Quantum simulator with the ability to harness the dynamics of complex quantum systems has emerged as a promising platform for probing exotic topological phases. Since the flexibility offered by various controllable quantum systems has enabled to gain insight into quantum simulation of such complicated problems, analog quantum simulator has recently shown its feasibility to tackle problems of exploring topological phases. However, digital quantum simulation and detection of topological phases still remain elusive. Here, we develop and experimentally realize the digital quantum simulation of topological phase with a solid-state quantum simulator at room temperature. Distinct from previous works dealing with static topological phases, the topological phases emulated here are Floquet topological phases. Furthermore, we also illustrate the procedure of digitally simulating a quantum quench and observing the nonequilibrium dynamics of Floquet topological phases. By means of quantum quench, the 0- and π-energy topological invariants are unambiguously detected through measuring time-averaged spin polarizations. Our experiment opens up a new avenue to digitally simulate and detect Floquet topological phases with fast-developed programmable quantum simulators.
The most typical ingredient of topologically protected quantum states are magnetic fluxes. In a system of spins, complex-valued interaction parameters give rise to a flux, if their phases do not add up to zero along a closed loop. Here we apply periodic driving, a powerful tool for quantum engineering, to a trapped-ion quantum simulator in order to generate such spin-spin interactions. We consider a simple driving scheme, consisting of a repeated series of locally quenched fields, and demonstrate the feasibility of this approach by studying the dynamics of a small system. An emblematic hallmar…
The kicked top is one of the paradigmatic models in the study of quantum chaos~[F.~Haake et al., \emph{Quantum Signatures of Chaos (Springer Series in Synergetics vol 54)} (2018)]. Recently it has been shown that the onset of quantum chaos in the kicked top can be related to the proliferation of Trotter errors in digital quantum simulation (DQS) of collective spin systems. Specifically, the proliferation of Trotter errors becomes manifest in expectation values of few-body observables strongly deviating from the target dynamics above a critical Trotter step, where the spectral statistics of the…
We demonstrate Floquet engineering in a basic yet scalable 2D architecture of individually trapped and controlled ions. Local parametric modulations of detuned trapping potentials steer the strength of long-range inter-ion couplings and the related Peierls phase of the motional state. In our proof-of-principle, we initialize large coherent states and tune modulation parameters to control trajectories, directions and interferences of the phonon flow. Our findings open a new pathway for future Floquet-based trapped-ion quantum simulators targeting correlated topological phenomena and dynamical g…
We experimentally observe Floquet Raman transitions in the weakly driven solid state spin system of nitrogen-vacancy center in diamond. The periodically driven spin system simulates a two-band Wannier-Stark ladder model, and allows us to observe coherent spin state transfer arising from Raman transition mediated by Floquet synthetic levels. It also leads to the prediction of analog photon-assisted Floquet Raman transition and dynamical localisation in a driven two-level quantum system. The demonstrated rich Floquet dynamics offers new capabilities to achieve effective Floquet coherent control …
For a digital quantum simulator (DQS) imitating a target system, we ask the following question: Under what conditions is the simulator dynamics similar to that of the target in the presence of coupling to a bath? In this paper, we derive conditions for close simulation for three different physical regimes, replacing previous heuristic arguments on the subject with rigorous statements. In fact, we find that the conventional wisdom that the simulation cycle time should always be short for good simulation need not always hold up. Numerical simulations of two specific examples strengthen the evide…
Resolving quantum many-body problems represents one of the greatest challenges in physics and physical chemistry, due to the prohibitively large computational resources that would be required by using classical computers. A solution has been foreseen by directly simulating the time evolution through sequences of quantum gates applied to arrays of qubits, i.e. by implementing a digital quantum simulator. Superconducting circuits and resonators are emerging as an extremely-promising platform for quantum computation architectures, but a digital quantum simulator proposal that is straightforwardly…
Periodically driven systems, or Floquet systems, exhibit many novel dynamics and interesting out-of-equilibrium phases of matter. Those phases arising with the quantum systems' symmetries, such as global $U(1)$ symmetry, can even show dynamical stability with symmetry-protection. Here we experimentally demonstrate a $U(1)$ symmetry-protected prethermal phase, via performing a digital-analog quantum simulation on a superconducting quantum processor. The dynamical stability of this phase is revealed by its robustness against external perturbations. We also find that the spin glass order paramete…
Rydberg Atoms in a Ladder Geometry: Quench Dynamics and Floquet Engineering
School of Physical Sciences, Indian Association for the Cultivation of Science（印度科学培养协会物理科学学院）；International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（塔塔基础研究所国际理论科学中心）
The critical point and the critical exponents for a phase transition can be determined using the Finite-Size Scaling (FSS) analysis. This method assumes that the phase transition occurs only in the infinite size limit. However, there has been a lot of interest recently in quantum phase transitions occuring in finite size systems such as a single two-level system interacting with a single bosonic mode e.g. in the Quantum Rabi Model (QRM). Since, these phase transitions occur at a finite system size, the traditional FSS method is rendered inapplicable for these cases. For cases like this, we pro…
The goal of digital quantum simulation is to approximate the dynamics of a given target Hamiltonian via a sequence of quantum gates, a procedure known as Trotterization. The quality of this approximation can be controlled by the so called Trotter step, that governs the number of required quantum gates per unit simulation time. The stroboscopic dynamics generated by Trotterization is effectively described by a time-independent Hamiltonian, referred to as the Floquet Hamiltonian. In this work, we propose Floquet Hamiltonian learning to reconstruct the experimentally realized Floquet Hamiltonian …
We propose a quantum algorithm for simulating spin models based on periodic modulation of transmon qubits. Using Floquet theory we derive an effective time-averaged Hamiltonian, which is of the general XYZ class, different from the isotropic XY Hamiltonian typically realised by the physical setup. As an example, we provide a simple recipe to construct a transverse Ising Hamiltonian in the Floquet basis. For a 1D system we demonstrate numerically the dynamical simulation of the transverse Ising Hamiltonian and quantum annealing to its ground state. We benchmark the Floquet approach with a digit…
The atomic Quantum Kicked Rotor is an outstanding "quantum simulator" for the exploration of transport in disordered quantum systems. Here we study experimentally the phase-shifted quantum kicked rotor, which we show to display properties close to an ideal disordered quantum system, opening new windows into the study of Anderson physics.
In quantum mechanics, adiabatic elimination is a standard tool that produces a low-lying reduced Hamiltonian for a relevant subspace of states, incorporating effects of its coupling to states with much higher energy. Suppose this powerful elimination approach is applied to quasi-energy states in periodically-driven systems, a critical question then arises that the violation of the adiabatic condition caused by driven forces challenges such a presence of spectral reduction in the non-equilibrium driven system. Here, both theoretically and experimentally, we newly reported two kinds of driven-in…
Dynamical quantum phase transitions (DQPTs) are characterized by nonanalytic behaviors of physical observables as functions of time. When a system is subject to time-periodic modulations, the nonanalytic signatures of its observables could recur periodically in time, leading to the phenomena of Floquet DQPTs. In this work, we systematically explore Floquet DQPTs in a class of periodically quenched one-dimensional system with chiral symmetry. By tuning the strength of quench, we find multiple Floquet DQPTs within a single driving period, with more DQPTs being observed when the system is initial…
A digital quantum simulator is an envisioned quantum device that can be pro- grammed to efficiently simulate any other local system. We demonstrate and investigate the digital approach to quantum simulation in a system of trapped ions. Using sequences of up to 100 gates and 6 qubits, the full time dynamics of a range of spin systems are digitally simulated. Interactions beyond those naturally present in our simulator are accurately reproduced and quantitative bounds are provided for the overall simulation quality. Our results demon- strate the key principles of digital quantum simulation and p…
Quantum annealing is a promising approach to heuristically solving difficult combinatorial optimization problems. However, the connectivity limitations in current devices lead to an exponential degradation of performance on general problems. We propose an architecture for a quantum annealer that achieves full connectivity and full programmability while using a number of physical resources only linear in the number of spins. We do so by application of carefully engineered periodic modulations of oscillator-based qubits, resulting in a Floquet Hamiltonian in which all the interactions are tunabl…
Simulating the topological phases of matter in synthetic quantum simulators is a topic of considerable interest. Given the universality of digital quantum simulators, the prospect of digitally simulating exotic topological phases is greatly enhanced. However, it is still an open question how to realize digital quantum simulation of topological phases of matter. Here, using common single- and two-qubit elementary quantum gates, we propose and demonstrate an approach to design topologically protected quantum circuits on the current generation of noisy quantum processors where spin-orbital coupli…
Recent progresses on Floquet topological phases have shed new light on time-dependant quantum systems, among which one-dimensional (1D) Floquet systems have been under extensive theoretical research. However, an unambiguous experimental observation of these 1D Floquet topological phases has still been lacking. Here, by periodically bending ultrathin metallic arrays of coupled corrugated waveguides, a photonic Floquet simulator was well designed and successfully fabricated to simulate the periodically driven Su-Schrieffer-Heeger model. Intriguingly, under moderate driven frequencies, we first e…
Digital quantum simulators are among the most appealing applications of a quantum computer. Here we propose a universal, scalable, and integrated quantum computing platform based on tunable nonlinear electromechanical nano-oscillators. It is shown that very high operational fidelities for single and two qubits gates can be achieved in a minimal architecture, where qubits are encoded in the anharmonic vibrational modes of mechanical nanoresonators, whose effective coupling is mediated by virtual fluctuations of an intermediate superconducting artificial atom. An effective scheme to induce large…
We study the behavior of errors in the quantum simulation of spin systems with long-range multi-body interactions resulting from the Trotter-Suzuki decomposition of the time-evolution operator. We identify a regime where the Floquet operator underlying the Trotter decomposition undergoes sharp changes even for small variations in the simulation step size. This results in a time evolution operator that is very different from the dynamics generated by the targeted Hamiltonian, which leads to a proliferation of errors in the quantum simulation. These regions of sharp change in the Floquet operato…
We propose the implementation of a digital quantum simulator for prototypical spin models in a circuit quantum electrodynamics architecture. We consider the feasibility of the quantum simulation of Heisenberg and frustrated Ising models in transmon qubits coupled to coplanar waveguide microwave resonators. Furthermore, we analyze the time evolution of these models and compare the ideal spin dynamics with a realistic version of the proposed quantum simulator. Finally, we discuss the key steps for developing the toolbox of digital quantum simulators in superconducting circuits.
One of the key applications for the emerging quantum simulators is to emulate the ground state of many-body systems, as it is of great interest in various fields from condensed matter physics to material science. Traditionally, in an analog sense, adiabatic evolution has been proposed to slowly evolve a simple Hamiltonian, initialized in its ground state, to the Hamiltonian of interest such that the final state becomes the desired ground state. Recently, variational methods have also been proposed and realized in quantum simulators for emulating the ground state of many-body systems. Here, we …
Many-body phenomena far from equilibrium present challenges beyond reach by classical computational resources. Digital quantum computers provide a possible way forward but noise limits their use in the near-term. We propose a scheme to simulate and characterize many-body Floquetsystems hosting a rich variety of phases that operates with a shallow depth circuit. Starting from a "clean" periodic circuit that simulates the dynamical evolution of a Floquet system, we introduce quasi-periodicity to the circuit parameters to prevent thermalization by introducing many-body localization. By inspecting…
We develop a Floquet protocol for long-range entanglement generation in the one-dimensional quantum Potts model, which generalizes the transverse-filed Ising model by allowing each spin to have $n>2$ states. We focus on the case of $n=3$, so that the model describes a chain of qutrits. The suggested protocol creates qutrit Bell-like pairs with non-local long-range entanglement that spans over the entire chain. We then conjecture that the proposed Floquet protocol is integrable and explicitly construct a few first non-trivial conserved quantities that commute with the stroboscopic evolution ope…
We provide a recipe for the digitalization of linear and nonlinear quantum optics in networks of superconducting qubits. By combining digital techniques with boson-qubit mappings we address relevant problems which are typically considered in analog simulators, such as the dynamical Casimir effect or molecular force fields, including nonlinearities. In this way, the benefits of digitalization are extended in principle to a new realm of physical problems. We present preliminary examples launched in IBM Q 5 Tenerife.
Floquet engineering provides a toolbox for the realization of novel quantum phases without static counterparts, while conventionally the realization may rely on the manipulation of complex temporal evolution. Here we propose a systematic and high-precision scheme to realize unconventional Floquet topological phases by engineering local band structures in particular momentum subspace called band inversion surfaces (BISs). This scheme is based on a new bulk-boundary correspondence that for a class of generic $d$-dimensional periodically driven systems, the local topological structure formed in e…
With quantum computers being out of reach for now, quantum simulators are the alternative devices for efficient and more exact simulation of problems that are challenging on conventional computers. Quantum simulators are classified into analog and digital, with the possibility of constructing "hybrid" simulators by combining both techniques. In this paper, we focus on analog quantum simulators of open quantum systems and address the limit that they can beat classical computers. In particular, as an example, we discuss simulation of the chlorosome light-harvesting antenna from green sulfur bact…
The past few years have witnessed the concrete and fast spreading of quantum technologies for practical computation and simulation. In particular, quantum computing platforms based on either trapped ions or superconducting qubits have become available for simulations and benchmarking, with up to few tens of qubits that can be reliably initialized, controlled, and measured. The present review aims at giving a comprehensive outlook on the state of art capabilities offered from these near-term noisy devices as universal quantum simulators, i.e. programmable quantum computers potentially able to c…
Towards a Digital Twin for the Ground to QEYSSat Quantum Link
Institute for Quantum Computing, University of Waterloo（量子计算研究所，滑铁卢大学）；Department of Physics and Astronomy, University of Waterloo（物理与天文学系，滑铁卢大学）；Department of Applied Mathematics, University of Waterloo（应用数学系，滑铁卢大学）；School of Physical and Chemical Sciences, University of Canterbury（物理与化学科学学院，坎特伯雷大学）；Department of Physics, Simon Fraser University（物理系，西蒙菲莎大学）
The discrete time crystal (DTC) is a recently discovered phase of matter that spontaneously breaks time-translation symmetry. Disorder-induced many-body-localization is required to stabilize a DTC to arbitrary times, yet an experimental investigation of this localized regime has proven elusive. Here, we observe the hallmark signatures of a many-body-localized DTC using a novel quantum simulation platform based on individually controllable $^{13}$C nuclear spins in diamond. We demonstrate the characteristic long-lived spatiotemporal order and confirm that it is robust for generic initial states…
We discuss monitoring the time evolution of an analog quantum simulator via a quantum non-demolition (QND) coupling to an auxiliary `clock' qubit. The QND variable of interest is the `energy' of the quantum many-body system, represented by the Hamiltonian of the quantum simulator. We describe a physical implementation of the underlying QND Hamiltonian for Rydberg atoms trapped in tweezer arrays using laser dressing schemes for a broad class of spin models. As an application, we discuss a quantum protocol for measuring the spectral form factor of quantum many-body systems, where the aim is to i…
