Fetching the paper…

Reading the bibliography…

2021

Hierarchical Qubit Maps and Hierarchical Quantum Error Correction

Klco, Natalie, Savage, Martin J.

Original
PDF
Post on X

Understand

We consider hierarchically implemented quantum error correction (HI-QEC), in which the fidelities of logical qubits are differentially optimized to enhance the capabilities of quantum devices in scientific applications.

By employing qubit representations that propagate hierarchies in simulated systems to those in logical qubit noise sensitivities, heterogeneity in the distribution of physical-to-logical qubits can be systematically structured.
For concreteness, we estimate HI-QEC's impact on surface code resources in computing low-energy observables to fixed precision, finding up to $\sim 60\%$ reductions in qubit requirements plausible in early error corrected simulations.
Hierarchical qubit maps are also possible without error correction in qubit and qudit systems where fidelities are non-uniform, either unintentionally or by design.

Hierarchical Qubit Maps and Hierarchical Quantum Error Correction · Around

Built on

Natalie Klco and Martin J. Savage, “Minimally entangled state preparation of localized wave functions on quantum computers,”
Original
1904
Earlier work this paper cites.
Natalie Klco, Jesse R. Stryker, and Martin J. Savage, “SU(2) non-Abelian gauge field theory in one dimension on digital quantum computers,”
Original
1908
Earlier work this paper cites.
Eric T. Holland, Kyle A. Wendt, Konstantinos Kravvaris, Xian Wu, W. Erich Ormand, Jonathan L DuBois, Sofia Quaglioni, and Francesco Pederiva, “Optimal Control for the Quantum Simulation of Nuclear Dynamics,”
Original
1908
Earlier work this paper cites.
Erik Gustafson, Patrick Dreher, Zheyue Hang, and Yannick Meurice, “Benchmarking quantum computers for real-time evolution of a ( 1 + 1 ) (1+1) field theory with error mitigation,”
Original
1910
Earlier work this paper cites.
Alfred Haar, “Zur theorie der orthogonalen funktionensysteme,”
1910
Earlier work this paper cites.
M. C. Bañuls et al. , “Simulating Lattice Gauge Theories within Quantum Technologies,”
Original
1911
Earlier work this paper cites.
Chinmay Mishra, Shane Thompson, Raphael Pooser, and George Siopsis, “Quantum Computation of the Massive Thirring Model,”
Original
1912
Earlier work this paper cites.
Natalie Klco and Martin J. Savage, “Systematically Localizable Operators for Quantum Simulations of Quantum Field Theories,”
Original
1912
Earlier work this paper cites.
J. L. Walsh, “A closed set of normal orthogonal functions,”
1923
Earlier work this paper cites.
John Kogut and Leonard Susskind, “Hamiltonian formulation of wilson’s lattice gauge theories,”
1975
Earlier work this paper cites.
E. Marinari, “The APE computer and lattice gauge theories,”
1986
Earlier work this paper cites.
P.W. Shor, “Fault-tolerant quantum computation,”
1996
Earlier work this paper cites.
Daniel Gottesman, “Stabilizer codes and quantum error correction,”
1997
Earlier work this paper cites.
Sergey B. Bravyi and Alexei Yu. Kitaev, “Quantum codes on a lattice with boundary,”
1998
Earlier work this paper cites.
Emanuel Knill, Raymond Laflamme, and Wojciech H. Zurek, “Resilient quantum computation: error models and thresholds,”
1998
Earlier work this paper cites.
Michael H Freedman and David A Meyer, “Projective plane and planar quantum codes,”
2001
Earlier work this paper cites.
Eric Dennis, Alexei Kitaev, Andrew Landahl, and John Preskill, “Topological quantum memory,”
2002
Earlier work this paper cites.
Natalie Klco and Martin J. Savage, “Fixed-point quantum circuits for quantum field theories,”
Original
2002
Earlier work this paper cites.
Andre He, Benjamin Nachman, Wibe A. de Jong, and Christian W. Bauer, “Zero-noise extrapolation for quantum-gate error mitigation with identity insertions,”
Original
2003
Earlier work this paper cites.
A.Yu. Kitaev, “Fault-tolerant quantum computation by anyons,”
2003
Earlier work this paper cites.
Chenyang Wang and John Preskill, “Confinement Higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory,”
2003
Earlier work this paper cites.

Similar

Tim Byrnes and Yoshihisa Yamamoto, “Simulating lattice gauge theories on a quantum computer,”
2006
Cited alongside, same era.
Jan F. Haase, Luca Dellantonio, Alessio Celi, Danny Paulson, Angus Kan, Karl Jansen, and Christine A. Muschik, “A resource efficient approach for quantum and classical simulations of gauge theories in particle physics,”
Original
2006
Cited alongside, same era.
Lena Funcke, Tobias Hartung, Karl Jansen, Stefan Kühn, Paolo Stornati, and Xiaoyang Wang, “Measurement Error Mitigation in Quantum Computers Through Classical Bit-Flip Correction,”
Original
2007
Cited alongside, same era.
Kübra Yeter-Aydeniz, George Siopsis, and Raphael C. Pooser, “Scattering in the Ising model with the quantum Lanczos algorithm,”
Original
2008
Cited alongside, same era.
Dorit Aharonov and Michael Ben-Or, “Fault-tolerant quantum computation with constant error rate,”

Then

John Preskill, “Quantum Computing in the NISQ era and beyond,”
2018
Later among the works it cites.
Suguru Endo, Simon C. Benjamin, and Ying Li, “Practical quantum error mitigation for near-future applications,”
2018
Later among the works it cites.
E. F. Dumitrescu, A. J. McCaskey, G. Hagen, G. R. Jansen, T. D. Morris, T. Papenbrock, R. C. Pooser, D. J. Dean, and P. Lougovski, “Cloud Quantum Computing of an Atomic Nucleus,”
Original
2018
Later among the works it cites.
N. Klco, E. F. Dumitrescu, A. J. McCaskey, T. D. Morris, R. C. Pooser, M. Sanz, E. Solano, P. Lougovski, and M. J. Savage, “Quantum-classical computation of Schwinger model dynamics using quantum computers,”
Original
2018
Later among the works it cites.
James R. Wootton and Daniel Loss, “Repetition code of 15 qubits,”
Original
2018

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

2008

Cited alongside, same era.

Alessandro Roggero, Chenyi Gu, Alessandro Baroni, and Thomas Papenbrock, “Preparation of excited states for nuclear dynamics on a quantum computer,”

2009

Cited alongside, same era.

Laird Egan, Dripto M. Debroy, Crystal Noel, Andrew Risinger, Daiwei Zhu, Debopriyo Biswas, Michael Newman, Muyuan Li, Kenneth R. Brown, Marko Cetina, and Christopher Monroe, “Fault-tolerant operation of a quantum error-correction code,”

2009

Cited alongside, same era.

Zohreh Davoudi, Indrakshi Raychowdhury, and Andrew Shaw, “Search for Efficient Formulations for Hamiltonian Simulation of non-Abelian Lattice Gauge Theories,”

2009

Cited alongside, same era.

Norman H. Christ, “QCDSP and QCDOC computers,”

2011

Cited alongside, same era.

Stephen P. Jordan, Keith S. M. Lee, and John Preskill, “Quantum algorithms for quantum field theories,”

2012

Cited alongside, same era.

Joao Barata, Niklas Mueller, Andrey Tarasov, and Raju Venugopalan, “Single-particle digitization strategy for quantum computation of a ϕ 4 \phi^{4} scalar field theory,”

2012

Cited alongside, same era.

H. Bombin, Ruben S. Andrist, Masayuki Ohzeki, Helmut G. Katzgraber, and M. A. Martin-Delgado, “Strong resilience of topological codes to depolarization,”

2012

Cited alongside, same era.

Later among the works it cites.

Alexandru Macridin, Panagiotis Spentzouris, James Amundson, and Roni Harnik, “Digital quantum computation of fermion-boson interacting systems,”

2018

Later among the works it cites.

Kubra Yeter-Aydeniz, Eugene F. Dumitrescu, Alex J. McCaskey, Ryan S. Bennink, Raphael C. Pooser, and George Siopsis, “Scalar Quantum Field Theories as a Benchmark for Near-Term Quantum Computers,”

2019

Later among the works it cites.

Frank Arute, Kunal Arya, Ryan Babbush, Dave Bacon, Joseph Bardin, Rami Barends, Rupak Biswas, Sergio Boixo, Fernando Brandao, David Buell, Brian Burkett, Yu Chen, Jimmy Chen, Ben Chiaro, Roberto Collins, William Courtney, Andrew Dunsworth, Edward Farhi, Brooks Foxen, Austin Fowler, Craig Michael Gidney, Marissa Giustina, Rob Graff, Keith Guerin, Steve Habegger, Matthew Harrigan, Michael Hartmann, Alan Ho, Markus Rudolf Hoffmann, Trent Huang, Travis Humble, Sergei Isakov, Evan Jeffrey, Zhang Jiang, Dvir Kafri, Kostyantyn Kechedzhi, Julian Kelly, Paul Klimov, Sergey Knysh, Alexander Korotkov, Fedor Kostritsa, Dave Landhuis, Mike Lindmark, Erik Lucero, Dmitry Lyakh, Salvatore Mandrà, Jarrod Ryan McClean, Matthew McEwen, Anthony Megrant, Xiao Mi, Kristel Michielsen, Masoud Mohseni, Josh Mutus, Ofer Naaman, Matthew Neeley, Charles Neill, Murphy Yuezhen Niu, Eric Ostby, Andre Petukhov, John Platt, Chris Quintana, Eleanor G. Rieffel, Pedram Roushan, Nicholas Rubin, Daniel Sank, Kevin J. Satzinger, Vadim Smelyanskiy, Kevin Jeffery Sung, Matt Trevithick, Amit Vainsencher, Benjamin Villalonga, Ted White, Z. Jamie Yao, Ping Yeh, Adam Zalcman, Hartmut Neven, and John Martinis, “Quantum supremacy using a programmable superconducting processor,”

2019

Later among the works it cites.

Natalie Klco and Martin J. Savage, “Digitization of scalar fields for quantum computing,”

2019

Later among the works it cites.

Mari Carmen Bañuls, Rainer Blatt, Jacopo Catani, Alessio Celi, Juan Ignacio Cirac, Marcello Dalmonte, Leonardo Fallani, Karl Jansen, Maciej Lewenstein, Simone Montangero, and et al., “Simulating lattice gauge theories within quantum technologies,”

2020

Later among the works it cites.

Quantum Computing UK, “Modeling probability distributions in Qiskit,”

2020

Later among the works it cites.

A. Romanenko, R. Pilipenko, S. Zorzetti, D. Frolov, M. Awida, S. Belomestnykh, S. Posen, and A. Grassellino, “Three-dimensional superconducting resonators at T < 20 T<20 mK with the photon lifetime up to τ = 2 \tau=2 seconds,”

2020

Later among the works it cites.

Anthony Ciavarella, Natalie Klco, and Martin J. Savage, “Trailhead for quantum simulation of SU(3) Yang-Mills lattice gauge theory in the local multiplet basis,”

2021

Closest in time.

Yasar Atas, Jinglei Zhang, Randy Lewis, Amin Jahanpour, Jan F. Haase, and Christine A. Muschik, “SU(2) hadrons on a quantum computer,”

2021

Closest in time.

Benjamin Hall, Alessandro Roggero, Alessandro Baroni, and Joseph Carlson, “Simulation of Collective Neutrino Oscillations on a Quantum Computer,”

2021

Closest in time.

Zijun Chen, Kevin J. Satzinger, Juan Atalaya, Alexander N. Korotkov, Andrew Dunsworth, Daniel Sank, Chris Quintana, Matt McEwen, Rami Barends, Paul V. Klimov, Sabrina Hong, Cody Jones, Andre Petukhov, Dvir Kafri, Sean Demura, Brian Burkett, Craig Gidney, Austin G. Fowler, Alexandru Paler, Harald Putterman, Igor Aleiner, Frank Arute, Kunal Arya, Ryan Babbush, Joseph C. Bardin, Andreas Bengtsson, Alexandre Bourassa, Michael Broughton, Bob B. Buckley, David A. Buell, Nicholas Bushnell, Benjamin Chiaro, Roberto Collins, William Courtney, Alan R. Derk, Daniel Eppens, Catherine Erickson, Edward Farhi, Brooks Foxen, Marissa Giustina, Ami Greene, Jonathan A. Gross, Matthew P. Harrigan, Sean D. Harrington, Jeremy Hilton, Alan Ho, Trent Huang, William J. Huggins, L. B. Ioffe, Sergei V. Isakov, Evan Jeffrey, Zhang Jiang, Kostyantyn Kechedzhi, Seon Kim, Alexei Kitaev, Fedor Kostritsa, David Landhuis, Pavel Laptev, Erik Lucero, Orion Martin, Jarrod R. McClean, Trevor McCourt, Xiao Mi, Kevin C. Miao, Masoud Mohseni, Shirin Montazeri, Wojciech Mruczkiewicz, Josh Mutus, Ofer Naaman, Matthew Neeley, Charles Neill, Michael Newman, Murphy Yuezhen Niu, Thomas E. O’Brien, Alex Opremcak, Eric Ostby, Bálint Pató, Nicholas Redd, Pedram Roushan, Nicholas C. Rubin, Vladimir Shvarts, 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, Yu Chen, Anthony Megrant, Julian Kelly, and Google Quantum AI, “Exponential suppression of bit or phase errors with cyclic error correction,”

2021

Closest in time.

C. Ryan-Anderson, J. G. Bohnet, K. Lee, D. Gresh, A. Hankin, J. P. Gaebler, D. Francois, A. Chernoguzov, D. Lucchetti, N. C. Brown, T. M. Gatterman, S. K. Halit, K. Gilmore, J. Gerber, B. Neyenhuis, D. Hayes, and R. P. Stutz, “Realization of real-time fault-tolerant quantum error correction,”

2021

Closest in time.

Jeongwan Haah, Matthew B. Hastings, Robin Kothari, and Guang Hao Low, “Quantum algorithm for simulating real time evolution of lattice hamiltonians,”

2021

Closest in time.

Alexandru Macridin, Andy C. Y. Li, Stephen Mrenna, and Panagiotis Spentzouris, “Bosonic field digitization for quantum computers,”

2021

Closest in time.

Natalie Klco, Alessandro Roggero, and Martin J. Savage, “Standard Model Physics and the Digital Quantum Revolution: Thoughts about the Interface,”

Original

2021

Closest in time.