One of the main topological invariants that characterizes several topologically ordered phases is the many-body Chern number (MBCN). Paradigmatic examples include several fractional quantum Hall phases, which are expected to be realized in different atomic and photonic quantum platforms in the near future. Experimental measurement and numerical computation of this invariant are conventionally based on the linear-response techniques that require having access to a family of states, as a function of an external parameter, which is not suitable for many quantum simulators. Here, we propose an ancilla-free experimental scheme for the measurement of this invariant, without requiring any knowledge of the Hamiltonian. Specifically, we use the statistical correlations of randomized measurements to infer the MBCN of a wave function. Remarkably, our results apply to disklike geometries that are more amenable to current quantum simulator architectures.

}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.126.050501}, author = {Cian, Ze-Pei and Dehghani, Hossein and Elben, Andreas and Vermersch, Benoit and Zhu, Guanyu and Barkeshli, Maissam and Zoller, Peter and Hafezi, Mohammad} } @article {16956, title = {Instantaneous braids and Dehn twists in topologically ordered states}, journal = {Phys. Rev. B}, volume = {102}, year = {2020}, month = {Aug}, pages = {075105}, doi = {10.1103/PhysRevB.102.075105}, url = {https://link.aps.org/doi/10.1103/PhysRevB.102.075105}, author = {Zhu, Guanyu and Lavasani, Ali and Barkeshli, Maissam} } @article {16666, title = {Many-body topological invariants from randomized measurements in synthetic quantum matter}, journal = {Science Advances}, volume = {6}, year = {2020}, abstract = {Many-body topological invariants, as quantized highly nonlocal correlators of the many-body wave function, are at the heart of the theoretical description of many-body topological quantum phases, including symmetry-protected and symmetry-enriched topological phases. Here, we propose and analyze a universal toolbox of measurement protocols to reveal many-body topological invariants of phases with global symmetries, which can be implemented in state-of-the-art experiments with synthetic quantum systems, such as Rydberg atoms, trapped ions, and superconducting circuits. The protocol is based on extracting the many-body topological invariants from statistical correlations of randomized measurements, implemented with local random unitary operations followed by site-resolved projective measurements. We illustrate the technique and its application in the context of the complete classification of bosonic symmetry-protected topological phases in one dimension, considering in particular the extended Su-Schrieffer-Heeger spin model, as realized with Rydberg tweezer arrays.

}, doi = {10.1126/sciadv.aaz3666}, url = {https://advances.sciencemag.org/content/6/15/eaaz3666}, author = {Elben, Andreas and Yu, Jinlong and Zhu, Guanyu and Hafezi, Mohammad and Pollmann, Frank and Zoller, Peter and Vermersch, Beno\^{\i}t} } @article {zhu_quantum_2020, title = {Quantum origami: {Transversal} gates for quantum computation and measurement of topological order}, 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 = {In topology, a torus remains invariant under certain nontrivial transformations known as modular transformations. In the context of topologically ordered quantum states of matter supported on a torus geometry in real space, these transformations encode the braiding statistics and fusion rules of emergent anyonic excitations and thus serve as a diagnostic of topological order. Moreover, modular transformations of higher genus surfaces, e.g., a torus with multiple handles, can enhance the computational power of a topological state, in many cases providing a universal fault-tolerant set of gates for quantum computation. However, due to the intrusive nature of modular transformations, which abstractly involve global operations, physical implementations of them in local systems have remained elusive. Here, we show that by engineering an effectively folded manifold corresponding to a multilayer topological system, modular transformations can be applied in a single shot by independent local unitaries, providing a novel class of transversal logical gates for fault-tolerant quantum computation. Specifically, we demonstrate that multilayer topological states with appropriate boundary conditions and twist defects allow modular transformations to be effectively implemented by a finite sequence of local SWAP gates between the layers. We further provide methods to directly measure the modular matrices, and thus the fractional statistics of anyonic excitations, providing a novel way to directly measure topological order. A more general theory of transversal gates and the deep connection to anyon symmetry transformation and symmetry-enriched topological orders are also discussed.}, doi = {10.1103/PhysRevResearch.2.013285}, author = {Zhu, Guanyu and Hafezi, Mohammad and Barkeshli, Maissam} } @article {16951, title = {Universal Logical Gates on Topologically Encoded Qubits via Constant-Depth Unitary Circuits}, journal = {Phys. Rev. Lett.}, volume = {125}, year = {2020}, month = {Jul}, pages = {050502}, doi = {10.1103/PhysRevLett.125.050502}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.125.050502}, author = {Zhu, Guanyu and Lavasani, Ali and Barkeshli, Maissam} } @article { ISI:000457704900001, title = {Interacting Qubit-Photon Bound States with Superconducting Circuits}, journal = {PHYSICAL REVIEW X}, volume = {9}, number = {1}, year = {2019}, month = {FEB 1}, pages = {011021}, issn = {2160-3308}, doi = {10.1103/PhysRevX.9.011021}, author = {Sundaresan, Neereja M. and Lundgren, Rex and Zhu, Guanyu and Gorshkov, V, Alexey and Houck, Andrew A.} } @article {ISI:000479005400008, title = {Photon Pair Condensation by Engineered Dissipation}, journal = {Phys. Rev. Lett.}, volume = {123}, number = {6}, year = {2019}, month = {AUG 6}, pages = {063602}, publisher = {AMER PHYSICAL SOC}, type = {Article}, abstract = {Dissipation can usually induce detrimental decoherence in a quantum system. However, engineered dissipation can be used to prepare and stabilize coherent quantum many-body states. Here, we show that, by engineering dissipators containing photon pair operators, one can stabilize an exotic dark state, which is a condensate of photon pairs with a phase-nematic order. In this system, the usual superfluid order parameter, i.e., single-photon correlation, is absent, while the photon pair correlation exhibits long-range order. Although the dark state is not unique due to multiple parity sectors, we devise an additional type of dissipators to stabilize the dark state in a particular parity sector via a diffusive annihilation process which obeys Glauber dynamics in an Ising model. Furthermore, we propose an implementation of these photon pair dissipators in circuit-QED architecture.}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.123.063602}, author = {Cian, Ze-Pei and Zhu, Guanyu and Chu, Su-Kuan and Seif, Alireza and DeGottardi, Wade and Jiang, Liang and Hafezi, Mohammad} } @article {14466, title = {Photonic quadrupole topological phases}, journal = {Nature Photonics}, year = {2019}, abstract = {The topological phases of matter are characterized using the Berry phase, a geometrical phase associated with the energy-momentum band structure. The quantization of the Berry phase and the associated wavefunction polarization manifest as remarkably robust physical observables, such as quantized Hall conductivity and disorder-insensitive photonic transport1{\textendash}5. Recently, a novel class of topological phases, called higher-order topological phases, were proposed by generalizing the fundamental relationship between the Berry phase and quantized polarization, from dipole to multipole moments6{\textendash}8. Here, we demonstrate photonic realization of the quantized quadrupole topological phase, using silicon photonics. In our two-dimensional second-order topological phase, we show that the quantization of the bulk quadrupole moment manifests as topologically robust zero-dimensional corner states. We contrast these topological states against topologically trivial corner states in a system without bulk quadrupole moment, where we observe no robustness. Our photonic platform could enable the development of robust on-chip classical and quantum optical devices with higher-order topological protection.

}, isbn = {1749-4893}, doi = {10.1038/s41566-019-0452-0}, url = {https://doi.org/10.1038/s41566-019-0452-0}, author = {Mittal, Sunil and Orre, Venkata Vikram and Zhu, Guanyu and Gorlach, Maxim A. and Poddubny, Alexander and Hafezi, Mohammad} } @article {ISI:000485187000003, title = {Quantum information scrambling through a high-complexity operator mapping}, journal = {Phys. Rev. A}, volume = {100}, number = {3}, year = {2019}, month = {SEP 6}, pages = {032309}, publisher = {AMER PHYSICAL SOC}, type = {Article}, abstract = {Quantum information scrambling has attracted much attention amid the effort to reconcile the conflict between quantum-mechanical unitarity and the thermalization irreversibility in many-body systems. Here we propose an unconventional mechanism to generate quantum information scrambling through a high-complexity mapping from logical to physical degrees-of-freedom that hides the logical information into nonseparable many-body correlations. Corresponding to this mapping, we develop an algorithm to efficiently sample a Slater-determinant wave function and compute all physical observables in dynamics with a polynomial cost in system size. The system shows information scrambling in the quantum many-body Hilbert space characterized by the spreading of Hamming distance. At late time we find emergence of classical diffusion dynamics in this quantum many-body system. We establish that the operator mapping enabled growth in an out-of-time-order correlator exhibits exponential-scrambling behavior. The quantum information-hiding mapping approach may shed light on the understanding of fundamental connections among computational complexity, information scrambling, and quantum thermalization.}, issn = {2469-9926}, doi = {10.1103/PhysRevA.100.032309}, author = {Li, Xiaopeng and Zhu, Guanyu and Han, Muxin and Wang, Xin} } @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 {ISI:000482956700001, title = {Universal logical gates with constant overhead: instantaneous Dehn twists for hyperbolic quantum codes}, journal = {Quantum}, volume = {3}, year = {2019}, month = {JUL 26}, publisher = {VEREIN FORDERUNG OPEN ACCESS PUBLIZIERENS QUANTENWISSENSCHAF}, type = {Article}, abstract = {A basic question in the theory of fault-tolerant quantum computation is to understand the fundamental resource costs for performing a universal logical set of gates on encoded qubits to arbitrary accuracy. Here we consider qubits encoded with constant space overhead (i.e. finite encoding rate) in the limit of arbitrarily large code distance d through the use of topological codes associated to triangulations of hyperbolic surfaces. We introduce explicit protocols to demonstrate how Dehn twists of the hyperbolic surface can be implemented on the code through constant depth unitary circuits, without increasing the space overhead. The circuit for a given Dehn twist consists of a permutation of physical qubits, followed by a constant depth local unitary circuit, where locality here is defined with respect to a hyperbolic metric that defines the code. Applying our results to the hyperbolic Fibonacci Turaev-Viro code implies the possibility of applying universal logical gate sets on encoded qubits through constant depth unitary circuits and with constant space overhead. Our circuits are inherently protected from errors as they map local operators to local operators while changing the size of their support by at most a constant factor; in the presence of noisy syndrome measurements, our results suggest the possibility of universal fault tolerant quantum computation with constant space overhead and time overhead of O(d/log d). For quantum circuits that allow parallel gate operations, this yields the optimal scaling of space-time overhead known to date.}, issn = {2521-327X}, author = {Lavasani, Ali and Zhu, Guanyu and Barkeshli, Maissam} } @article {ISI:000428598700001, title = {Hardware-efficient fermionic simulation with a cavity-QED system}, journal = {NPJ QUANTUM INFORMATION}, volume = {4}, year = {2018}, month = {FEB 27}, pages = {16}, publisher = {NATURE PUBLISHING GROUP}, type = {Article}, abstract = {In digital quantum simulation of fermionic models with qubits, non-local maps for encoding are often encountered. Such maps require linear or logarithmic overhead in circuit depth which could render the simulation useless, for a given decoherence time. Here we show how one can use a cavity-QED system to perform digital quantum simulation of fermionic models. In particular, we show that highly nonlocal Jordan-Wigner or Bravyi-Kitaev transformations can be efficiently implemented through a hardware approach. The key idea is using ancilla cavity modes, which are dispersively coupled to a qubit string, to collectively manipulate and measure qubit states. Our scheme reduces the circuit depth in each Trotter step of the Jordan-Wigner encoding by a factor of N-2, comparing to the scheme for a device with only local connectivity, where N is the number of orbitals for a generic two-body Hamiltonian. Additional analysis for the Fermi-Hubbard model on an N x N square lattice results in a similar reduction. We also discuss a detailed implementation of our scheme with superconducting qubits and cavities.}, \%\%Address = {MACMILLAN BUILDING, 4 CRINAN ST, LONDON N1 9XW, ENGLAND}, issn = {2056-6387}, doi = {10.1038/s41534-018-0065-3}, author = {Zhu, Guanyu and Subasi, Yigit and Whitfield, James D. and Hafezi, Mohammad} } @article { ISI:000447301700001, title = {Optical control over bulk excitations in fractional quantum Hall systems}, journal = {PHYSICAL REVIEW B}, volume = {98}, number = {15}, year = {2018}, month = {OCT 15}, pages = {155124}, issn = {2469-9950}, doi = {10.1103/PhysRevB.98.155124}, author = {Grass, Tobias and Gullans, Michael and Bienias, Przemyslaw and Zhu, Guanyu and Ghazaryan, Areg and Ghaemi, Pouyan and Hafezi, Mohammad} } @article { ISI:000445733100006, title = {Optical Lattice with Torus Topology}, journal = {PHYSICAL REVIEW LETTERS}, volume = {121}, number = {13}, year = {2018}, month = {SEP 26}, pages = {133002}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.121.133002}, author = {Kim, Hwanmun and Zhu, Guanyu and Porto, V, J. and Hafezi, Mohammad} } @article {ISI:000390255800002, title = {Measurement of many-body chaos using a quantum clock}, journal = {PHYSICAL REVIEW A}, volume = {94}, number = {6}, year = {2016}, month = {DEC 22}, pages = {062329}, abstract = {There has been recent progress in understanding chaotic features in many-body quantum systems. Motivated by the scrambling of information in black holes, it has been suggested that the time dependence of out-of-time-ordered (OTO) correlation functions such as < O-2(t)O-1(0)O-2(t)O-1(0)> is a faithful measure of quantum chaos. Experimentally, these correlators are challenging to access since they apparently require access to both forward and backward time evolution with the system Hamiltonian. Here we propose a protocol to measure such OTO correlators using an ancilla that controls the direction of time. Specifically, by coupling the state of the ancilla to the system Hamiltonian of interest, we can emulate the forward and backward time propagation, where the ancilla plays the role of a quantum clock. Within this scheme, the continuous evolution of the entire system (the system of interest and the ancilla) is governed by a time-independent Hamiltonian. We discuss the implementation of our protocol with current circuit-QED technology for a class of interacting Hamiltonians. Our protocol is immune to errors that could occur when the direction of time evolution is externally controlled by a classical switch.}, issn = {2469-9926}, doi = {10.1103/PhysRevA.94.062329}, author = {Zhu, Guanyu and Hafezi, Mohammad and Grover, Tarun} } @article {ISI:000388280000002, title = {Measurement Protocol for the Entanglement Spectrum of Cold Atoms}, journal = {PHYSICAL REVIEW X}, volume = {6}, number = {4}, year = {2016}, month = {NOV 17}, pages = {041033}, abstract = {Entanglement, and, in particular, the entanglement spectrum, plays a major role in characterizing many-body quantum systems. While there has been a surge of theoretical works on the subject, no experimental measurement has been performed to date because of the lack of an implementable measurement scheme. Here, we propose a measurement protocol to access the entanglement spectrum of many-body states in experiments with cold atoms in optical lattices. Our scheme effectively performs a Ramsey spectroscopy of the entanglement Hamiltonian and is based on the ability to produce several copies of the state under investigation, together with the possibility to perform a global swap gate between two copies conditioned on the state of an auxiliary qubit. We show how the required conditional swap gate can be implemented with cold atoms, either by using Rydberg interactions or coupling the atoms to a cavity mode. We illustrate these ideas on a simple (extended) Bose-Hubbard model where such a measurement protocol reveals topological features of the Haldane phase.}, issn = {2160-3308}, doi = {10.1103/PhysRevX.6.041033}, author = {Pichler, Hannes and Zhu, Guanyu and Seif, Alireza and Zoller, Peter and Hafezi, Mohammad} }