, Alex Pizzuto, John Platt, Rebecca Potter, Orion Pritchard, Leonid P. Pryadko, Chris Quintana, Ganesh Ramachandran, Matthew J. Reagor, David M. Rhodes, Gabrielle Roberts, Eliott Rosenberg, Emma Rosenfeld, Pedram Roushan, Nicholas C. Rubin, Negar Saei, Daniel Sank, Kannan Sankaragomathi, Kevin J. Satzinger, Henry F. Schurkus, Christopher Schuster, Andrew W. Senior, Michael J. Shearn, Aaron Shorter, Noah Shutty, Vladimir Shvarts, Shraddha Singh, Volodymyr Sivak, Jindra Skruzny, Spencer Small, Vadim Smelyanskiy, W. Clarke Smith, Rolando D. Somma, Sofia Springer, George Sterling, Doug Strain, Jordan Suchard, Aaron Szasz, Alex Sztein, Douglas Thor, Alfredo Torres, M. Mert Torunbalci, Abeer Vaishnav, Justin Vargas, Sergey Vdovichev, Guifre Vidal, Benjamin Villalonga, Catherine Vollgraff Heidweiller, Steven Waltman, Shannon X. Wang, Brayden Ware, Kate Weber, Theodore White, Kristi Wong, Bryan W. K. Woo, Cheng Xing, Z. Jamie Yao, Ping Yeh, Bicheng Ying, Juhwan Yoo, Noureldin Yosri, Grayson Young, Adam Zalcman, Yaxing Zhang, Ningfeng Zhu, Nicholas Zobrist

Unitary Block Optimization for Variational Quantum Algorithms

Lucas Slattery, Benjamin Villalonga, Bryan K. Clark

Variational quantum algorithms are a promising hybrid framework for solving chemistry and physics problems with broad applicability to optimization as well. They are particularly well suited for noisy intermediate scale quantum (NISQ) computers. In this paper, we describe the unitary block optimization scheme (UBOS) and apply it to two variational quantum algorithms: the variational quantum eigensolver (VQE) and variational time evolution. The goal of VQE is to optimize a classically intractable parameterized quantum wave function to target a physical state of a Hamiltonian or solve an optimization problem. UBOS is an alternative to other VQE optimization schemes with a number of advantages including fast convergence, less sensitivity to barren plateaus, the ability to tunnel through some local minima and no hyperparameters to tune. We additionally describe how UBOS applies to real and imaginary time-evolution (TUBOS).

The Quantum Approximate Optimization Algorithm at High Depth for MaxCut on Large-Girth Regular Graphs and the Sherrington-Kirkpatrick Model

Joao Basso, Edward Farhi, Kunal Marwaha, Benjamin Villalonga, Leo Zhou

The Quantum Approximate Optimization Algorithm (QAOA) finds approximate solutions to combinatorial optimization problems. Its performance monotonically improves with its depth $p$. We apply the QAOA to MaxCut on large-girth $D$-regular graphs. We give an iterative formula to evaluate performance for any $D$ at any depth $p$. Looking at random $D$-regular graphs, at optimal parameters and as $D$ goes to infinity, we find that the $p=11$ QAOA beats all classical algorithms (known to the authors) that are free of unproven conjectures. While the iterative formula for these $D$-regular graphs is derived by looking at a single tree subgraph, we prove that it also gives the ensemble-averaged performance of the QAOA on the Sherrington-Kirkpatrick (SK) model defined on the complete graph. We also generalize our formula to Max-$q$-XORSAT on large-girth regular hypergraphs. Our iteration is a compact procedure, but its computational complexity grows as $O(p^2 4^p)$. This iteration is more efficient than the previous procedure for analyzing QAOA performance on the SK model, and we are able to numerically go to $p=20$. Encouraged by our findings, we make the optimistic conjecture that the QAOA, as $p$ goes to infinity, will achieve the Parisi value. We analyze the performance of the quantum algorithm, but one needs to run it on a quantum computer to produce a string with the guaranteed performance.

Information Scrambling in Computationally Complex Quantum Circuits

Xiao Mi, Pedram Roushan, Chris Quintana, Salvatore Mandra, Jeffrey Marshall, Charles Neill, Frank Arute, Kunal Arya, Juan Atalaya, Ryan Babbush, Joseph C. Bardin, Rami Barends, Andreas Bengtsson, Sergio Boixo, Alexandre Bourassa, Michael Broughton, Bob B. Buckley, David A. Buell, Brian Burkett, Nicholas Bushnell, Zijun Chen, Benjamin Chiaro, Roberto Collins, William Courtney, Sean Demura, Alan R. Derk, Andrew Dunsworth, Daniel Eppens, Catherine Erickson, Edward Farhi, Austin G. Fowler, Brooks Foxen, Craig Gidney, Marissa Giustina, Jonathan A. Gross, Matthew P. Harrigan, Sean D. Harrington, Jeremy Hilton, Alan Ho, Sabrina Hong, Trent Huang, William J. Huggins, L. B. Ioffe, Sergei V. Isakov, Evan Jeffrey, Zhang Jiang, Cody Jones, Dvir Kafri, Julian Kelly, Seon Kim, Alexei Kitaev, Paul V. Klimov, Alexander N. Korotkov, Fedor Kostritsa, David Landhuis, Pavel Laptev, Erik Lucero, Orion Martin, Jarrod R. McClean, Trevor McCourt, Matt McEwen, Anthony Megrant, Kevin C. Miao, Masoud Mohseni, Wojciech Mruczkiewicz, Josh Mutus, Ofer Naaman, Matthew Neeley, Michael Newman, Murphy Yuezhen Niu, Thomas E. O'Brien, Alex Opremcak, Eric Ostby, Balint Pato, Andre Petukhov, Nicholas Redd, Nicholas C. Rubin, Daniel Sank, Kevin J. Satzinger, Vladimir Shvarts, Doug Strain, Marco Szalay, Matthew D. Trevithick, Benjamin Villalonga, Theodore White, Z. Jamie Yao, Ping Yeh, Adam Zalcman, Hartmut Neven, Igor Aleiner, Kostyantyn Kechedzhi, Vadim Smelyanskiy, Yu Chen

Interaction in quantum systems can spread initially localized quantum information into the many degrees of freedom of the entire system. Understanding this process, known as quantum scrambling, is the key to resolving various conundrums in physics. Here, by measuring the time-dependent evolution and fluctuation of out-of-time-order correlators, we experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We engineer quantum circuits that distinguish the two mechanisms associated with quantum scrambling, operator spreading and operator entanglement, and experimentally observe their respective signatures. We show that while operator spreading is captured by an efficient classical model, operator entanglement requires exponentially scaled computational resources to simulate. These results open the path to studying complex and practically relevant physical observables with near-term quantum processors.

Observation of disorder-induced superfluidity

Nicole Ticea, Elias Portoles, Eliott Rosenberg, Alexander Schuckert, Aaron Szasz, Bryce Kobrin, Nicolas Pomata, Pranjal Praneel, Connie Miao, Shashwat Kumar, Ella Crane, Ilya Drozdov, Yuri Lensky, Sofia Gonzalez-Garcia, Thomas Kiely, Dmitry Abanin, Amira Abbas, Rajeev Acharya, Laleh Aghababaie Beni, Georg Aigeldinger, Ross Alcaraz, Sayra Alcaraz, Markus Ansmann, Frank Arute, Kunal Arya, Walt Askew, Nikita Astrakhantsev, Juan Atalaya, Ryan Babbush, Brian Ballard, Hector Bates, Andreas Bengtsson, Majid Bigdeli Karimi, Alexander Bilmes, Simon Bilodeau, Felix Borjans, Alexandre Bourassa, Jenna Bovaird, Dylan Bowers, Leon Brill, Peter Brooks, Michael Broughton, David A. Browne, Brett Buchea, Bob B. Buckley, Tim Burger, Brian Burkett, Jamal Busnaina, Nicholas Bushnell, Anthony Cabrera, Juan Campero, Hung-Shen Chang, Silas Chen, Zijun Chen, Ben Chiaro, Liang-Ying Chih, Agnetta Y. Cleland, Bryan Cochrane, Matt Cockrell, Josh Cogan, Paul Conner, Harold Cook, Rodrigo G. Cortiñas, William Courtney, Alexander L. Crook, Ben Curtin, Sayan Das, Martin Damyanov, Dripto M. Debroy, Stijn J. de Graaf, Laura De Lorenzo, Sean Demura, Lucia B. De Rose, Agustin Di Paolo, Paul Donohoe, Andrew Dunsworth, Valerie Ehimhen, Alec Eickbusch, Aviv Moshe Elbag, Lior Ella, Mahmoud Elzouka, David Enriquez, Catherine Erickson, Lara Faoro, Vinicius S. Ferreira, Marcos Flores, Leslie Flores Burgos, Sam Fontes, Ebrahim Forati, Jeremiah Ford, Brooks Foxen, Masaya Fukami, Alan Wing Lun Fung, Lenny Fuste, Suhas Ganjam, Gonzalo Garcia, Christopher Garrick, Robert Gasca, Helge Gehring, Robert Geiger, Élie Genois, William Giang, Dar Gilboa, James E. Goeders, Edward C. Gonzales, Raja Gosula, Alejandro Grajales Dau, Dietrich Graumann, Joel Grebel, Alex Greene, Jonathan A. Gross, Jose Guerrero, Tan Ha, Steve Habegger, Tanner Hadick, Ali Hadjikhani, Monica Hansen, Matthew P. Harrigan, Sean D. Harrington, Jeanne Hartshorn, Stephen Heslin, Paula Heu, Oscar Higgott, Reno Hiltermann, Jeremy Hilton, Hsin-Yuan Huang, Mike Hucka, Christopher Hudspeth, Ashley Huff, William J. Huggins, Evan Jeffrey, Shaun Jevons, Zhang Jiang, Xiaoxuan Jin, Cody Jones, Chaitali Joshi, Pavol Juhas, Andreas Kabel, Dvir Kafri, Hui Kang, Kiseo Kang, Amir H. Karamlou, Ryan Kaufman, Kostyantyn Kechedzhi, Julian Kelly, Tanuj Khattar, Mostafa Khezri, Seon Kim, Paul V. Klimov, Can M. Knaut, Alexander N. Korotkov, Fedor Kostritsa, John Mark Kreikebaum, Ryuho Kudo, Arun Kumar, Ben Kueffler, Vladislav D. Kurilovich, Vitali Kutsko, Nathan Lacroix, Tiano Lange-Dei, Brandon W. Langley, Pavel Laptev, Kim-Ming Lau, Emma Leavell, Loick Le Guevel, Justin Ledford, Joy Lee, Kenny Lee, Brian J. Lester, Wendy Leung, Matthew T. Lloyd, Lily L Li, Wing Yan Li, Ming Li, Alexander T. Lill, William P. Livingston, Aditya Locharla, Erik Lucero, Daniel Lundahl, Aaron Lunt, Sid Madhuk, Aniket Maiti, Ashley Maloney, Salvatore Mandrà, Leigh S. Martin, Orion Martin, Eric Mascot, Paul Masih Das, Dmitri Maslov, Melvin Mathews, Cameron Maxfield, Jarrod R. McClean, Matt McEwen, Seneca Meeks, Anthony Megrant, Kevin C. Miao, Reza Molavi, Sebastian Molina, Shirin Montazeri, Charles Neill, Michael Newman, Anthony Nguyen, Murray Nguyen, Chia-Hung Ni, Murphy Yuezhen Niu, Nicholas Noll, Logan Oas, William D. Oliver, Raymond Orosco, Kristoffer Ottosson, Alice Pagano, Sherman Peek, David Peterson, Alex Pizzuto, Rebecca Potter, Orion Pritchard, Michael Qian, Chris Quintana, Arpit Ranadive, Ganesh Ramachandran, Matthew J. Reagor, Rachel Resnick, David M. Rhodes, Daniel Riley, Gabrielle Roberts, Roberto Rodriguez, Emma Ropes, Eliott Rosenberg, Emma Rosenfeld, Dario Rosenstock, Elizabeth Rossi, David A. Rower, Robert Salazar, Kannan Sankaragomathi, Murat Can Sarihan, Kevin J. Satzinger, Sebastian Schroeder, Henry F. Schurkus, Aria Shahingohar, Michael J. Shearn, Aaron Shorter, Vladimir Shvarts, Volodymyr Sivak, Spencer Small, W. Clarke Smith, David A. Sobel, Barrett Spells, Sofia Springer, George Sterling, Jordan Suchard, Alexander Sztein, Madeline Taylor, Jothi Priyanka Thiruraman, Douglas Thor, Dogan Timucin, Eifu Tomita, Alfredo Torres, M. Mert Torunbalci, Hao Tran, Abeer Vaishnav, Justin Vargas, Sergey Vdovichev, Benjamin Villalonga, Catherine Vollgraff Heidweiller, Meghan Voorhees, Steven Waltman, Jonathan Waltz, Shannon X. Wang, Danni Wang, Brayden Ware, James D. Watson, Yonghua Wei, Travis Weidel, Theodore White, Kristi Wong, Bryan W. K. Woo, Christopher J. Wood, Maddy Woodson, Cheng Xing, Z. Jamie Yao, Ping Yeh, Bicheng Ying, Juhwan Yoo, Noureldin Yosri, Elliot Young, Grayson Young, Adam Zalcman, Ran Zhang, Yaxing Zhang, Ningfeng Zhu, Nicholas Zobrist, Zhenjie Zou, Sergio Boixo, Hartmut Neven, Vadim Smelyanskiy, Guifre Vidal, Erich Mueller, Trond Andersen, Lev Ioffe, Andre Petukhov, Mohammad Hafezi, Pedram Roushan

Thermalization and Criticality on an Analog-Digital Quantum Simulator

Trond I. Andersen, Nikita Astrakhantsev, Amir H. Karamlou, Julia Berndtsson, Johannes Motruk, Aaron Szasz, Jonathan A. Gross, Alexander Schuckert, Tom Westerhout, Yaxing Zhang, Ebrahim Forati, Dario Rossi, Bryce Kobrin, Agustin Di Paolo, Andrey R. Klots, Ilya Drozdov, Vladislav D. Kurilovich, Andre Petukhov, Lev B. Ioffe, Andreas Elben, Aniket Rath, Vittorio Vitale, Benoit Vermersch, Rajeev Acharya, Laleh Aghababaie Beni, Kyle Anderson, Markus Ansmann, Frank Arute, Kunal Arya, Abraham Asfaw, Juan Atalaya, Brian Ballard, Joseph C. Bardin, Andreas Bengtsson, Alexander Bilmes, Gina Bortoli, Alexandre Bourassa, Jenna Bovaird, Leon Brill, Michael Broughton, David A. Browne, Brett Buchea, Bob B. Buckley, David A. Buell, Tim Burger, Brian Burkett, Nicholas Bushnell, Anthony Cabrera, Juan Campero, Hung-Shen Chang, Zijun Chen, Ben Chiaro, Jahan Claes, Agnetta Y. Cleland, Josh Cogan, Roberto Collins, Paul Conner, William Courtney, Alexander L. Crook, Sayan Das, Dripto M. Debroy, Laura De Lorenzo, Alexander Del Toro Barba, Sean Demura, Paul Donohoe, Andrew Dunsworth, Clint Earle, Alec Eickbusch, Aviv Moshe Elbag, Mahmoud Elzouka, Catherine Erickson, Lara Faoro, Reza Fatemi, Vinicius S. Ferreira, Leslie Flores Burgos, Austin G. Fowler, Brooks Foxen, Suhas Ganjam, Robert Gasca, William Giang, Craig Gidney, Dar Gilboa, Marissa Giustina, Raja Gosula, Alejandro Grajales Dau, Dietrich Graumann, Alex Greene, Steve Habegger, Michael C. Hamilton, Monica Hansen, Matthew P. Harrigan, Sean D. Harrington, Stephen Heslin, Paula Heu, Gordon Hill, Markus R. Hoffmann, Hsin-Yuan Huang, Trent Huang, Ashley Huff, William J. Huggins, Sergei V. Isakov, Evan Jeffrey, Zhang Jiang, Cody Jones, Stephen Jordan, Chaitali Joshi, Pavol Juhas, Dvir Kafri, Hui Kang, Kostyantyn Kechedzhi, Trupti Khaire, Tanuj Khattar, Mostafa Khezri, Mária Kieferová, Seon Kim, Alexei Kitaev, Paul V. Klimov, Alexander N. Korotkov, Fedor Kostritsa, John Mark Kreikebaum, David Landhuis, Brandon W. Langley, Pavel Laptev, Kim-Ming Lau, Loïck Le Guevel, Justin Ledford, Joonho Lee, Kenny Lee, Yuri D. Lensky, Brian J. Lester, Wing Yan Li, Alexander T. Lill, Wayne Liu, William P. Livingston, Aditya Locharla, Daniel Lundahl, Aaron Lunt, Sid Madhuk, Ashley Maloney, Salvatore Mandrà, Leigh S. Martin, Orion Martin, Steven Martin, Cameron Maxfield, Jarrod R. McClean, Matt McEwen, Seneca Meeks, Kevin C. Miao, Amanda Mieszala, Sebastian Molina, Shirin Montazeri, Alexis Morvan, Ramis Movassagh, Charles Neill, Ani Nersisyan, Michael Newman, Anthony Nguyen, Murray Nguyen, Chia-Hung Ni, Murphy Yuezhen Niu, William D. Oliver, Kristoffer Ottosson, Alex Pizzuto, Rebecca Potter, Orion Pritchard, Leonid P. Pryadko, Chris Quintana, Matthew J. Reagor, David M. Rhodes, Gabrielle Roberts, Charles Rocque, Eliott Rosenberg, Nicholas C. Rubin, Negar Saei, Kannan Sankaragomathi, Kevin J. Satzinger, Henry F. Schurkus, Christopher Schuster, Michael J. Shearn, Aaron Shorter, Noah Shutty, Vladimir Shvarts, Volodymyr Sivak, Jindra Skruzny, Spencer Small, W. Clarke Smith, Sofia Springer, George Sterling, Jordan Suchard, Marco Szalay, Alex Sztein, Douglas Thor, Alfredo Torres, M. Mert Torunbalci, Abeer Vaishnav, Sergey Vdovichev, Benjamin Villalonga, Catherine Vollgraff Heidweiller, Steven Waltman, Shannon X. Wang, Theodore White, Kristi Wong, Bryan W. Woo, Cheng Xing, Z. Jamie Yao, Ping Yeh, Bicheng Ying, Juhwan Yoo, Noureldin Yosri, Grayson Young, Adam Zalcman, Ningfeng Zhu, Nicholas Zobrist, Hartmut Neven, Ryan Babbush, Sergio Boixo, Jeremy Hilton, Erik Lucero, Anthony Megrant, Julian Kelly, Yu Chen, Vadim Smelyanskiy, Guifre Vidal, Pedram Roushan, Andreas M. Lauchli, Dmitry A. Abanin, Xiao Mi

Establishing the Quantum Supremacy Frontier with a 281 Pflop/s Simulation

Benjamin Villalonga, Dmitry Lyakh, Sergio Boixo, Hartmut Neven, Travis S. Humble, Rupak Biswas, Eleanor G. Rieffel, Alan Ho, Salvatore Mandrà

Noisy Intermediate-Scale Quantum (NISQ) computers are entering an era in which they can perform computational tasks beyond the capabilities of the most powerful classical computers, thereby achieving "Quantum Supremacy", a major milestone in quantum computing. NISQ Supremacy requires comparison with a state-of-the-art classical simulator. We report HPC simulations of hard random quantum circuits (RQC), which have been recently used as a benchmark for the first experimental demonstration of Quantum Supremacy, sustaining an average performance of 281 Pflop/s (true single precision) on Summit, currently the fastest supercomputer in the World. These simulations were carried out using qFlex, a tensor-network-based classical high-performance simulator of RQCs. Our results show an advantage of many orders of magnitude in energy consumption of NISQ devices over classical supercomputers. In addition, we propose a standard benchmark for NISQ computers based on qFlex.