%0 Journal Article %J Phys. Rev. Research %D 2022 %T Implementing a Fast Unbounded Quantum Fanout Gate Using Power-Law Interactions %A Andrew Y. Guo %A Abhinav Deshpande %A Su-Kuan Chu %A Zachary Eldredge %A Przemyslaw Bienias %A Dhruv Devulapalli %A Yuan Su %A Andrew M. Childs %A Alexey V. Gorshkov %X

The standard circuit model for quantum computation presumes the ability to directly perform gates between arbitrary pairs of qubits, which is unlikely to be practical for large-scale experiments. Power-law interactions with strength decaying as 1/rα in the distance r provide an experimentally realizable resource for information processing, whilst still retaining long-range connectivity. We leverage the power of these interactions to implement a fast quantum fanout gate with an arbitrary number of targets. Our implementation allows the quantum Fourier transform (QFT) and Shor's algorithm to be performed on a D-dimensional lattice in time logarithmic in the number of qubits for interactions with α≤D. As a corollary, we show that power-law systems with α≤D are difficult to simulate classically even for short times, under a standard assumption that factoring is classically intractable. Complementarily, we develop a new technique to give a general lower bound, linear in the size of the system, on the time required to implement the QFT and the fanout gate in systems that are constrained by a linear light cone. This allows us to prove an asymptotically tighter lower bound for long-range systems than is possible with previously available techniques. 

%B Phys. Rev. Research %V 4 %8 10/27/2022 %G eng %U https://arxiv.org/abs/2007.00662 %N L042016 %R https://doi.org/10.1103/PhysRevResearch.4.L042016 %0 Journal Article %J Phys. Rev. Lett. %D 2020 %T Destructive Error Interference in Product-Formula Lattice Simulation %A Minh C. Tran %A Su-Kuan Chu %A Yuan Su %A Andrew M. Childs %A Alexey V. Gorshkov %X

Quantum computers can efficiently simulate the dynamics of quantum systems. In this paper, we study the cost of digitally simulating the dynamics of several physically relevant systems using the first-order product formula algorithm. We show that the errors from different Trotterization steps in the algorithm can interfere destructively, yielding a much smaller error than previously estimated. In particular, we prove that the total error in simulating a nearest-neighbor interacting system of n sites for time t using the first-order product formula with r time slices is O(nt/r+nt3/r2) when nt2/r is less than a small constant. Given an error tolerance ε, the error bound yields an estimate of max{O(n2t/ε),O(n2t3/2/ε1/2)} for the total gate count of the simulation. The estimate is tighter than previous bounds and matches the empirical performance observed in Childs et al. [PNAS 115, 9456-9461 (2018)]. We also provide numerical evidence for potential improvements and conjecture an even tighter estimate for the gate count. 

%B Phys. Rev. Lett. %V 124 %8 6/4/2020 %G eng %U https://arxiv.org/abs/1912.11047 %N 220502 %R https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.124.220502 %0 Journal Article %J Phys. Rev. Lett. %D 2019 %T Photon pair condensation by engineered dissipation %A Ze-Pei Cian %A Guanyu Zhu %A Su-Kuan Chu %A Alireza Seif %A Wade DeGottardi %A Liang Jiang %A Mohammad Hafezi %X

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. 

%B Phys. Rev. Lett. %V 123 %8 04/02/2019 %G eng %U https://arxiv.org/abs/1904.00016 %N 063602 %R 10.1103/PhysRevLett.123.063602 %0 Journal Article %J Phys. Rev. Lett %D 2019 %T Scale-Invariant Continuous Entanglement Renormalization of a Chern Insulator %A Su-Kuan Chu %A Guanyu Zhu %A James R. Garrison %A Zachary Eldredge %A Ana Valdés Curiel %A Przemyslaw Bienias %A I. B. Spielman %A Alexey V. Gorshkov %X

The multi-scale entanglement renormalization ansatz (MERA) postulates the existence of quantum circuits that renormalize entanglement in real space at different length scales. Chern insulators, however, cannot have scale-invariant discrete MERA circuits with 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 wavefunction with 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. 

%B Phys. Rev. Lett %V 122 %8 03/27/2019 %G eng %U https://arxiv.org/abs/1807.11486 %N 120502 %R https://doi.org/10.1103/PhysRevLett.122.120502 %0 Journal Article %D 2018 %T Two-Dimensional Dilaton Gravity Theory and Lattice Schwarzian Theory %A Su-Kuan Chu %A Chen-Te Ma %A Chih-Hung Wu %X
We report a holographic study of a two-dimensional dilaton gravity theory with the Dirichlet boundary condition for the cases of non-vanishing and vanishing cosmological constants. Our result shows that the boundary theory of the two-dimensional dilaton gravity theory with the Dirichlet boundary condition for the case of non-vanishing cosmological constants is the Schwarzian term coupled to a dilaton field, while for the case of vanishing cosmological constant, a theory does not have a kinetic term. We also include the higher derivative term R2, where R is the scalar curvature that is coupled to a dilaton field. We find that the form of the boundary theory is not modified perturbatively. Finally, we show that a lattice holographic picture is realized up to the second-order perturbation of boundary cut-off ε2 under a constant boundary dilaton field and the non-vanishing cosmological constant by identifying the lattice spacing a of a lattice Schwarzian theory with the boundary cut-off ε of the two-dimensional dilaton gravity theory. 
%G eng %U https://arxiv.org/abs/1802.04599