Quantum simulators have the potential to shed light on the study of quantum many-body systems and materials, offering unique insights into various quantum phenomena. While adiabatic evolution has been conventionally employed for state preparation, it faces challenges when the system evolves too quickly or the coherence time is limited. In such cases, shortcuts to adiabaticity, such as spatiotemporal quenches, provide a promising alternative. This paper numerically investigates the application of spatiotemporal quenches in the two-dimensional transverse field Ising model with ferromagnetic interactions, focusing on the emergence of the ground state and its correlation properties at criticality when the gap vanishes. We demonstrate the effectiveness of these quenches in rapidly preparing ground states in critical systems. Our simulations reveal the existence of an optimal quench front velocity at the emergent speed of light, leading to minimal excitation energy density and correlation lengths of the order of finite system sizes we can simulate. These findings emphasize the potential of spatiotemporal quenches for efficient ground state preparation in quantum systems, with implications for the exploration of strongly correlated phases and programmable quantum computing.
Quantum simulators have the potential to shed light on the study of quantum many-body systems and materials, offering unique insights into various quantum phenomena. While adiabatic evolution has been conventionally employed for state preparation, it faces challenges when the system evolves too quickly or the coherence time is limited. In such cases, shortcuts to adiabaticity, such as spatiotemporal quenches, provide a promising alternative. This paper numerically investigates the application of spatiotemporal quenches in the two-dimensional transverse field Ising model with ferromagnetic interactions, focusing on the emergence of the ground state and its correlation properties at criticality when the gap vanishes. We demonstrate the effectiveness of these quenches in rapidly preparing ground states in critical systems. Our simulations reveal the existence of an optimal quench front velocity at the emergent speed of light, leading to minimal excitation energy density and correlation lengths of the order of finite system sizes we can simulate. These findings emphasize the potential of spatiotemporal quenches for efficient ground state preparation in quantum systems, with implications for the exploration of strongly correlated phases and programmable quantum computing.
Quantum simulators have the potential to shed light on the study of quantum many-body systems and materials, offering unique insights into various quantum phenomena. Although adiabatic evolution has been conventionally employed for state preparation, it faces challenges when the system evolves too quickly or the coherence time is limited. In such cases, shortcuts to adiabaticity, such as spatiotemporal quenches, provide a promising alternative. This paper numerically investigates the application of spatiotemporal quenches in the two-dimensional transverse field Ising model with ferromagnetic interactions, focusing on the emergence of the ground state and its correlation properties at criticality when the gap vanishes. We demonstrate the effectiveness of these quenches in rapidly preparing ground states in critical systems. Our simulations reveal the existence of an optimal quench front velocity at the emergent speed of light, leading to minimal excitation energy density and correlation lengths of the order of finite system sizes we can simulate. These findings emphasize the potential of spatiotemporal quenches for efficient ground state preparation in quantum systems, with implications for the exploration of strongly correlated phases and programmable quantum computing.
Spatiotemporal quenches are efficient at preparing ground states of critical Hamiltonians that have emergent low-energy descriptions with Lorentz invariance [Agarwal, Bhatt, and Sondhi, Phys. Rev. Lett. 120, 210604 (2018)]. The critical transverse field Ising model with nearest-neighbor interactions, for instance, maps to free fermions with a relativistic low energy dispersion. However, spin models realized in artificial quantum simulators based on neutral Rydberg atoms, or trapped ions, generically exhibit long-range power-law decay of interactions with $J(r)\ensuremath{\sim}1/{r}^{\ensuremath{\alpha}}$ for a wide range of $\ensuremath{\alpha}$. In this paper, we study the fate of spatiotemporal quenches in these models with a fixed velocity v for the propagation of the quench front, using the numerical time-dependent variational principle. For $\ensuremath{\alpha}\ensuremath{\gtrsim}3$, where the critical theory is suggested to have a dynamical critical exponent z=1, our simulations show that optimal cooling is achieved when the front velocity v approaches c, the effective speed of excitations in the critical model. The energy density is inhomogeneously distributed in space, with prominent hot regions populated by excitations copropagating with the quench front, and cold regions populated by counterpropagating excitations. Lowering $\ensuremath{\alpha}$ largely blurs the boundaries between these regions. For $\ensuremath{\alpha}<3$, we find that the Doppler cooling effect disappears, as expected from renormalization group results for the critical model, which suggest a dispersion $\ensuremath{\omega}\ensuremath{\sim}{q}^{z}$ with z<1. Instead, we show that excitations are controlled by two relevant length scales whose ratio is related to that of the front velocity to a threshold velocity that ultimately determines the adiabaticity of the quench.
The ability to efficiently prepare ground states of quantum Hamiltonians via adiabatic protocols is typically limited by the smallest energy gap encountered during the quantum evolution. This presents a key obstacle for quantum simulation and realizations of adiabatic quantum algorithms in large systems, particularly when the adiabatic gap vanishes exponentially with system size. Using QuEra's Aquila programmable quantum simulator based on Rydberg atom arrays, we experimentally demonstrate a method to circumvent such limitations. Specifically, we develop and test a "sweep-quench-sweep" quantum algorithm in which the incorporation of a quench step serves as a remedy to the diverging adiabatic timescale. These quenches introduce a macroscopic reconfiguration between states separated by an extensively large Hamming distance, akin to quantum many-body scars. Our experiments show that this approach significantly outperforms the adiabatic algorithm, illustrating that such quantum quench algorithms can provide a shortcut to adiabaticity for large-scale many-body quantum systems.
We revisit the problem of \textit{real-time} quantum dynamics of the paradigmatic two dimensional transverse-field Ising model using the recently developed fuzzy sphere regularization scheme. By linearly ramping the transverse field from the paramagnetic phase to criticality, we study the finite-time scaling behavior of the squared order parameter ⟨mz2⟩, the excitation energy density Q, and the two-point correlation function of mz. We establish numerically that, at intermediate quench rate, ⟨mz2⟩ follows the conventional Kibble-Zurek prediction set by the critical exponents of the 3D Ising universality class, and the correlation function exhibits the expected exponential decay whose correlation length can be used to estimate the non-universal scaling coefficient in the freeze-out time/length. In contrast, the excitation energy density Q does not reach the same scaling regime at available system sizes due to large effective finite-size gap from symmetry-enforced level sparsity in the energy spectrum. At slow quench rates the universal quasi-adiabatic scaling for both ⟨mz2⟩ and Q is recovered. Since the fuzzy sphere construction can realize not only the Ising conformal field theory (CFT), but a broad family of (2+1)d CFTs, our results establish a route to the real-time critical dynamics of strongly coupled CFTs that are otherwise computationally challenging to study.
We propose a spatiotemporal quench protocol that allows for the fast preparation of ground states of gapless models with Lorentz invariance. Assuming the system initially resides in the ground state of a corresponding massive model, we show that a superluminally moving "front" that locally quenches the mass, leaves behind it (in space) a state arbitrarily close to the ground state of the gapless model. Importantly, our protocol takes time O(L) to produce the ground state of a system of size ∼L^{d} (d spatial dimensions), while a fully adiabatic protocol requires time ∼O(L^{2}) to produce a state with exponential accuracy in L. The physics of the dynamical problem can be understood in terms of relativistic rarefaction of excitations generated by the mass front. We provide proof of concept by solving the proposed quench exactly for a system of free bosons in arbitrary dimensions, and for free fermions in d=1. We discuss the role of interactions and UV effects on the free-theory idealization, before numerically illustrating the usefulness of the approach via simulations on the quantum Heisenberg spin chain.
The quantum dynamics of many-qubit systems is an outstanding problem that has recently driven significant advances in both numerical methods and programmable quantum processing units. In this work, we employ a comprehensive toolbox of state-of-the-art numerical approaches to classically simulate the dynamics of the two-dimensional transverse field Ising model. Our methods include three different tensor network techniques -- matrix product states, tree-tensor networks, and two-dimensional tensor-networks under the belief propagation approximation -- as well as time-dependent variational Monte Carlo with Neural Quantum States. We focus on two paradigmatic dynamical protocols: (i) quantum annealing through a critical point and (ii) post-quench dynamics. Our extensive results show the quantitative predictions of various state-of-the-art numerical methods providing a benchmark for future numerical investigations and experimental studies with the aim to push the limitations on classical and QPUs. In particular, our work connects classical simulability to different regimes associated with quantum dynamics in Rydberg arrays - namely, quasi-adiabatic dynamics, the Kibble-Zurek mechanism, and quantum quenches.