Session F54: Quantum Information Science in AMO Physics

Quantum Simulation of many-body physics with accuracy guarantees

Several quantum hardware platforms, while being unable to perform fully fault-tolerant quantum computation, can still be operated as analogue quantum simulators for addressing many-body problems. However, due to the presence of errors and without explicit error correction, both (a) the extent to which the output of the quantum simulator can be trusted, and (b) if the quantum simulators provide a computational advantage over classical algorithms, remain unclear.

In this work we aim to theoretically answer both of these questions. We consider the use of noisy analogue quantum simulators for computing physically relevant properties of many-body systems both in  equilibrium and undergoing dynamics. We first propose a system-size independent criteria of stability against extensive errors, which if satisfied by the many-body models to be simulated, would allow us to compute its thermodynamic limit within a hardware-error limited but system-size independent precision on a noisy quantum simulator. We prove that this criteria is satisfied for various many-body models, including Gaussian fermion models, as well as for several (non-gaussian) spin systems. Remarkably, for Gaussian fermion models, our analysis shows the stability of translationally invariant observables in critical models inspite of them have long-range correlations. Furthermore, we analyze how this stability may lead to a quantum advantage, for the problem of computing the thermodynamic limits of many-body models, in the presence of a constant error rate and without any explicit error correction.

Finally, we outline and analyze concrete quantum simulation tasks, together with their implementation, for measuring local observables in both dynamics and steady state of spatially local master equations. We show that these tasks are stable to both coherent and incoherent errors in the simulator. Furthermore, we show a super-polynomial speedup, for the problem of dynamics, or an exponential speedup, for the problem of fixed points, can be obtained on a noisy quantum simulator over currently available classical algorithms.   

Probing Su–Schrieffer–Heeger-like behavior in a tilted synthetic flux ladder

Tilted optical lattice systems have been widely used in both quantum metrology and quantum simulations. In recent years, progress has been made to combine tilted optical lattices with optical lattice clocks using fermionic alkaline-earth atoms (AEAs), resulting in a new platform with pristine quantum coherence and exquisite quantum control. In addition, the fermionic AEAs, with their n internal levels, have unique SU(n) symmetric collisions. This platform offers new capabilities to simulate and understand spin-orbit-coupled, interacting many-body fermionic systems. In this talk, I discuss our theoretical studies of quantum dynamics of two-level fermionic atoms in a tilted synthetic flux ladder, where we see a non-trivial interplay of the tilt, the nearest-neighbor hopping and the spin-orbit-coupled laser drives. In a specific parameter regime, accessible under current conditions, we can simulate a tilted Su–Schrieffer–Heeger (SSH) model with tunable inter- and intra-cell couplings without the need of an additional superlattice potential. The topologically trivial and non-trivial phases of the untilted SSH model manifest on the long-time dynamics of chiral Bloch oscillations, which can be accessed via Ramsey spectroscopy. Our work paves the way to understand dynamics in tilted, multi-level quantum many-body systems.   

Oral: Optimizing quantum logic spectroscopy for molecular state control

Quantum logic spectroscopy (QLS) is a powerful technique for precision measurements, enabling the control and non-destructive detection of molecular ion states that are challenging to manipulate otherwise[1]. While experimentally demonstrated, this method is limited by blackbody radiation exciting numerous hyperfine states, requiring a large number of measurements for state preparation and spectroscopic data collection. To address this challenge, we perform Monte Carlo simulations of a new protocol involving a two-step process. First, we couple at most half the total number of rotational states to a chosen normal mode shared between the molecular and logic ions, followed by a projective measurement of their motional state. By consistently repeating these two steps, we can gradually reduce the large state space to a single pure quantum state. The process is optimized to account for degeneracies and off-resonant couplings by observing the dynamics through the transition matrix of the Markovian state model, which encodes information about how external laser pulses affect the probability distribution of the molecular state space. Additionally, the study explores the application of optimal control theory in designing robust laser pulses. This protocol reduces the number of measurements from linear to logarithmic scaling, improving our ability to manipulate molecular states and potentially observe parity violation signatures in molecules[2], or facilitate transduction between trapped ion qubits and photons[3].

[1] Chou, Cw., Kurz, C., Hume, D. et al. Preparation and coherent manipulation of pure quantum states of a single molecular ion. Nature 545, 203–207 (2017). 

[2] Arie Landau, Eduardus, Doron Behar, Eliana Ruth Wallach, Lukáš F. Pašteka, Shirin Faraji, Anastasia Borschevsky, Yuval Shagam; Chiral molecule candidates for trapped ion spectroscopy by ab initio calculations: From state preparation to parity violation. J. Chem. Phys. 21 September 2023; 159 (11): 114307. 

[3] Lin, Y., Leibrandt, D.R., Leibfried, D. et al. Quantum entanglement between an atom and a molecule. Nature 581, 273–277 (2020).   

Molecular Entanglement Witness by Absorption Spectroscopy in Polariton Chemistry

Maintaining molecular entanglement at room temperature and detecting multipartite entanglement features of macroscopic molecular systems remain key challenges for understanding the non-trivial quantum effect in chemical quantum dynamics. Here, we study the quantum Fisher information, a central concept in quantum metrology, as a multipartite entanglement witness. We generalize the entanglement witness functional related to quantum Fisher information regarding non-identical local response operators and show that it is a good molecular entanglement witness for ultrastrong light-matter coupling in cavity quantum electrodynamics and even a multi-molecular entanglement witness during the superradiance phase transition. We further connect quantum Fisher information to the dipole correlator, which suggests that molecular entanglement could be detected by linear absorption spectrum at finite temperatures. Our work proposes a general protocol to sufficiently measure molecular entanglement for chemical systems at room temperature in experiments and demonstrate the long-lived multi-molecular entanglement in the polariton chemistry systems.   

Building graph states with optically trapped molecules

Molecular quantum systems offer a promising architecture for measurement-based quantum computing. These systems are highly controllable, optically addressable, and typically admit a natural two-particle dipole-dipole interaction. In this talk, we will discuss how to use molecular rotational levels of optically trapped bi-alkali systems to build graph states via the dipole-dipole interaction under Floquet dressing. We will demonstrate the scalability of our results. Additionally, we will discuss possible generalizations from two- and three-level systems to greater numbers of rotational levels, as well as more complex states such as multigraph and hypergraph states.   

Numerical study of entangled helical spin currents in a spinor Bose-Einstein condensate

We numerically study the dynamics of perfectly helical spin currents where two counter-propagating spin currents are quantum-mechanically entangled. A spin-1 condensate is initially prepared at the m = 0 magnetic sublevel in a one-dimensional torus. The atoms are assumed to interact via the s-wave scattering channel which parametrically generates an entangled pair of m = 1 and -1 atoms from two m = 0 atoms. The pair of m = 1 and -1 atoms acquire oppositely directed momenta via the Bragg diffraction, while they maintain the quantum-mechanical spin correlations. As a result, a nonzero spin current flows in the torus with no net mass current.   

Super-Exponential Scrambing and Slow Entanglement Growth in the Deep Hilbert Space of All-to-All Systems

Quantum dynamics of spin systems with uniform all-to-all interactions have often been studied in the totally symmetric space (TSS) of maximal total spin. However, the TSS states are atypical in the full many-body Hilbert space. We explore several aspects of the all-to-all quantum dynamics away from the TSS, and reveal surprising features of the "deep Hilbert space'' (DHS). We study the out-of-time order correlator (OTOC) in the infinite-temperature ensemble of the full Hilbert space and show that the OTOC can grow super-exponentially in the large-N limit, due to the fast dynamics in an unbounded phase space. By a similar mechanism, the Krylov complexity grows explosively. We also study the entanglement growth in a quantum quench from a DHS product state, i.e., one of non-aligned spins that resemble the DHS infinite-temperature ensemble with respect to the statistics of the collective spins. Using a field-theoretical method, We exactly calculate the entanglement entropy in the large-N limit. We show that, unlike in TSS, fast OTOC growth does not imply fast entanglement growth in the DHS.   

Quantum coherence controls the nature of equilibration and thermalization in coupled chaotic systems

A bipartite system whose subsystems are fully quantum chaotic and coupled by a perturbative interaction with a tunable strength is a paradigmatic model for investigating how isolated quantum systems relax toward an equilibrium. It is found that quantum coherence of the initial product states in the energy eigenbasis of the subsystems—quantified by the off-diagonal elements of the subsystem density matrices—can be viewed as a resource for equilibration and thermalization as manifested by the entanglement generated. Results are given for four distinct perturbation strength regimes, the ultraweak, weak, intermediate, and strong regimes. For each, three types of tensor product states are considered for the initial state: uniform superpositions, random superpositions, and individual subsystem eigenstates. A universal timescale is identified involving the interaction strength parameter. In particular, maximally coherent initial product states (a form of uniform superpositions) thermalize under time evolution for any perturbation strength in spite of the fact that in the ultraweak perturbative regime the underlying eigenstates of the system have a tensor product structure and are not at all thermal-like; though the time taken to thermalize tends to infinity as the interaction vanishes. Moreover, it is shown that in the ultraweak regime the initial entanglement growth of the system whose initial states are maximally coherent is quadratic-in-time, in contrast to the widely observed linear behavior.   

Efficient Local Classical Shadow Tomography with Number Conservation

Quantum state tomography aims to produce a complete classical description of the state of a quantum system: a prohibitive task requiring exponential resources. Recent works have taken a different approach. They build an efficient classical description of the state, the so-called classical shadow, that can accurately capture properties of interest such as few-body observables, but is a poor approximation to the entire density matrix. The protocol is simple to implement and predicts observables much more efficiently and accurately than other techniques. It has accordingly developed into an important experimental tool.

The original local shadow protocol does not apply to systems with fundamental number conservation laws, such as cold atomic systems. This is a serious shortcoming. We propose and analyze a new local shadow tomographic protocol adapted to such systems. Our ``All-Pairs'' protocol is simple to implement, tomographically complete, and efficiently invertible. Our analytic treatment relies on the representation theory of the permutation group. We provide a reference implementation and demonstrate the efficiency on simulated data.   

Spectra and phase transition in Grover's algorithm with systematic noise

In this work, we present a study of Grover's search algorithm in the presence of systematic noise. By modeling the Grover operator within one timestep as a Floquet unitary, we showed that the bulk quasi-energy spectrum is well-captured by the first-order perturbation theory. Using the random matrix theory of an effective Hamiltonian, we obtain the scaling of the critical disorder for the algorithm. In addition, we also derive semi-analytical results for the oscillation frequency of the target state in the presence of noise.