Built on

Classification of quantum cellular automata
Original
M. Freedman and M. B. Hastings · 1902
Earlier work this paper cites.
Clifford quantum cellular automata: Trivial group in 2d and Witt group in 3d
Original
Jeongwan Haah · 1907
Earlier work this paper cites.
The group structure of quantum cellular automata
Original
Michael Freedman, Jeongwan Haah, and Matthew B. Hastings · 1910
Earlier work this paper cites.
Restrictions on realizable unitary operations imposed by symmetry and locality
Original
Iman Marvian · 2003
Earlier work this paper cites.
Reversible quantum cellular automata
B. Schumacher and R. F. Werner · 2004
Earlier work this paper cites.
Unitarity plus causality implies localizability
Original
Pablo Arrighi, Vincent Nesme, and Reinhard Werner · 2010
Earlier work this paper cites.
Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
Original
Xie Chen, Zheng-Cheng Gu, and Xiao-Gang Wen · 2010
Earlier work this paper cites.
Index theory of one dimensional quantum walks and cellular automata
Original
D. Gross, V. Nesme, H. Vogts, and R. F. Werner · 2012
Earlier work this paper cites.
A converse to lieb-robinson bounds in one dimension using index theory
Original
Daniel Ranard, Michael Walter, and Freek Witteveen · 2012
Earlier work this paper cites.

Similar

Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws
Original
Vedika Khemani, Ashvin Vishwanath, and D. A. Huse · 2018
Cited alongside, same era.
Diffusive hydrodynamics of out-of-time-ordered correlators with charge conservation
Original
Tibor Rakovszky, Frank Pollmann, and C. W. von Keyserlingk · 2018
Cited alongside, same era.
Interacting invariants for floquet phases of fermions in two dimensions
Original
Lukasz Fidkowski, Hoi Chun Po, Andrew C. Potter, and Ashvin Vishwanath · 2019
Cited alongside, same era.
Invertible subalgebras
Original
Jeongwan Haah · 2023
Cited alongside, same era.
Sequential quantum circuits as maps between gapped phases

Then

Learning quantum states prepared by shallow circuits in polynomial time
Original
Zeph Landau and Yunchao Liu · 2024
Later among the works it cites.
Approximate unitary k k -designs from shallow, low-communication circuits
Original
Nicholas LaRacuente and Felix Leditzky · 2024
Later among the works it cites.
Quantum cellular automata on symmetric subalgebras
Original
Ruochen Ma, Yabo Li, and Meng Cheng · 2024
Later among the works it cites.
Random unitaries in extremely low depth
Original
Thomas Schuster, Jonas Haferkamp, and Hsin-Yuan Huang · 2024
Later among the works it cites.
Anticoncentration and magic spreading under ergodic quantum dynamics
Original

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…

Reading the bibliography…

2025

Short remarks on shallow unitary circuits

Haah, Jeongwan

Understand

(i) We point out that every local unitary circuit of depth smaller than the linear system size is easily distinguished from a global Haar random unitary if there is a conserved quantity that is a sum of local operators.

This is always the case with a continuous onsite symmetry or with a local energy conservation law.
(ii) We explain a simple algorithm for a formulation of the shallow unitary circuit learning problem and relate it to an open question on strictly locality-preserving unitaries (quantum cellular automata).
(iii) We show that any translation-invariant quantum cellular automaton in $D$-dimensional lattice of volume $V$ can be implemented using only $O(V)$ local gates in a staircase fashion using invertible subalgebra pumping.

Built on

Classification of quantum cellular automata
Original
M. Freedman and M. B. Hastings · 1902
Earlier work this paper cites.
Clifford quantum cellular automata: Trivial group in 2d and Witt group in 3d
Original
Jeongwan Haah · 1907
Earlier work this paper cites.
The group structure of quantum cellular automata
Original
Michael Freedman, Jeongwan Haah, and Matthew B. Hastings · 1910
Earlier work this paper cites.
Restrictions on realizable unitary operations imposed by symmetry and locality
Original
Iman Marvian · 2003
Earlier work this paper cites.
Reversible quantum cellular automata
B. Schumacher and R. F. Werner · 2004
Earlier work this paper cites.
Unitarity plus causality implies localizability
Original
Pablo Arrighi, Vincent Nesme, and Reinhard Werner · 2010
Earlier work this paper cites.
Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
Original
Xie Chen, Zheng-Cheng Gu, and Xiao-Gang Wen · 2010
Earlier work this paper cites.
Index theory of one dimensional quantum walks and cellular automata
Original
D. Gross, V. Nesme, H. Vogts, and R. F. Werner · 2012
Earlier work this paper cites.
A converse to lieb-robinson bounds in one dimension using index theory
Original
Daniel Ranard, Michael Walter, and Freek Witteveen · 2012
Earlier work this paper cites.

Similar

Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws
Original
Vedika Khemani, Ashvin Vishwanath, and D. A. Huse · 2018
Cited alongside, same era.
Diffusive hydrodynamics of out-of-time-ordered correlators with charge conservation
Original
Tibor Rakovszky, Frank Pollmann, and C. W. von Keyserlingk · 2018
Cited alongside, same era.
Interacting invariants for floquet phases of fermions in two dimensions
Original
Lukasz Fidkowski, Hoi Chun Po, Andrew C. Potter, and Ashvin Vishwanath · 2019
Cited alongside, same era.
Invertible subalgebras
Original
Jeongwan Haah · 2023
Cited alongside, same era.
Sequential quantum circuits as maps between gapped phases

Then

Learning quantum states prepared by shallow circuits in polynomial time
Original
Zeph Landau and Yunchao Liu · 2024
Later among the works it cites.
Approximate unitary k k -designs from shallow, low-communication circuits
Original
Nicholas LaRacuente and Felix Leditzky · 2024
Later among the works it cites.
Quantum cellular automata on symmetric subalgebras
Original
Ruochen Ma, Yabo Li, and Meng Cheng · 2024
Later among the works it cites.
Random unitaries in extremely low depth
Original
Thomas Schuster, Jonas Haferkamp, and Hsin-Yuan Huang · 2024
Later among the works it cites.
Anticoncentration and magic spreading under ergodic quantum dynamics
Original

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…

Original

Xie Chen, Arpit Dua, Michael Hermele, David T. Stephen, Nathanan Tantivasadakarn, Robijn Vanhove, and Jing-Yu Zhao · 2024

Cited alongside, same era.

Learning quantum Hamiltonians from high-temperature Gibbs states and real-time evolutions

Original

Jeongwan Haah, Robin Kothari, and Ewin Tang · 2024

Cited alongside, same era.

Learning shallow quantum circuits

Original

Hsin-Yuan Huang, Yunchao Liu, Michael Broughton, Isaac Kim, Anurag Anshu, Zeph Landau, and Jarrod R. McClean · 2024

Cited alongside, same era.

Learning state preparation circuits for quantum phases of matter

Original

Hyun-Soo Kim, Isaac H. Kim, and Daniel Ranard · 2024

Cited alongside, same era.

Emanuele Tirrito, Xhek Turkeshi, and Piotr Sierant · 2024

Later among the works it cites.

Topological phases of unitary dynamics: Classification in Clifford category

Original

Jeongwan Haah · 2025

Closest in time.

Unitary k-designs from random number-conserving quantum circuits

Original

Sumner N. Hearth, Michael O. Flynn, Anushya Chandran, and Chris R. Laumann · 2025

Closest in time.

Hamiltonian dynamics learning: A scalable approach to quantum process characterization

Original

Yusen Wu, Yukun Zhang, Chuan Wang, and Xiao Yuan · 2025

Closest in time.