Session Z50: Advanced Methods for Modelling Quantum Systems

High-performance simulation of Rydberg atom arrays with tensor networks

Analog Hamiltonian Simulation (AHS) is a computational paradigm, that follows the original Feynman’s proposal of simulation of complex quantum systems using a highly controllable analogue system.

AHS is becoming an actively growing field of quantum computing with the leading hardware platforms based on the reconfigurable Rydberg atom arrays. Neutral atom simulators allow to study in-situ non-trivial quantum phases of matter such as topological spin liquids and can be a used as quantum annealers to solve classical combinatorial problems, such as weighted Maximum Independent Set (wMIS).

Despite a significant interest in the neutral atom arrays in quantum computing community, there is a lack of software tooling and high performance simulation software packages to study dynamics of Rydberg systems, in particular based on modern tensor network methods.

By leveraging Julia implementation of iTensor tensor network package we were able to simulate AHS programs, that are emulating annealing protocol for Quantum Approximate Optimization Algorithm (QAOA) for solving wMIS problems on randomized 2D graphs comprising ~250 atoms. By employing TEBD algorithm we showed that even a modest matrix product states bond dimension is sufficient to achieve a high fidelity solution of the wMIS problem.   

Exponential acceleration of collective quantum tunneling in the transverse field Ising model using high frequency AC drives (Part 1)

Macroscopic quantum tunneling (MQT), where an extensive number of quantum degrees of freedom change configuration simultaneously to cross a large intermediate energy barrier, is a spectacular, and elusive, phenomenon in many-body physics. Because MQT rates generically decay exponentially in system size, they are naturally very slow, and extremely sensitive to noise, control error and other similar issues. As MQT transitions also act as a bottleneck to quantum optimization algorithms, accelerating MQT is of significant scientific and practical interest. In this talk, we build on the concept of Symphonic Tunneling introduced in Mossi et al (arXiv:2306.10632), where MQT is accelerated by tuning AC fields based on details of the underlying system, to consider very high frequency drives. We consider the ferromagnetic N-spin transition in transverse field Ising models, and show that if the amplitude and frequency of the drive is allowed to increase logarithmically in system size, the collective tunneling rate between ferromagnetic states can cross over from exponential to polynomial (empirically, linear) in system size, without meaningfully heating the system. We discuss the theoretical derivation of this effect in 1d, and its extension to higher dimensions.   

Oral: Exponential acceleration of collective quantum tunneling in the transverse field Ising model using high frequency AC drives - Part 2

In this talk, we numerically explore the acceleration of macroscopic quan-

tum tunneling (MQT) in transverse field Ising models through the use of high

frequency AC drives. Using time evolved block decimation in 1d, and full state

simulation methods in 2d, we identify a parameter space where the scaling of

the tunneling rate crosses over from exponential to linear in N . This scaling is

achieved through the application of a high-frequency drive where the amplitude

and frequency both increase logarithmically in system size. We demonstrate

robust sinusoidal “cat-state” oscillations between the two dressed ferromagnetic

ground states, that heating can be minimized, and that long ranged ferromag-

netic order may persist in this regime. Further, we estimate that using suitable

error mitigation techniques (e.g. Nature 618, 500 (2023)), this effect should be

testable at the 100+ qubit scale using present or near-term quantum computers.

These results thus present a challenge of genuine scientific interest for NISQ-era

quantum hardware.   

Fast Simulation of High-Depth QAOA Circuits

Classical simulation is a vital tool for algorithm design, tuning, and validation. We present a simulator for the Quantum Approximate Optimization Algorithm (QAOA). Our simulator is designed with the goal of reducing the computational cost of QAOA parameter optimization and supports both CPU and GPU execution. Our central observation is that the computational cost of both simulating the QAOA state andcomputing the QAOA objective to be optimized canbe reduced by precomputing the diagonal Hamiltonian encoding the problem. We reduce the time for a typical QAOA parameter optimization by eleven times for n = 26 qubits compared to a state-of-the-art GPU quantum circuit simulator. 

The simulator supports various QAOA problems such as MaxCut, LABS and portfolio optimization, as well as usage of Hamming weight preserving mixers.

Our simulator supports a variety of hardware from CPU to large-scale distributed GPU supercomputers. We demonstrate scaling of distributed simulations and compare MPI communication with custom communication implemented in the cuQuantum library. Our simulator is available on GitHub: https://github.com/jpmorganchase/QOKit   

New tensor network tools for and beyond Rydberg systems

Tensor network methods offer potential features to support and improve the development and benchmarking of quantum processing units (QPUs). Their flexibility to simulate circuits directly or as Schrödinger and Lindblad equation enables a digital twin for a Rydberg atom QPU; both approaches are supported by the Quantum TEA library. Herein, we start from the pulse level, continue via compilation and optimization, and reach up to the full simulation of an 8x8 grid of strontium-88 atoms. We encode the two fine-structure states of the qubit and an additional Rydberg state; the latter is used for the entangling operation. The digital twin simulation of the QPU performs a parallel application of gates resulting in a Greenberger-Horne-Zeilinger state. The procedure is under the influence of crosstalk due to the long-range Rydberg interaction of CZ gates executing in parallel. We apply the new approaches for measurements, optimizations for higher-dimensional systems with and without long-range interactions, and parallelization for high-performance computing clusters to other systems in condensed matter and quantum information.   

Simulation of plasmonic behaviors in extended Hubbard model using tensor networks

We simulate the collective plasmonic behaviors in fermionic systems using an extended Hubbard model and utilizing various tensor network techniques to overcome the severe scaling limitation of exact diagonalization in such systems. By coupling the system with quantum emitters through dipole interactions and beyond, we observe the dynamical flow of quantum information through the system. We measure the quality of these collective excitations using metrics such as the Generalized Plasmonicity Index. Furthermore, we explore the transport dynamics in these systems while they are coupled to source and drain leads. By utilizing a mixed-basis quantum reservoir approach, we ameliorate the rapid growth of entanglement in time evolution simulations. This allows us to extend the feasibility of tensor networks techniques for simulations to longer time scales.   

Constant-depth preparation of matrix product states with adaptive quantum circuits

Matrix product states comprise a broad class of physically interesting entangled states highly relevant to condensed matter physics, quantum chemistry, and quantum machine learning. While it is well known that any matrix product state can be exactly prepared using a linear-depth circuit, decoherence limits current NISQ-era processors to fairly shallow-depth circuits, inhibiting the preparation of matrix product states larger than a few sites. In this talk, I will present a general method capable of deterministically preparing a wide variety of matrix product states in constant depth, including paradigmatic examples such as the AKLT state, the GHZ state, and the Majumdar-Ghosh state. I will show how the core ingredients of this algorithm -- unitary gates, midcircuit measurements, classical feedforward, and symmetries of the target state -- can be blended to produce a completely deterministic protocol, despite the use of non-unitary circuit components. Finally, I will show that our constant-depth, measurement-assisted approach experimentally outperforms its unitary linear-depth counterpart in the prepartion of the AKLT state on an IBM Quantum processor.   

Macrostates versus Microstates in the Classical Simulation of Critical Phenomena in Quench Dynamics of 1D Ising Models

We study critical phenomena in the quench dynamics of one-dimensional (1D) Ising models using truncated Matrix Product States (MPS). While accurate calculation of the full many-body state (microstate) is typically intractable due to the volume-law growth of entanglement, when simulating phases of matter associated with the macrostates of many-body systems, a precise specification of an exact microstate is rarely required. Here we simulate the critical behavior of a Z₂ symmetry breaking dynamical quantum phase transition for a nonintegrable transverse field Ising model with long-range interactions. Our simulations show that even when high-fidelity simulation of the full many-body state is intractable due to exponential scaling with system size, macroscopic quantities like order parameters, the critical point, and critical exponents of a phase transition can be efficiently simulated. We also estimate long-time correlation lengths of the integrable 1D nearest-neighbor transverse field Ising model, finding that properties like long-time correlation lengths, that depend on the exact microstate can also be efficiently simulated because they can be extracted from the short duration behavior of the dynamics. The tractability of simulation using truncated MPS is explained based on quantum chaos and equilibration in the model. We find a counterintuitive inverse relationship, whereby local expectation values are most easily approximated for the most chaotic systems whose exact many-body state is most intractable.   

Efficient tensor network simulation of IBM's Eagle kicked Ising experiment

I will present an accurate and efficient classical simulation of a kicked Ising quantum system on the heavy-hexagon lattice. A simulation of this system was recently performed on a 127 qubit quantum processor using noise mitigation techniques to enhance accuracy (Nature volume 618, p.500-505 (2023)). By adopting a tensor network approach that reflects the geometry of the lattice and is approximately contracted using belief propagation, we perform a classical simulation that is significantly more accurate and precise than the results obtained from the quantum processor and many other classical methods. We quantify the tree-like correlations of the wavefunction in order to explain the accuracy of our belief propagation-based approach. We also show how our method allows us to perform simulations of the system to long times in the thermodynamic limit, corresponding to a quantum computer with an infinite number of qubits. Our tensor network approach has broader applications for simulating the dynamics of quantum systems with tree-like correlations.   

Benchmarking time evolution algorithms for quantum advantage

Recent hardware advances have brought quantum simulations of quantum dynamics close to the limits of classical simulability. A recent subject of debate has been where exactly the quantum advantage regime begins for this class of quantum simulation tasks. In response to a recent quantum dynamics experiment from IBM, a series of classical approaches have been proposed that efficiently capture the simulated dynamics with accuracy comparable to or exceeding that of the quantum computer. However, the complexity of many classical algorithms increases exponentially with simulation time, which calls into question the utility of these methods beyond the times reached in the quantum simulation experiments. With the understanding that hardware coherence times are steadily improving, we report benchmarking results for a recently proposed tensor network algorithm that uses belief propagation as an approximate contraction heuristic. The focus of our tests is on determining, for a given system size, how much accuracy is maintained with increasing simulation time for this approximate tensor network algorithm. We comment on the implications of these benchmarks for future quantum computing experiments, in particular on the circuit depths that may be necessary in order to challenge the algorithm's regime of validity.   

Hybrid Quantum-Classical Simulation for Non-Perturbative Jet Production Dynamics at Scale with CUDA Quantum

The generation of jets in high-energy collisions probes the real-time behavior of the QCD vacuum and how it is influenced by the presence of high-momentum color charges. Addressing this challenge from a theoretical perspective necessitates a real-time, non-perturbative approach. It is worth noting that the Schwinger model (a description of QED in 1+1 dimensions) shares numerous common characteristics with QCD, such as confinement, chiral symmetry breaking, and the presence of vacuum fermion condensate. It can moreover be approximated by a many-body quantum Hamiltonian and is amenable to near-term quantum simulations.

As a significant step towards developing this approach, we present our findings from GPU-driven hybrid quantum-classical simulations of the massive Schwinger model in the presence of a pair of hard external particles. It produces a set-up similar to the one leading to the production of jets in high-energy collisions. We investigate how the presence of these propagating jets affects the vacuum chiral condensate, as well as the quantum entanglement between the jets as they fragment. This work is performed on NERSC's Perlmutter system leveraging the multi-node multi-GPU architecture using NVIDIA’s CUDA Quantum, which is a software development kit for quantum and integrated quantum-classical programming.   

False vacuum decay in Rydberg atom quantum simulators: Classical emulation over the parameter space

The expansion and cooling of the universe may have caused it to settle into a false vacuum state. A false vacuum would decay into the true vacuum through nucleation and potentially produce an observable signature. The phenomenon of false vacuum decay is difficult to probe in its field-theoretic form in physical cosmology, but it can be investigated more easily in analogue quantum simulators with strongly-coupled matter. Recent work has examined false vacuum decay in spin chains with the ferromagnetic Ising model and XXZ ladder, determining the relevant parameter range and quantifying the features of some important observables. We investigate false vacuum decay in Rydberg atom chains with the antiferromagnetic Rydberg Hamiltonian, using local detuning to achieve confinement and nucleation. We use classical emulation to examine the decay dynamics over a broad space of waveform inputs, notably studying the Neel order parameter. We constrain the parameter range for false vacuum decay and characterize the dynamics at the core and boundary of this regime.   

Simulating fermionic scattering using a digital quantum computing approach

Collider experiments play a central role in understanding the subatomic structure of matter, as well as developing and verifying the fundamental theory of elementary particle interactions. However, comprehending scattering processes at a fundamental level in theory remains a significant challenge. The necessary involved time evolution and the with time rapidly increasing bond dimension in Tensor Networks make simulating the scattering process with this classical method challenging. On the other hand, quantum computers hold great promise to efficiently simulate real-time dynamics of lattice field theories. In this work, we take the first step in this direction toward simulating fermionic scattering using a digital-quantum computing approach. Specifically, we propose a method based on Givens rotation to prepare the initial state of the fermionic scattering process, which consists of two fermionic wave packets with opposite momenta. With a time evolution operator based on the underlying Hamiltonian acting on the initial state, the two fermionic wave packets propagate and interact with each other. Using the lattice Thirring model as the test bed and the Qiskit Statevector simulator, we observe an elastic scattering between fermions and anti-fermions in the strong interaction region. In addition, we clearly observe an entanglement production in the scattering process. We consider our work also as an indispensable step towards a quantum simulation of a scattering process on a real quantum device.