@article {liu_circuit_2020,
title = {Circuit complexity across a topological phase transition},
journal = {Phys. Rev. Res.},
volume = {2},
number = {1},
year = {2020},
note = {Place: ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA Publisher: AMER PHYSICAL SOC Type: Article},
month = {mar},
abstract = {We use Nielsen{\textquoteright}s geometric approach to quantify the circuit complexity in a one-dimensional Kitaev chain across a topological phase transition. We find that the circuit complexities of both the ground states and nonequilibrium steady states of the Kitaev model exhibit nonanalytical behaviors at the critical points, and thus can be used to detect both equilibrium and dynamical topological phase transitions. Moreover, we show that the locality property of the real-space optimal Hamiltonian connecting two different ground states depends crucially on whether the two states belong to the same or different phases. This provides a concrete example of classifying different gapped phases using Nielsen{\textquoteright}s circuit complexity. We further generalize our results to a Kitaev chain with long-range pairing, and we discuss generalizations to higher dimensions. Our result opens up an avenue for using circuit complexity as a tool to understand quantum many-body systems.},
doi = {10.1103/PhysRevResearch.2.013323},
author = {Liu, Fangli and Whitsitt, Seth and Curtis, Jonathan B. and Lundgren, Rex and Titum, Paraj and Yang, Zhi-Cheng and Garrison, James R. and Gorshkov, V, Alexey}
}
@article {eldredge_entanglement_2020,
title = {Entanglement bounds on the performance of quantum computing architectures},
journal = {Phys. Rev. Res.},
volume = {2},
number = {3},
year = {2020},
note = {Place: ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA Publisher: AMER PHYSICAL SOC Type: Article},
month = {aug},
abstract = {There are many possible architectures of qubit connectivity that designers of future quantum computers will need to choose between. However, the process of evaluating a particular connectivity graph{\textquoteright}s performance as a quantum architecture can be difficult. In this paper, we show that a quantity known as the isoperimetric number establishes a lower bound on the time required to create highly entangled states. This metric we propose counts resources based on the use of two-qubit unitary operations, while allowing for arbitrarily fast measurements and classical feedback. We use this metric to evaluate the hierarchical architecture proposed by A. Bapat et al. [Phys. Rev. A 98, 062328 (2018)] and find it to be a promising alternative to the conventional grid architecture. We also show that the lower bound that this metric places on the creation time of highly entangled states can be saturated with a constructive protocol, up to a factor logarithmic in the number of qubits.},
doi = {10.1103/PhysRevResearch.2.033316},
author = {Eldredge, Zachary and Zhou, Leo and Bapat, Aniruddha and Garrison, James R. and Deshpande, Abhinav and Chong, Frederic T. and Gorshkov, V, Alexey}
}
@article {ISI:000474892400001,
title = {Locality and Digital Quantum Simulation of Power-Law Interactions},
journal = {Phys. Rev. X},
volume = {9},
number = {3},
year = {2019},
month = {JUL 10},
pages = {031006},
publisher = {AMER PHYSICAL SOC},
type = {Article},
abstract = {The propagation of information in nonrelativistic quantum systems obeys a speed limit known as a Lieb-Robinson bound. We derive a new Lieb-Robinson bound for systems with interactions that decay with distance r as a power law, 1/r(alpha). The bound implies an effective light cone tighter than all previous bounds. Our approach is based on a technique for approximating the time evolution of a system, which was first introduced as part of a quantum simulation algorithm by Haah et al., FOCS{\textquoteright} 18. To bound the error of the approximation, we use a known Lieb-Robinson bound that is weaker than the bound we establish. This result brings the analysis full circle, suggesting a deep connection between Lieb-Robinson bounds and digital quantum simulation. In addition to the new Lieb-Robinson bound, our analysis also gives an error bound for the Haah et al. quantum simulation algorithm when used to simulate power-law decaying interactions. In particular, we show that the gate count of the algorithm scales with the system size better than existing algorithms when alpha > 3D (where D is the number of dimensions).},
issn = {2160-3308},
doi = {10.1103/PhysRevX.9.031006},
author = {Tran, Minh C. and Guo, Andrew Y. and Su, Yuan and Garrison, James R. and Eldredge, Zachary and Foss-Feig, Michael and Childs, Andrew M. and Gorshkov, Alexey V.}
}
@article {ISI:000485202800004,
title = {Probing Ground-State Phase Transitions through Quench Dynamics},
journal = {Phys. Rev. Lett.},
volume = {123},
number = {11},
year = {2019},
month = {SEP 11},
pages = {115701},
publisher = {AMER PHYSICAL SOC},
type = {Article},
abstract = {The study of quantum phase transitions requires the preparation of a many-body system near its ground state, a challenging task for many experimental systems. The measurement of quench dynamics, on the other hand, is now a routine practice in most cold atom platforms. Here we show that quintessential ingredients of quantum phase transitions can be probed directly with quench dynamics in integrable and nearly integrable systems. As a paradigmatic example, we study global quench dynamics in a transverse-field Ising model with either short-range or long-range interactions. When the model is integrable, we discover a new dynamical critical point with a nonanalytic signature in the short-range correlators. The location of the dynamical critical point matches that of the quantum critical point and can be identified using a finite-time scaling method. We extend this scaling picture to systems near integrability and demonstrate the continued existence of a dynamical critical point detectable at prethermal timescales. We quantify the difference in the locations of the dynamical and quantum critical points away from (but near) integrability. Thus, we demonstrate that this method can be used to approximately locate the quantum critical point near integrability. The scaling method is also relevant to experiments with finite time and system size, and our predictions are testable in near-term experiments with trapped ions and Rydberg atoms.},
issn = {0031-9007},
doi = {10.1103/PhysRevLett.123.115701},
author = {Titum, Paraj and Iosue, Joseph T. and Garrison, James R. and Gorshkov, Alexey V. and Gong, Zhe-Xuan}
}
@article {ISI:000462935500003,
title = {Scale-Invariant Continuous Entanglement Renormalization of a Chern Insulator},
journal = {Phys. Rev. Lett.},
volume = {122},
number = {12},
year = {2019},
month = {MAR 27},
pages = {120502},
publisher = {AMER PHYSICAL SOC},
type = {Article},
abstract = {The multiscale entanglement renormalization ansatz (MERA) postulates the existence of quantum circuits that renormalize entanglement in real space at different length scales. Chem insulators, however, cannot have scale-invariant discrete MERA circuits with a finite bond dimension. In this Letter, we show that the continuous MERA (cMERA), a modified version of MERA adapted for field theories, possesses a fixed point wave function with a nonzero Chern number. Additionally, it is well known that reversed MERA circuits can be used to prepare quantum states efficiently in time that scales logarithmically with the size of the system. However, state preparation via MERA typically requires the advent of a full-fledged universal quantum computer. In this Letter, we demonstrate that our cMERA circuit can potentially be realized in existing analog quantum computers, i.e., an ultracold atomic Fermi gas in an optical lattice with light-induced spin-orbit coupling.},
issn = {0031-9007},
doi = {10.1103/PhysRevLett.122.120502},
author = {Chu, Su-Kuan and Zhu, Guanyu and Garrison, James R. and Eldredge, Zachary and Curiel, Ana Valdes and Bienias, Przemyslaw and Spielman, I. B. and Gorshkov, V, Alexey}
}
@article {10551,
title = {Asymmetric Particle Transport and Light-Cone Dynamics Induced by Anyonic Statistics},
journal = {Phys. Rev. Lett.},
volume = {121},
year = {2018},
month = {Dec},
pages = {250404},
doi = {10.1103/PhysRevLett.121.250404},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.121.250404},
author = {Liu, Fangli and Garrison, James R. and Deng, Dong-Ling and Gong, Zhe-Xuan and Gorshkov, Alexey V.}
}
@article { ISI:000432971400001,
title = {Does a Single Eigenstate Encode the Full Hamiltonian?},
journal = {PHYSICAL REVIEW X},
volume = {8},
number = {2},
year = {2018},
month = {APR 30},
pages = {021026},
issn = {2160-3308},
doi = {10.1103/PhysRevX.8.021026},
author = {Garrison, James R. and Grover, Tarun}
}
@article { ISI:000454419500004,
title = {Unitary entanglement construction in hierarchical networks},
journal = {PHYSICAL REVIEW A},
volume = {98},
number = {6},
year = {2018},
month = {DEC 26},
pages = {062328},
abstract = {The construction of large-scale quantum computers will require modular architectures that allow physical resources to be localized in easy-to-manage packages. In this work we examine the impact of different graph structures on the preparation of entangled states. We begin by explaining a formal framework, the hierarchical product, in which modular graphs can be easily constructed. This framework naturally leads us to suggest a class of graphs, which we dub hierarchies. We argue that such graphs have favorable properties for quantum information processing, such as a small diameter and small total edge weight, and use the concept of Pareto efficiency to identify promising quantum graph architectures. We present numerical and analytical results on the speed at which large entangled states can be created on nearest-neighbor grids and hierarchy graphs. We also present a scheme for performing circuit placement-the translation from circuit diagrams to machine qubits-on quantum systems whose connectivity is described by hierarchies.},
issn = {2469-9926},
doi = {10.1103/PhysRevA.98.062328},
author = {Bapat, Aniruddha and Eldredge, Zachary and Garrison, James R. and Deshpande, Abhinav and Chong, Frederic T. and Gorshkov, Alexey V.}
}
@article { ISI:000412061700002,
title = {Extracting Entanglement Geometry from Quantum States},
journal = {PHYSICAL REVIEW LETTERS},
volume = {119},
number = {14},
year = {2017},
month = {OCT 2},
issn = {0031-9007},
doi = {10.1103/PhysRevLett.119.140502},
author = {Hyatt, Katharine and Garrison, James R. and Bauer, Bela}
}
@article { ISI:000416232300009,
title = {Lieb-Robinson bounds on n-partite connected correlation functions},
journal = {PHYSICAL REVIEW A},
volume = {96},
number = {5},
year = {2017},
month = {NOV 27},
issn = {2469-9926},
doi = {10.1103/PhysRevA.96.052334},
author = {Tran, Minh Cong and Garrison, James R. and Gong, Zhe-Xuan and Gorshkov, Alexey V.}
}