Nicholas Rubin
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Fast electronic structure quantum simulation by spectrum amplification
Qiushi Han
Dominic Berry
Alec White
Albert Eugene DePrince III
Guang Hao Low
Robbie King
Rolando Somma
arXiv:2502.15882 (2025)
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The most advanced techniques using fault-tolerant quantum computers to estimate the ground-state energy of a chemical Hamiltonian involve compression of the Coulomb operator through tensor factorizations, enabling efficient block-encodings of the Hamiltonian. A natural challenge of these methods is the degree to which block-encoding costs can be reduced. We address this challenge through the technique of spectrum amplification, which magnifies the spectrum of the low-energy states of Hamiltonians that can be expressed as sums of squares. Spectrum amplification enables estimating ground-state energies with significantly improved cost scaling in the block encoding normalization factor $\Lambda$ to just $\sqrt{2\Lambda E_{\text{gap}}}$, where $E_{\text{gap}} \ll \Lambda$ is the lowest energy of the sum-of-squares Hamiltonian. To achieve this, we show that sum-of-squares representations of the electronic structure Hamiltonian are efficiently computable by a family of classical simulation techniques that approximate the ground-state energy from below. In order to further optimize, we also develop a novel factorization that provides a trade-off between the two leading Coulomb integral factorization schemes-- namely, double factorization and tensor hypercontraction-- that when combined with spectrum amplification yields a factor of 4 to 195 speedup over the state of the art in ground-state energy estimation for models of Iron-Sulfur complexes and a CO$_{2}$-fixation catalyst.
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Drug Design on Quantum Computers
Leticia Gonzalez
Christofer Tautermann
Horst Weiss
Michael Streif
Raffaele Santagati
Clemens Utschig-Utschig
Robert Parrish
Markus Oppel
Alán Aspuru-Guzik
Matthias Degroote
Elica Kyoseva
Nathan Wiebe
Nikolaj Moll
Nature Physics (2024)
Preview abstract
The promised industrial applications of quantum computers often rest on their anticipated ability to perform accurate, efficient quantum chemical calculations. Computational drug discovery relies on accurate predictions of how candidate drugs interact with their targets in a cellular environment involving several thousands of atoms at finite temperatures. Although quantum computers are still far from being used as daily tools in the pharmaceutical industry, here we explore the challenges and opportunities of applying quantum computers to drug design. We discuss where these could transform industrial research and identify the substantial further developments needed to reach this goal.
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Quantum Computation of Stopping power for Inertial Fusion Target Design
Andrew Baczewski
Alec White
Dominic Berry
Alina Kononov
Joonho Lee
Proceedings of the National Academy of Sciences, 121 (2024), e2317772121
Preview abstract
Stopping power is the rate at which a material absorbs the kinetic energy of a charged particle passing through it - one of many properties needed over a wide range of thermodynamic conditions in modeling inertial fusion implosions. First-principles stopping calculations are classically challenging because they involve the dynamics of large electronic systems far from equilibrium, with accuracies that are particularly difficult to constrain and assess in the warm-dense conditions preceding ignition. Here, we describe a protocol for using a fault-tolerant quantum computer to calculate stopping power from a first-quantized representation of the electrons and projectile. Our approach builds upon the electronic structure block encodings of Su et al. [PRX Quantum 2, 040332 2021], adapting and optimizing those algorithms to estimate observables of interest from the non-Born-Oppenheimer dynamics of multiple particle species at finite temperature. We also work out the constant factors associated with a novel implementation of a high order Trotter approach to simulating a grid representation of these systems. Ultimately, we report logical qubit requirements and leading-order Toffoli costs for computing the stopping power of various projectile/target combinations relevant to interpreting and designing inertial fusion experiments. We estimate that scientifically interesting and classically intractable stopping power calculations can be quantum simulated with
roughly the same number of logical qubits and about one hundred times more Toffoli gates than is required for state-of-the-art quantum simulations of industrially relevant molecules such as FeMoCo or P450.
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Rapid initial state preparation for the quantum simulation of strongly correlated molecules and materials
Seunghoon Lee
Tae In Kim
Yu Tong
Garnet Chan
Lin Lin
Dominic Berry
Alec White
arXiv:2409.11748 (2024)
Preview abstract
Studies on quantum algorithms for ground state energy estimation often assume perfect ground state preparation; however, in reality the initial state will have imperfect overlap with the true ground state. Here we address that problem in two ways: by faster preparation of matrix product state (MPS) approximations, and more efficient filtering of the prepared state to find the ground state energy. We show how to achieve unitary synthesis with a Toffoli complexity about $7 \times$ lower than that in prior work, and use that to derive a more efficient MPS preparation method. For filtering we present two different approaches: sampling and binary search. For both we use the theory of window functions to avoid large phase errors and minimise the complexity. We find that the binary search approach provides better scaling with the overlap at the cost of a larger constant factor, such that it will be preferred for overlaps less than about 0.003. Finally, we estimate the total resources to perform ground state energy estimation of FeMoco and Iron cluster systems by estimating ground state overlap on an MPS initial state through extrapolation. With a modest bond dimension of 4000 we estimate a 0.96 overlap squared value producing total resources of $7.5 \times 10^{10}$ Toffoli gates; validating naive estimates where we assume perfect ground state overlap. These extrapolations allay practical concerns of exponential overlap decay in challenging-to-compute chemical systems.
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Expressing and Analyzing Quantum Algorithms with Qualtran
Anurudh Peduri
Charles Yuan
arXiv::2409.04643 (2024)
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Quantum computing's transition from theory to reality has spurred the need for novel software tools to manage the increasing complexity, sophistication, toil, and chance for error of quantum algorithm development. We present Qualtran, an open-source library for representing and analyzing quantum algorithms. Using carefully chosen abstractions and data structures, we can simulate and test algorithms, automatically generate information-rich diagrams, and tabulate resource requirements. Qualtran offers a \emph{standard library} of algorithmic building blocks that are essential for modern cost-minimizing compilations. Its capabilities are showcased through the re-analysis of key algorithms in Hamiltonian simulation, chemistry, and cryptography. The resulting architecture-independent resource counts can be forwarded to our implementation of cost models to estimate physical costs like wall-clock time and number of physical qubits assuming a surface-code architecture. Qualtran provides a foundation for explicit constructions and reproducible analysis, fostering greater collaboration within the quantum algorithm development community. We believe tools like Qualtran will accelerate progress in the field.
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Stable quantum-correlated many-body states through engineered dissipation
Sara Shabani
Dripto Debroy
Jerome Lloyd
Alexios Michailidis
Andrew Dunsworth
Bill Huggins
Markus Hoffmann
Alexis Morvan
Josh Cogan
Ben Curtin
Guifre Vidal
Bob Buckley
Tom O'Brien
John Mark Kreikebaum
Rajeev Acharya
Joonho Lee
Ningfeng Zhu
Shirin Montazeri
Sergei Isakov
Jamie Yao
Clarke Smith
Rebecca Potter
Sean Harrington
Jeremy Hilton
Paula Heu
Alexei Kitaev
Alex Crook
Fedor Kostritsa
Kim Ming Lau
Dmitry Abanin
Trent Huang
Aaron Shorter
Steve Habegger
Gina Bortoli
Charles Rocque
Vladimir Shvarts
Alfredo Torres
Anthony Megrant
Charles Neill
Michael Hamilton
Dar Gilboa
Lily Laws
Nicholas Bushnell
Ramis Movassagh
Mike Shearn
Wojtek Mruczkiewicz
Desmond Chik
Leonid Pryadko
Xiao Mi
Brooks Foxen
Frank Arute
Alejo Grajales Dau
Yaxing Zhang
Lara Faoro
Alexander Lill
JiunHow Ng
Justin Iveland
Marco Szalay
Orion Martin
Juhwan Yoo
Michael Newman
William Giang
Alex Opremcak
Amanda Mieszala
William Courtney
Andrey Klots
Wayne Liu
Pavel Laptev
Charina Chou
Paul Conner
Rolando Somma
Vadim Smelyanskiy
Benjamin Chiaro
Grayson Young
Tim Burger
ILYA Drozdov
Agustin Di Paolo
Jimmy Chen
Marika Kieferova
Michael Broughton
Negar Saei
Juan Atalaya
Markus Ansmann
Pavol Juhas
Murray Ich Nguyen
Yuri Lensky
Roberto Collins
Élie Genois
Jindra Skruzny
Igor Aleiner
Yu Chen
Reza Fatemi
Leon Brill
Ashley Huff
Doug Strain
Monica Hansen
Noah Shutty
Ebrahim Forati
Dave Landhuis
Kenny Lee
Ping Yeh
Kunal Arya
Henry Schurkus
Cheng Xing
Cody Jones
Edward Farhi
Raja Gosula
Andre Petukhov
Alexander Korotkov
Ani Nersisyan
Christopher Schuster
George Sterling
Kostyantyn Kechedzhi
Trond Andersen
Alexandre Bourassa
Kannan Sankaragomathi
Vinicius Ferreira
Science, 383 (2024), pp. 1332-1337
Preview abstract
Engineered dissipative reservoirs have the potential to steer many-body quantum systems toward correlated steady states useful for quantum simulation of high-temperature superconductivity or quantum magnetism. Using up to 49 superconducting qubits, we prepared low-energy states of the transverse-field Ising model through coupling to dissipative auxiliary qubits. In one dimension, we observed long-range quantum correlations and a ground-state fidelity of 0.86 for 18 qubits at the critical point. In two dimensions, we found mutual information that extends beyond nearest neighbors. Lastly, by coupling the system to auxiliaries emulating reservoirs with different chemical potentials, we explored transport in the quantum Heisenberg model. Our results establish engineered dissipation as a scalable alternative to unitary evolution for preparing entangled many-body states on noisy quantum processors.
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Dynamics of magnetization at infinite temperature in a Heisenberg spin chain
Tomaž Prosen
Vedika Khemani
Rhine Samajdar
Jesse Hoke
Sarang Gopalakrishnan
Andrew Dunsworth
Bill Huggins
Markus Hoffmann
Alexis Morvan
Josh Cogan
Ben Curtin
Guifre Vidal
Bob Buckley
Tom O'Brien
John Mark Kreikebaum
Rajeev Acharya
Joonho Lee
Ningfeng Zhu
Shirin Montazeri
Sergei Isakov
Jamie Yao
Clarke Smith
Rebecca Potter
Sean Harrington
Jeremy Hilton
Paula Heu
Alexei Kitaev
Alex Crook
Fedor Kostritsa
Kim Ming Lau
Dmitry Abanin
Trent Huang
Aaron Shorter
Steve Habegger
Steven Martin
Gina Bortoli
Seun Omonije
Richard Ross Allen
Charles Rocque
Vladimir Shvarts
Alfredo Torres
Anthony Megrant
Charles Neill
Michael Hamilton
Dar Gilboa
Lily Laws
Nicholas Bushnell
Kyle Anderson
Ramis Movassagh
David Rhodes
Mike Shearn
Wojtek Mruczkiewicz
Desmond Chik
Leonid Pryadko
Xiao Mi
Brooks Foxen
Frank Arute
Alejo Grajales Dau
Yaxing Zhang
Lara Faoro
Alexander Lill
Gordon Hill
JiunHow Ng
Justin Iveland
Marco Szalay
Orion Martin
Juan Campero
Juhwan Yoo
Michael Newman
William Giang
Gonzalo Garcia
Alex Opremcak
Amanda Mieszala
William Courtney
Andrey Klots
Wayne Liu
Pavel Laptev
Paul Conner
Rolando Somma
Vadim Smelyanskiy
Benjamin Chiaro
Grayson Young
Tim Burger
ILYA Drozdov
Agustin Di Paolo
Jimmy Chen
Marika Kieferova
Hung-Shen Chang
Michael Broughton
Negar Saei
Juan Atalaya
Markus Ansmann
Pavol Juhas
Murray Ich Nguyen
Yuri Lensky
Roberto Collins
Élie Genois
Jindra Skruzny
Yu Chen
Reza Fatemi
Leon Brill
Seneca Meeks
Ashley Huff
Doug Strain
Monica Hansen
Noah Shutty
Ebrahim Forati
Doug Thor
Dave Landhuis
Kenny Lee
Ping Yeh
Kunal Arya
Henry Schurkus
Cheng Xing
Cody Jones
Edward Farhi
Vlad Sivak
Raja Gosula
Andre Petukhov
Clint Earle
Alexander Korotkov
Ani Nersisyan
Christopher Schuster
George Sterling
Trond Andersen
Alexandre Bourassa
Salvatore Mandra
Kannan Sankaragomathi
Vinicius Ferreira
Science, 384 (2024), pp. 48-53
Preview abstract
Understanding universal aspects of quantum dynamics is an unresolved problem in statistical mechanics. In particular, the spin dynamics of the one-dimensional Heisenberg model were conjectured as to belong to the Kardar-Parisi-Zhang (KPZ) universality class based on the scaling of the infinite-temperature spin-spin correlation function. In a chain of 46 superconducting qubits, we studied the probability distribution of the magnetization transferred across the chain’s center, P(M). The first two moments of P(M) show superdiffusive behavior, a hallmark of KPZ universality. However, the third and fourth moments ruled out the KPZ conjecture and allow for evaluating other theories. Our results highlight the importance of studying higher moments in determining dynamic universality classes and provide insights into universal behavior in quantum systems.
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Fault-Tolerant Quantum Simulation of Materials Using Bloch Orbitals
Sabrina Sicolo
Alec White
Michael Kuehn
Michael Kaicher
Dominic Berry
Eugene DePrince III
Joonho Lee
PRX Quantum, 4 (2023), pp. 040303
Preview abstract
The simulation of chemistry is among the most promising applications of quantum computing. However, most prior work exploring algorithms for block encoding, time evolving, and sampling in the eigenbasis of electronic structure Hamiltonians has either focused on modeling finite-sized systems, or has required a large number of plane-wave basis functions. In this work, we extend methods for quantum simulation with Bloch orbitals constructed from symmetry-adapted atom-centered orbitals so that one can model periodic ab initio Hamiltonians using only a modest number of basis functions. We focus on adapting existing algorithms based on combining qubitization with tensor factorizations of the Coulomb operator. Significant modifications of those algorithms are required to obtain an asymptotic speedup leveraging translational (or, more broadly, Abelian) symmetries. We implement block encodings using known tensor factorizations and a new Bloch orbital form of tensor hypercontraction. Finally, we estimate the resources required to deploy our algorithms to classically challenging model materials relevant to the chemistry of lithium nickel oxide battery cathodes within the surface code. We find that even with these improvements, the quantum runtime of these algorithms is on the order of thousands of days and further algorithmic improvements are required to make realistic quantum simulation of materials practical.
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Quantum Simulation of Realistic Materials in First Quantization Using Non-local Pseudopotentials
Ahmed Elnabawy
Gabriele Ahlers
Albert Eugene DePrince III
Christian Gogolin
Dominic Berry
Joonho Lee
arXiv:2312.07654 (2023)
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This paper improves and demonstrates the usefulness of the first quantized plane-wave algorithms for the quantum simulation of electronic structure, developed by Babbush et al. and Su et al. We describe the first quantum algorithm for first quantized simulation that accurately includes pseudopotentials. We focus on the Goedecker-Tetter-Hutter (GTH) pseudopotential, which is among the most accurate and widely used norm-conserving pseudopotentials enabling the removal of core electrons from the simulation. The resultant screened nuclear potential regularizes cusps in the electronic wavefunction so that orders of magnitude fewer plane waves are required for a chemically accurate basis. Despite the complicated form of the GTH pseudopotential, we are able to block encode the associated operator without significantly increasing the overall cost of quantum simulation. This is surprising since simulating the nuclear potential is much simpler without pseudopotentials, yet is still the bottleneck. We also generalize prior methods to enable the simulation of materials with non-cubic unit cells, which requires nontrivial modifications. Finally, we combine these techniques to estimate the block-encoding costs for commercially relevant instances of heterogeneous catalysis (e.g. carbon monoxide adsorption on transition metals) and compare to the quantum resources needed to simulate materials in second quantization. We conclude that for computational cells with many particles, first quantization often requires meaningfully less spacetime volume.
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Purification-Based Quantum Error Mitigation of Pair-Correlated Electron Simulations
Christian Gogolin
Vincent Elfving
Fotios Gkritsis
Oumarou Oumarou
Gian-Luca R. Anselmetti
Masoud Mohseni
Andrew Dunsworth
William J. Huggins
Markus Rudolf Hoffmann
Alexis Morvan
Josh Godfrey Cogan
Ben Curtin
Guifre Vidal
Bob Benjamin Buckley
Trevor Johnathan Mccourt
Thomas E O'Brien
John Mark Kreikebaum
Rajeev Acharya
Joonho Lee
Ningfeng Zhu
Shirin Montazeri
Sergei Isakov
Jamie Yao
Clarke Smith
Rebecca Potter
Sean Harrington
Jeremy Patterson Hilton
Alex Crook
Fedor Kostritsa
Kim Ming Lau
Dmitry Abanin
Trent Huang
Aaron Shorter
Steve Habegger
Richard Ross Allen
Vladimir Shvarts
Alfredo Torres
Stefano Polla
Anthony Megrant
Charles Neill
Michael C. Hamilton
Dar Gilboa
Lily MeeKit Laws
Nicholas Bushnell
Kyle Anderson
Ramis Movassagh
Mike Shearn
Wojtek Mruczkiewicz
Desmond Chun Fung Chik
Xiao Mi
Brooks Riley Foxen
Frank Carlton Arute
Alejandro Grajales Dau
Yaxing Zhang
Lara Faoro
Alexander T. Lill
Jiun How Ng
Justin Thomas Iveland
Marco Szalay
Orion Martin
Juhwan Yoo
Michael Newman
William Giang
Alex Opremcak
William Courtney
Andrey Klots
Wayne Liu
Pavel Laptev
Paul Conner
Rolando Diego Somma
Vadim Smelyanskiy
Benjamin Chiaro
Grayson Robert Young
Tim Burger
Ilya Drozdov
Jimmy Chen
Marika Kieferova
Michael Blythe Broughton
Juan Atalaya
Markus Ansmann
Pavol Juhas
Murray Nguyen
Daniel Eppens
Roberto Collins
Jindra Skruzny
Igor Aleiner
Yu Chen
Reza Fatemi
Leon Brill
Ashley Anne Huff
Doug Strain
Ebrahim Forati
Dave Landhuis
Kenny Lee
Ping Yeh
Kunal Arya
Cody Jones
Edward Farhi
Andre Gregory Petukhov
Alexander Korotkov
Ani Nersisyan
Christopher Schuster
Kostyantyn Kechedzhi
Trond Ikdahl Andersen
Alexandre Bourassa
Kannan Aryaperumal Sankaragomathi
Nature Physics (2023)
Preview abstract
An important measure of the development of quantum computing platforms has been the simulation of increasingly complex physical systems. Prior to fault-tolerant quantum computing, robust error mitigation strategies are necessary to continue this growth. Here, we study physical simulation within the seniority-zero electron pairing subspace, which affords both a computational stepping stone to a fully correlated model, and an opportunity to validate recently introduced ``purification-based'' error-mitigation strategies. We compare the performance of error mitigation based on doubling quantum resources in time (echo verification) or in space (virtual distillation), 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.
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