Session G51: Hamiltonian Simulation

Improved state preparation for first-quantized simulation of electronic structure

In this talk, we present several improvements to state preparation algorithms for the first-quantized simulation of electronic structure. We show that the cost of preparing physically meaningful initial states, either for ground state energy estimation or for dynamical simulation, can be dramatically reduced when compared with the naive linear scaling in the basis set size. We address the preparation of both Hartree-Fock and post-Hartree-Fock states derived from efficient classical calculations, and provide a general prescription that allows for a variety of work on second-quantized simulations in a typical Gaussian basis set to be used to construct initial states for first-quantized simulations in a plane wave basis. The main improvements come from leveraging tensor network methods, but we also use modern compilation techniques designed to reduce the number of non-Clifford gates required for our state preparation scheme.   

Benchmarking Quantum Chemistry Simulations on Heterogeneous Systems using CUDA Quantum

The integration of GPUs in quantum chemistry simulations is crucial due to complex computational demands, particularly when studying molecular structures of intermediate and large sizes such as CO, H2O, NH2-, and CO2, etc. Utilizing the CUDA Quantum software development kit, we enable scalable simulations on heterogeneous systems. Our research, performed on NERSC's Perlmutter system, highlights large-scale multi-GPU simulations and compares the performance between commonly used approaches such as VQE, the Adaptive VQE and the Number-Preserving Ansatz algorithms. Furthermore, we leverage domain-specific knowledge to enhance the efficiency of quantum computations, thereby advancing the scope and precision of our simulations.   

A quantum materials simulator based on Coulomb-confined quantum dots

One of the significant promises of quantum technology is the ability to simulate complex materials for applications such as novel electronics and improved electrodes for batteries. Analogue quantum simulators based on semiconductor quantum dots have already started to investigate these types of problems with the realisation of one-dimensional correlated phases, ferromagnetism, and resonating valence bond states. However, all these quantum simulators have been well within the reach of classical simulation techniques due to the small number of sites and particles. Here, we show that atomically precise Coulomb-confined quantum dots allow for the controllable simulation of two-dimensional quantum materials. Using the sub-nanometre precision of these quantum simulators we simulate a metal-to-insulator transition (MIT) of interacting electrons on a square extended Fermi-Hubbard lattice of 15,000 sites---well beyond the limit of classical simulations. The collective behaviour of the lattice is measured using magneto-transport measurements where we see the opening of an energy gap driven by electron-electron interactions (a Mott insulator). These analogue devices provide a promising route for quantum simulation of interacting electrons on arbitrary two-dimensional lattices such as quantum spin liquids, topological quantum matter, and unconventional superconductivity.   

Digital quantum simulation of controlled molecular dynamics in first quantization

A longstanding goal is to use laser fields to coherently control the dynamics of quantum systems, such as atoms and molecules. In pursuit of this goal, simulations are essential for designing laser fields that achieve a desired control outcome. In this talk, we investigate the viability of quantum computers for performing these simulations in the presence of low-probability logical errors. We specifically consider simulating controlled molecular dynamics on quantum computers using Trotterized, time-dependent Hamiltonian simulation algorithms within a grid-based, first-quantized representation. We discuss the algorithm formulation, its asymptotic costs, and its compilation into Clifford + T gates. We then present numerical results for simulations of a controlled hydrogenic system. These numerical illustrations explore the impact of uncorrected logical errors, as well as Trotter error, on the simulation outcomes.   

Qutrit Circuits and Algebraic Relations: A Pathway to Efficient Spin-1 Hamiltonian Simulation

Quantum information processing has witnessed significant advancements through the application of qubit-based techniques within universal gate sets. Recently, exploration beyond the qubit paradigm to d-dimensional quantum units or qudits has opened new avenues for improving computational efficiency. This paper delves into the qudit-based approach, particularly addressing the challenges presented in the high-fidelity implementation of qudit-based circuits due to increased complexity. As an innovative approach towards enhancing qudit circuit fidelity, we explore algebraic relations, such as the Yang-Baxter-like turnover equation, that may enable circuit compression and optimization. The paper introduces the turnover relation for the three-qutrit time propagator and its potential use in reducing circuit depth. We further investigate whether this relation can be generalized for higher-dimensional quantum circuits, including a focused study on the one-dimensional spin-1 Heisenberg model. Our work outlines both rigorous and numerically efficient approaches to potentially achieve this generalization, providing a foundation for further explorations in the field of qudit-based quantum computing.   

Anomaly inflow, foliation, and measurement-based quantum simulation of abelian lattice gauge theories

Lattice gauge theory has been a fundamental formulation in theoretical physics, with relevance to quantum information science, high-energy physics, and condensed matter physics. Motivated by Measurement-Based Quantum Computation, we explore a family of custom-designed resource states for Ising/gauge theories, employing adaptive measurement on bulk qubits. We demonstrate that the sequential measurement drives the Hamiltonian quantum simulation of lattice Ising/gauge theories at the boundary of resource states. The tailor-made entanglers for the resource state result in symmetry-protected topological orders concerning higher-form symmetries. I will discuss the connections of our setup to concepts in high-energy and condensed matter physics, including anomaly inflow, dualities, and the foliation of quantum error-correcting codes.   

Measurement Based Simulation of Geometric Gates in Topological Qubits on NISQ Devices

While the adiabatic exchange of Majorana zero modes (MZMs) enables a non-universal set of geometrically protected gates, realising an experimental implementation of MZM braiding remains challenging. In an alternative proposal, charge-parity measurement of two neighboring MZMs supports braiding by teleportation. Moreover, owing to the lack of definitive evidence of MZMs in semiconducting systems, there have been several simulations of MZMs on NISQ devices which more naturally lend themselves to braiding. In this work, teleportation based braiding about MZM Y-junctions are simulated by multi-qubit Pauli-parity measurements on an encoded state. Single qubit geometric S-phase gates and entangling two-qubit gates may be shown within the encoded space with two-qubit joint measurements alone, whilst partial phase rotations such as a T-phase gate require at least one three-qubit joint measurement. These relatively small scale circuits offer both novel measurement based geometric gates as well as a measurement based demonstration of quantum Hamiltonian simulation.   

An efficient quantum algorithm for building effective Hamiltonians on fault-tolerant hardware

The construction of accurate effective Hamiltonians for interacting quantum systems is a long-standing problem in many-body quantum mechanics. We present a novel quantum algorithm for constructing effective Hamiltonians built upon the methodology of density matrix downfolding (DMD). We provide formal theoretical developments in downfolding, including the novel concept of Hamiltonian compressibility, show that a quantum implementation of DMD addresses the main systematic errors present in the classical implementation --- sampling of low-energy states in the physical theory --- and provide circuits for implementing DMD on fault-tolerant quantum hardware. We also provide rigorous resource estimates at the logical and physical level for the case of a doped 2-D Fermi-Hubbard model and a large cuprate supercell.   

Quantum Simulation of the Bosonic Kitaev Chain‏

There has been a growing interest in simulating topological physics in non-Hermitian lattice models. In this work, we utilize our analog quantum simulation (AQS) platform to realize the bosonic counterpart of the fermionic Kitaev chain, a 1D tight-binding model with nearest-neighbor hopping and pairing terms. Despite its Hermitian nature, the bosonic Kitaev chain displays intriguing non-Hermitian characteristics, such as chiral transport and sensitivity to boundary conditions. In this experiment, we utilize a multimode superconducting parametric cavity to simulate the bosonic Kitaev chain in a synthetic frequency dimension. On our AQS platform, the frequency modes correspond to the lattice sites, and the complex hopping and pairing are created through parametric pumping at the difference and sum of mode frequencies, respectively. We demonstrate precursors of nontrivial topology and the non-Hermitian skin effect: chiral transport, localization of the quadrature wavefunctions, and sensitivity to boundary conditions. Our platform has great potential for studying genuine non-Hermitian quantum dynamics.   

Expanding Hardware-Efficiently Manipulable Hilbert Space via Hamiltonian Embedding

The realization of quantum computing is fundamentally based on the precise manipulation of Hilbert spaces of underlying quantum devices. The conventional wisdom relies on circuit synthesis techniques to decompose sophisticated operations on Hilbert space to a set of universal elementary gates. Although providing a universal solution, this hardware-agnostic strategy typically leads to deep quantum circuits for interesting quantum algorithms, which makes them infeasible for implementation on near-term quantum devices. 

In this paper, we propose a technique named Hamiltonian embedding that simulates a desired Hamiltonian evolution by embedding it into the evolution of a large and structured quantum system, which, however, allows more efficient manipulation via hardware-native operations. We conduct a systematic study of this embedding technique and demonstrate a significant computational resource save for implementing prominent quantum applications. As a result, we can experimentally realize quantum walks on complicated graphs (e.g., binary trees, glued-tree graphs), quantum spatial search, and the simulation of real-space Schrödinger equations on trapped-ion and neutral-atom platforms today. Given the fundamental role of Hamiltonian evolution in quantum algorithm design, our technique significantly expands the horizon of implementable quantum advantage in the NISQ era.   

Efficient Spin-1 Ground States Preparation with Qutrit-based Quantum Hardware

Recent developments in Noisy Intermediate Scale Quantum (NISQ) devices have gained traction due to their capability to simulate many-body systems. Simulating higher spin systems with such devices, unlike spin ½ systems, requires multiple qubits to encode each spin site. This introduces an additional level of complexity when simulating higher spin systems in order to characterize their eigenstates and dynamics. In this work, we extend the existing qubit gate set to include single qutrit gates obtained by accessing the second excited state of IBM Quantum's hardware. We achieve this by running calibration experiments to construct the appropriate microwave pulse sequences which produce a set of single qutrit gates. To then demonstrate the efficacy of these gates, we simulate one-dimensional spin-1 systems and their ground states by mapping the states of each site to those of a 3-level transmon for varying chain lengths. The efficiency of qutrit encoding to prepare ground states demonstrated here suggests that qutrits could be used to study interesting physics of spin-1 systems more elegantly than the conventional qubit-based simulation.   

Digital Simulations of Fermion-Boson Models on a Quantum Computer

Performing simulations of many-body correlated systems formed both by fermions and bosons on quantum computers is a demanding challenge. Current techniques are often based on digital approaches encoding all degrees of freedom into the qubits and simulating, for instance, the time evolution. These encoding methods, though, have been found to be very inefficient. We propose an alternative architecture to solve this problem, which is based on a superconducting platform with transmons coupled to additional resonators traditionally used for quantum-information storage. This architecture expands the native set of gates of the quantum processor by adding an entangling gate between the transmons, which encode the fermions, and the resonators, which store the bosons without any need for approximations related to the truncation of the bosonic Fock space. We illustrate the potential of our approach by presenting a number of examples for the Trotterized time evolution of models from solid-state physics and quantum optics.