Publications

You can also find most of my papers on the arXiv (which is sometimes more up-to-date than this list).

Papers

Dissipative Quantum Gibbs Sampling

Daniel Zhang, Jan Lukas Bosse, Toby Cubitt
arXiv:2304.04526[quant-ph]

Dissipative ground state preparation and the Dissipative Quantum Eigensolver

Toby S. Cubitt
arXiv:2303.11962[quant-ph]

Fitting time-dependent Markovian dynamics to noisy quantum channels

Emilio Onorati, Tamara Kohler, Toby S. Cubitt
arXiv:2303.08936[quant-ph]

A mathematical framework for quantum Hamiltonian simulation and duality

Harriet Apel and Toby Cubitt
arXiv:2208.11941[quant-ph] [39 pages]

Towards near-term quantum simulation of materials

Laura Clinton, Toby Cubitt, Brian Flynn, Filippo Maria Gambetta, Joel Klassen, Ashley Montanaro, Stephen Piddock, Raul A. Santos and Evan Sheridan
arXiv:2205.15256[quant-ph] [94 pages]

Phase Estimation of Local Hamiltonians on NISQ Hardware

Laura Clinton, Johannes Bausch, Joel Klassen, Toby Cubitt
New Journal of Physics 25.3: 033027 (2023)
arXiv:2110.13584[quant-ph]

Undecidability of the Spectral Gap (full version)

Toby S. Cubitt, David Perez-Garcia and Michael M. Wolf
Forum of Mathematics Pi, 10:e14 (2022)
arXiv:1502.04573[quant-ph] [127 pages]

Fitting quantum noise models to tomography data

Emilio Onorati, Tamara Kohler, Toby Cubitt
arXiv:2103.17243[quant-ph] [56 pages]

Uncomputably Complex Renormalisation Group Flows

James D. Watson, Emilio Onorati, Toby S. Cubitt
Nature Communications 13, 7618 (2022)
arXiv:2102.05145[quant-ph] [88 pages]

General conditions for universality of Quantum Hamiltonians

Tamara Kohler, Stephen Piddock, Johannes Bausch, Toby Cubitt
PRX Quantum 3:010308 (2022)
arXiv:2101.12319[quant-ph] [22 pages]

Translationally-Invariant Universal Quantum Hamiltonians in 1D

Tamara Kohler, Stephen Piddock, Johannes Bausch and Toby Cubitt
Annales Henri Poincaré, 23, p.223–254 (2021)
arXiv:2003.13753[quant-ph] [31 pages]

Hamiltonian Simulation Algorithms for Near-Term Quantum Hardware

Laura Clinton, Johannes Bausch and Toby Cubitt
Nature Communications 12(1), 4929 (2021)
arXiv:2003.06886[quant-ph] [63 pages]

Compact fermion to qubit mappings

Charles Derby, Joel Klassen, Johannes Bausch, Toby Cubitt
Phys. Rev. B 104:035118 (2021)
Combines arXiv:2003.06939[quant-ph] and arXiv:2003.07125[quant-ph]

Mitigating Errors in Local Fermionic Encodings

Johannes Bausch, Toby Cubitt, Charles Derby and Joel Klassen
arXiv:2003.07125[quant-ph] [23 pages]

Uncomputability of Phase Diagrams

Johannes Bausch, Toby S. Cubitt and James D. Watson
Nature Communications 12(1), 1, (2021)
arXiv:1910.01631[quant-ph] [64 pages]

Toy Models of Holographic Duality between local Hamiltonians

Tamara Kohler and Toby Cubitt
J. High Energy Phys. 2019:17 (2019)
arXiv:1810.08992[hep-th] [62 pages]

History-state Hamiltonians are critical

Carlos E. González-Guillén and Toby S. Cubitt
arXiv:1810.06528[quant-ph] [35 pages]

Undecidability of the Spectral Gap in One Dimension

Johannes Bausch, Toby Cubitt, Angelo Lucia and David Perez-Garcia
Phys. Rev. X 10, 031038 (2020)
arxiv:1810.01858[quant-ph] [54 pages]

The Unsolvable Problem

Toby Cubitt, David Perez-Garcia and Michael Wolf
Scientific American, Volume 319, Issue 4, October 2018
(Cover article; selected for 2018 “Scientific American Articles of the Year” special issue, and for 2019 “Best Writing on Mathematics” Princeton University Press anthology.)

Translationally invariant universal classical Hamiltonians

Tamara Kohler and Toby Cubitt
J. Stat. Phys. 176:1 p228–261 (2019)
arxiv:1807.01715[cond-mat.stat-mech] [44 pages]

Universal Quantum Hamiltonians

Toby Cubitt, Ashley Montanaro and Stephen Piddock
Proc. Natl. Acad. Sci. 115:38 p9497–9502 (2018)
arXiv:1701.05182[quant-ph] [82 pages]

Comment on “On the uncomputability of the spectral gap”

Toby S. Cubitt, David Perez-Garcia and Michael M. Wolf
arXiv:1603.00825[quant-ph]

Universal Refocusing of Systematic Quantum Noise

Imdad S. B. Sardharwalla, Toby S. Cubitt, Aram W. Harrow and Noah Linden
arXiv:1602.07963[quant-ph]

Size-Driven Quantum Phase Transitions

Johannes Bausch, Toby S. Cubitt, Angelo Lucia, David Perez-Garcia and Michael M. Wolf
Proc. Natl. Acad. Sci. 115:1, p19–23 (2018) [18 pages]
arXiv:1512.05687[quant-ph]

The Complexity of Translationally-Invariant Spin Chains with Low Local Dimension

Johannes Bausch, Toby Cubitt and Maris Ozols
Annales Henri Poincaré, 18:11, p3449–3513 (2017) [63 pages]
arXiv:1605.01718[quant-ph]
(Winner of 2018 AHP-Birkhauser Prize for “most remarkable paper published in Annales Henri Poincaré”.)

Fundamental Limitations in the Purifications of Tensor Networks

G. De las Cuevas, T. S. Cubitt, J.I. Cirac, M. M. Wolf and D. Perez-Garcia
J. Math. Phys. 57, 071902 (2016) [8 pages]
arXiv:1512.05709[quant-ph]

The Complexity of Divisibility

Johannes Bausch and Toby S. Cubitt
J. Linear Alg. 504, p64–107 (2016) [50 pages]
arXiv:1411.7380[math.PR]

Complexity Classification of Local Hamiltonian Problems

Toby Cubitt and Ashley Montanaro
SIAM J. on Computing, 45:2, p268–316 (2016) [50 pages]
arXiv:1311.3161[quant-ph]

Simple Universal Models Capture all Classical Spin Physics

Gemma de las Cuevas and Toby S. Cubitt
Science, 351:6278, p1180-1183 (2016) [47 pages]
arXiv:1406.5955[cond-mat.stat-mech]

Area law for fixed points of rapidly mixing dissipative quantum systems

F. G. S. L. Brandao, T. S. Cubitt, A. Lucia, S. Michalakis and D. Perez-Garcia
J. Math. Phys. 56, 102202 (2015) [17 pages]
arXiv:1505.02776[quant-ph]

Undecidability of the Spectral Gap (short version)

Toby S. Cubitt, David Perez-Garcia and Michael M. Wolf
Nature, 528, p207–211, (2015)
arXiv:1502.04135[quant-ph] (short version)

Quantum reverse hypercontractivity

T. Cubitt, M. Kastoryano, A. Montanaro and K. Temme
J. Math. Phys. 56, 102204 (2015) [14 pages]
arXiv:1504.06143[quant-ph]

Rapid Mixing and Stability of Quantum Dissipative Systems

Toby S. Cubitt, Angelo Lucia, Spyridon Michalakis, and David Perez-Garcia
Phys. Rev. A 91, 040302 (2015)
arXiv:1409.7809[quant-ph]

Unbounded Number of Channel Uses may be Required to Detect Quantum Capacity

D. Elkouss, S. Strelchuck, W. Matthews, M. Ozols, D. Perez-Garcia and T. S. Cubitt
Nature Communications 6, 7739 (2015) [11 pages]
arXiv:1408.5115[quant-ph]

An Information-Theoretic Proof of the Constructive Commutative Quantum Lovász Local Lemma

M. Schwarz, T. S. Cubitt and Frank Verstraete
arXiv:1311.6474[quant-ph]

Complexity Classification of Local Hamiltonian Problems

Toby Cubitt and Ashley Montanaro
IEEE 55th Annual Symposium on Foundations of Computer Science (FOCS), p120–129 (2014)
arXiv:1311.3161[quant-ph]

Bounds on Entanglement Assisted Source-Channel Coding via the Lovász Theta Number and its Variants

Toby Cubitt, Laura Mancinska, David Roberson, Simone Severini, Dan Stahlke and Andreas Winter
IEEE Trans. Inform. Theory 60, 7330 (2014) [15 pages]
arXiv:1310.7120[quant-ph]

Stability of local quantum dissipative systems

Toby S. Cubitt, Angelo Lucia, Spyridon Michalakis, and David Perez-Garcia
Commun. Math. Phys. 337, 1275 (2015) [38 pages]
arXiv:1303.4744[quant-ph]

Preparing Topological PEPS on a Quantum Computer

M. Schwarz, K. Temme, F. Verstraete, D. Perez-Garcia and T. S. Cubitt
Phys. Rev. A, 88, 032321 (2013) (Editors’ suggestion)
arXiv:1211.4050[quant-ph]

Are Problems in Quantum Information Theory (Un)decidable?

Michael M. Wolf, Toby S. Cubitt and David Perez-Garcia
arXiv:1111.5425[quant-ph]

Entanglement can Completely Defeat Quantum Noise

Jianxin Chen, Toby S. Cubitt, Aram W. Harrow and Graeme Smith
Phys. Rev. Lett. 107, 250504 (2011) (Editor’s suggestion)
arXiv:1109.0540[quant-ph]
(highlighted in APS Physics article)

Extracting Dynamical Equations from Experimental Data is NP-Hard

Toby S. Cubitt, Jens Eisert and Michael M. Wolf
Phys. Rev. Lett. 108, 120503 (2012) (Editor’s suggestion)
arXiv:1005.0005[quant-ph]
(highlighted in Science NOW article and in APS Physics article)

Zero-Error Channel Capacity and Simulation Assisted by Non-Local Correlations

T. S. Cubitt, D. Leung, W. Matthews and A. Winter
IEEE Trans. Inform. Theory 57:8, 5509–5523 (2011) [15 pages]
arXiv:1003.3195[quant-ph]

Super-duper-activation of the zero-error quantum capacity

Jianxin Chen, Toby S. Cubitt, Aram W. Harrow and Graeme Smith
IEEE International Symposium on Information Theory (ISIT), p2695–2697 (2010)

An Extreme Form of Superactivation for Quantum Zero-Error Capacities

Toby S. Cubitt and Graeme Smith
IEEE Trans. Inform. Theory 58:3, 1953–1961 (2012) [9 pages]
arXiv:0912.2737[quant-ph]

Improving Zero-Error Classical Communication with Entanglement

T. S. Cubitt, D. Leung, W. Matthews and A. Winter
Phys. Rev. Lett. 104, 230503 (2010)
arXiv:0911.5300[quant-ph]

The Complexity of Relating Quantum Channels to Master Equations

Toby S. Cubitt, Jens Eisert and Michael M. Wolf
Commun. Math. Phys. 310, 383–417 (2012) [35 pages]
arXiv:0908.2128[quant-ph]

Superactivation of the Asymptotic Zero-Error Classical Capacity of a Quantum Channel

Toby S. Cubitt, Jianxin Chen and Aram W. Harrow
IEEE Trans. Inform. Theory 57:12, 8114–8126 (2011) [8 pages]
arXiv:0906.2547[quant-ph]

Non-Secret Correlations can be Used to Distribute Secrecy

Joonwoo Bae, Toby S. Cubitt and Antonio Acín
Phys. Rev. A 79, 032304 (2009)
arXiv:0806.1606[quant-ph]

The Structure of Degradable Quantum Channels

Toby S. Cubitt, Mary Beth Ruskai and Graeme Smith
J. Math. Phys. 49, 102104 (2008) [27 pages]
arXiv:0802.1460[quant-ph]

Counterexamples to Additivity of Minimum Output p-Rényi Entropy for p close to 0

Toby S. Cubitt, Aram W. Harrow, Debbie Leung, Ashley Montanaro and Andreas Winter
Commun. Math. Phys. 284, 281–290 (2008) [9 pages]
arXiv:0712.3628[quant-ph]

Assessing non-Markovian Dynamics

M. M. Wolf, J. Eisert, T. S. Cubitt and J.I. Cirac
Phys. Rev. Lett. 101, 150402 (2008)
arXiv:0711.3172[quant-ph]

On the Dimension of Subspaces with Bounded Schmidt Rank

Toby S. Cubitt, Ashley Montanaro and Andreas Winter
J. Math. Phys. 49, 022107 (2008)
arXiv:0706.0705[quant-ph]

Engineering Correlation and Entanglement Dynamics in Spin Systems

T. S. Cubitt and J.I. Cirac
Phys. Rev. Lett. 100, 180406 (2008)
arXiv:quant-ph/0701053

Entanglement in the Stabilizer Formalism

David Fattal, Toby S. Cubitt, Yoshihisa Yamamoto, Sergey Bravyi and Isaac L. Chuang
arXiv:quant-ph/0406168

Entanglement Flow in Multipartite Systems

T. S. Cubitt, F. Verstraete and J.I. Cirac
Phys. Rev. A 71, 052308 (2005) [12 pages]
arXiv:quant-ph/0404179

Separable States can be Used to Distribute Entanglement

T. S. Cubitt, F. Verstraete, W. Dür, J.I. Cirac
Phys. Rev. Lett. 91, 037902 (2003)
arXiv:quant-ph/0302168
(highlighted in Science NOW article)

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Publications

Papers

Dissipative Quantum Gibbs Sampling

Dissipative ground state preparation and the Dissipative Quantum Eigensolver

Fitting time-dependent Markovian dynamics to noisy quantum channels

A mathematical framework for quantum Hamiltonian simulation and duality

Towards near-term quantum simulation of materials

Phase Estimation of Local Hamiltonians on NISQ Hardware

Undecidability of the Spectral Gap (full version)

Computational Complexity of the Ground State Energy Density Problem

Holographic duality between local Hamiltonians from random tensor networks

A Note on the Second Spectral Gap Incompleteness Theorem

Fitting quantum noise models to tomography data

Uncomputably Complex Renormalisation Group Flows

General conditions for universality of Quantum Hamiltonians

Translationally-Invariant Universal Quantum Hamiltonians in 1D

Hamiltonian Simulation Algorithms for Near-Term Quantum Hardware

Compact fermion to qubit mappings

Mitigating Errors in Local Fermionic Encodings

Uncomputability of Phase Diagrams

Toy Models of Holographic Duality between local Hamiltonians

History-state Hamiltonians are critical

Undecidability of the Spectral Gap in One Dimension

The Unsolvable Problem

Translationally invariant universal classical Hamiltonians

Universal Quantum Hamiltonians

Comment on “On the uncomputability of the spectral gap”

Universal Refocusing of Systematic Quantum Noise

Size-Driven Quantum Phase Transitions

The Complexity of Translationally-Invariant Spin Chains with Low Local Dimension

Fundamental Limitations in the Purifications of Tensor Networks

The Complexity of Divisibility

Complexity Classification of Local Hamiltonian Problems

Simple Universal Models Capture all Classical Spin Physics

Area law for fixed points of rapidly mixing dissipative quantum systems

Undecidability of the Spectral Gap (short version)

Quantum reverse hypercontractivity

Rapid Mixing and Stability of Quantum Dissipative Systems

Unbounded Number of Channel Uses may be Required to Detect Quantum Capacity

An Information-Theoretic Proof of the Constructive Commutative Quantum Lovász Local Lemma

Complexity Classification of Local Hamiltonian Problems

Bounds on Entanglement Assisted Source-Channel Coding via the Lovász Theta Number and its Variants

Stability of local quantum dissipative systems

Preparing Topological PEPS on a Quantum Computer

Are Problems in Quantum Information Theory (Un)decidable?

Entanglement can Completely Defeat Quantum Noise

Extracting Dynamical Equations from Experimental Data is NP-Hard

Zero-Error Channel Capacity and Simulation Assisted by Non-Local Correlations

Super-duper-activation of the zero-error quantum capacity

An Extreme Form of Superactivation for Quantum Zero-Error Capacities

Improving Zero-Error Classical Communication with Entanglement

The Complexity of Relating Quantum Channels to Master Equations

Superactivation of the Asymptotic Zero-Error Classical Capacity of a Quantum Channel

Non-Secret Correlations can be Used to Distribute Secrecy

The Structure of Degradable Quantum Channels

Counterexamples to Additivity of Minimum Output p-Rényi Entropy for p close to 0

Assessing non-Markovian Dynamics

On the Dimension of Subspaces with Bounded Schmidt Rank

Engineering Correlation and Entanglement Dynamics in Spin Systems

Entanglement in the Stabilizer Formalism

Entanglement Flow in Multipartite Systems

Separable States can be Used to Distribute Entanglement

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