Session E09: Quantum simulation

Emergent spacetimes from Hermitian and non-Hermitian quantum dynamics

We show that quantum dynamics of any systems with SU(1, 1) symmetry give rise to emergent Anti-de Sitter spacetimes in 2+1 dimensions (AdS2+1). Using the continuous circuit depth, a quantum evolution is mapped to a trajectory in AdS2+1. Whereas the time measured in laboratories becomes either the proper time or the proper distance, quench dynamics follow geodesics of AdS2+1. Such a geometric approach provides a unified interpretation of a wide range of prototypical phenomena that appear disconnected. For instance, the light cone of AdS2+1 underlies the critical coupling in single/two-mode squeezing, expansions of unitary fermions released from harmonic traps, the onsite of parametric amplifications, and the exceptional points that represent the PT-symmetry breaking in non-Hermitian systems. Our work provides a transparent means to optimize quantum controls by exploiting shortest paths in the emergent spacetimes. It also allows experimentalists to engineer emergent spacetimes and induce tunnelings between different AdS2+1.   

Effective Hamiltonian Theory from a Quantum Method of Averaging

We provide a useful method of deriving the time-averaged Hamiltonian of a quantum system that includes non-harmonic perturbations and naturally preserves hermiticity to the desired order of approximation. This is achieved using a Quantum Method of Averaging formalism that, in addition to extending the periodic/harmonic perturbation requirement of prior effective theories, provides a simple convergence requirement, presents a validity condition at each order, and bounds the approximation errors. We will demonstrate the capabilities of the method using examples relevant to the AMO community.   

Quantum Fluctuation Theorem of the Quantum Work Conditioned on the Initial Energy Measurement

The two-time measurement scheme is a standard approach to the quantum fluctuation theorem. However, the second energy measurement will destroy the quantum coherence and correlations; therefore, the informational contribution to the maximal work relation will be erased by the second measurement. To solve this problem, the one-time measurement (OTM) scheme, where the stochastic work is determined by the expectation value of the energy conditioned on the initial measurement, was proposed to derive a Jarzynski equality that leads to a tighter bound on the maximal work relation. However, the detailed fluctuation theorem clarifying the backward process has not been investigated. In this presentation, we present the derivation of the detailed fluctuation theorem in the OTM, and verify the derived fluctuation theorem via quantum computer.   

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Quantum simulation of lattice gauge theories (LGTs) has been a subject of intense interest in high energy and condensed matter physics because computing dynamics and ground states is classically hard. In addition to fermionic sectors, which can be efficiently encoded with qubits, many lattice gauge theories contain bosonic excitations, which have an infinite Hilbert space leading to extremely high gate counts when encoded on qubits, thus threatening the ability of quantum simulation to address theories which contain bosons. Extensive progress has recently been made in the fabrication and control of microwave cavity resonators, which naturally host a bosonic Hilbert space and are coupled to transmon qubits, and may therefore be able to more efficiently encode the bosonic sectors of LGTs, though these systems are still in development. Despite the excitement linked to this mixed qubit-boson platform, it is unclear whether the currently available hardware would outperform all-qubit hardware for the simulation of lattice gauge theories in terms of gate counts, circuit fidelities, and total number of shots. This is hard to verify because: the relative complexity of simulating gauge-theoretic operators with qubit-boson hardware vs qubit-only hardware is unknown, due to the lack of compiler we must design the fermion-boson gates in the mixed qubit-boson hardware, the effects of noise for deep, multi-qubit/qumode circuits required for high fidelity simulations have yet to be quantified. Considerable previous literature exists on novel approaches for simulating LGTs but these methods are challenging to extend to higher dimensions. In this paper, we provide an example of an experimental architecture for a 1+1D mixed boson-fermion system which efficiently performs ground state preparation for both the Z2 gauge theory coupled to bosonic matter and the Schwinger model and show, using 'Bosonic Qiskit' which we previously developed, that it would dramatically outperform all-qubit systems, featuring much lower gate counts by three orders of magnitude, far higher circuit fidelities, and fewer total shots to successfully capture the essential physics of these theories.   

: Exploring of critical phenomena with a Cs Rydberg simulator

Phase transitions and critical phenomena are subjects of active studies in statistical physics from both theoretical and experimental perspectives. Conformal field theory (CFT) describes systems that are invariant under conformal transformations. It captures low-energy physics that plays the dominant role at the critical point. We use neutral atom arrays in optical tweezers to explore CFTs via analog quantum simulation. The Hamiltonian of this system supports an Ising Z2 phase transition. The critical point can be described by an Ising CFT. In our experiment, we prepare Cs atoms into a ring geometry to incorporate periodic boundary conditions. By precisely tuning the simulator to criticality, we directly measure critical correlations of primary CFT fields to read off their scaling dimensions. This study could help improve our understanding of CFT fixed point theories and at the same time, offer valuable insights into benchmarking quantum simulators.   

Quantum synchronization via weak symmetry breaking.

Symmetries of a microscopic Hamiltonian strongly constrain both the thermodynamics and dynamics of isolated systems in thermal equilibrium. Far from equilibrium however, the role of symmetry in determining local dynamics is not universally understood. To this end, we uncover a mechanism that yields synchronized relaxation of local observables mediated by a weakly broken, continuous symmetry. We provide a family of strongly interacting spin models which exemplify this phenomenon, including a quantum generalization of the Kuramoto model, whose classical synchronization transition is well studied. Remarkably, signatures of this phenomena are visible even when restricting to global measurement, making our theory relevant to a diverse set of quantum systems ranging from ensembles of nitrogen vacancy centers in diamond to reconfigurable atom arrays. Finally, we give evidence that these collective dynamics generate metrologically useful states, even in systems where the preparation of spin squeezed states is precluded.   

Direct observation of geometric-phase interference in dynamics around a conical intersection

Conical intersections in molecular systems are geometry points where two potential energy surfaces have the same energy and govern processes such as light harvesting, vision, photocatalysis, and chemical reactivity.They act as funnels between electronic states of molecules, allowing rapid and efficient relaxation during molecular dynamics. In addition, when a nuclear wavepacket encircles a conical intersection, the wavefunction experiences a geometric phase, which affects the outcome of the reaction through quantum-mechanical interference. Past experiments have measured indirect signatures of geometric phases in scattering patterns and spectroscopic observables, but there has been no direct observation of the underlying wavepacket interference. Here, we experimentally observe geometric-phase interference in the dynamics of a nuclear wavepacket travelling around an engineered conical intersection in a programmable trapped-ion quantum simulator. To achieve this, we develop a new technique to reconstruct the two-dimensional wavepacket densities of a trapped ion. Experiments agree with the theoretical model, demonstrating the ability of analog quantum simulators---such as those realised using trapped ions---to accurately describe nuclear quantum effects. These results demonstrate a path to deploying analog quantum simulators for solving some of the most difficult problems in molecular dynamics.   

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Unitary circuit models provide a useful lens on the universal aspects of the dynamics of many-body quantum systems. Here, we consider random circuits composed of Clifford gates which enable simulations of large system sizes even on classical computers. We study different circuit geometries, including one-dimensional random circuits with long-range gates, as well as Floquet circuits in one and two dimension where short-ranged gates are spatially random but periodic in time. We show that random Clifford circuits can faithfully capture the interplay of hydrodynamic transport and entanglement growth, where the buildup of entanglement is constrained by the presence of a conservation law in the system. Furthermore, by simulating the spreading of local operators, we demonstrate that Clifford circuits can exhibit signatures of both, localization and ergodicity, depending on the circuit geometry. In this context, we also study the spectral form factor of the Floquet Clifford unitary and unveil that it exhibits an exponential ramp, similar to quasi-free fermions with chaotic single-particle dynamics. Our work explores the possibility of simulating exotic nonequilibrium quantum phenomena using Clifford circuits and elucidates the differences and similarities between Clifford dynamics and more generic types of quantum systems.   

Towards Simulating a Dissipative Quantum Phase Transition using Trapped Ions

Dynamics in open quantum systems is defined by the competition between unitary evolution and non-unitary operations, like measurements and/or interaction with the environment. Recent theoretical studies (Sierant,2022, Quantum,6,638) in the field have predicted the existence of a dissipative phase transition (DPT) in a periodically driven, long-range interacting quantum spin chain between a ferromagnetic ordered phase and a paramagnetic disordered phase as a function of resetting probabilities after coherent evolution. We can probe this driven-dissipative out-equilibrium dynamics using our trapped ion quantum simulator. To do so, we have developed a high optical access vacuum chamber which houses a linear, three-dimensional, blade trap to confine chains of Yb⁺ ions. Using our 0.3 NA and 0.6 NA re-entrant windows, we realize global, tunable Ising type interactions (coherent) to couple spins with counter-propagating Raman beams and localized dissipation (resetting) with site resolved optical pumping beams, respectively. We report on the latest developments in the calibration and minimization of the ion-ion crosstalk of the < 2μm individual beam waist/ion. We further discuss the local optical pumping scheme’s ability to prepare arbitrary product states and its versatility to achieve unexplored quantum many body physics beyond DPT using our simulator.