Abstract Quantum simulation is a foundational application for quantum computers, projected to offer insights into complex quantum systems beyond the reach of classical computation. However, with the exception of Trotter-based methods, which suffer from suboptimal scaling with respect to simulation precision, existing simulation techniques are, for the most part, too intricate to implement on early fault-tolerant quantum hardware. We propose a quantum Hamiltonian dynamics simulation algorithm that aims to be both straightforward to implement and, at the same time, have near-optimal scaling in simulation precision.
Abstract Quantum simulation is a foundational application for quantum computers, projected to offer insights into complex quantum systems beyond the reach of classical computation. However, with the exception of Trotter-based methods, which suffer from suboptimal scaling with respect to simulation precision, existing simulation techniques are, for the most part, too intricate to implement on early fault-tolerant quantum hardware. We propose a quantum Hamiltonian dynamics simulation algorithm that aims to be both straightforward to implement and, at the same time, have near-optimal scaling in simulation precision.
We describe a simple quantum algorithm to simulate time-dependent Hamiltonian, extending the methodology of quantum signal processing. The framework achieves optimal scaling up to some factor with respect to other parameters, and nearly optimal in inverse of error tolerance, which could be improved to optimal scaling under certain input models. As applications, we discuss the problem of simulating generalized lattice system and time-periodic, or Floquet system, showing that our framework provides a neater yet highly efficient solution, achieving optimal/nearly optimal scaling in all parameters. In particular, our method also paves a new way for studying phase transition on quantum computer, extending the reach of quantum simulation.
We describe a quantum algorithm to simulate the time-dependent Hamiltonian, extending the methodology of quantum signal processing. The framework achieves optimal scaling up to some factor with respect to other parameters, and is nearly optimal in inverse of error tolerance, which could be improved to optimal scaling under certain input models. As applications, we discuss the problem of simulating tje generalized lattice system and time-periodic, or Floquet system, showing that our framework provides a neater yet highly efficient solution, achieving nearly optimal scaling in all parameters. In particular, our method also paves a new way for studying phase transition on quantum computer, extending the reach of quantum simulation.
Quantum-enhanced Hamiltonian simulation offers a promising approach to modeling complex quantum systems, addressing limitations inherent in classical Hamiltonian methods. This paper explores the creation of a novel quantum algorithm to enhance the representation of a Hamiltonian, enabling a more precise and efficient simulation of dynamical behavior. We propose a method that integrates quantum operators directly into the Hamiltonian structure, thereby providing a richer representation of the system's dynamics and potentially unlocking novel insights into complex quantum phenomena. The research focuses on demonstrating the efficacy of this approach through simulations of a specific, yet illustrative, quantum system, highlighting its potential to improve the accuracy and computational efficiency of simulations of intricate quantum systems. The core mechanism involves a layered approach combining existing Hamiltonian techniques with quantum-enhanced representation, leading to a shift in computational capabilities.
Quantum mechanical problems are among the hardest to simulate and, in some cases, remain intractable even for the most powerful computers. Quantum computing has emerged as a new technological platform to address such challenges, with rapid advances in recent years. Yet, current quantum devices remain noisy and limited in scale. Hence, it is essential to identify classically hard problems of practical interest and tractable with existing quantum devices. Among potential applications, the real-time simulation of quantum systems is one of the most promising to deliver an early, practical quantum advantage. This doctoral thesis is therefore centered around simulating quantum dynamics on quantum devices. We first present an overview of the most relevant quantum algorithms for quantum dynamics, highlighting respective advantages and limitations. Further, we identify relevant problems within quantum dynamics that could benefit from quantum simulation in the near future. Second, we propose a method for benchmarking hardware and error mitigation algorithms that is based on well-understood theoretical results and suffers from no scaling issues. The resulting quality metric is intuitive and transferable to other applications. We successfully implement the scheme on up to 133 qubits, demonstrating coherent evolution up to a two-qubit gate depth of 28, featuring 1396 two-qubit gates, before noise becomes prevalent. Third, we propose a novel variant of probabilistic error amplification to implement open quantum dynamics, relying on characterizing and altering hardware noise to mimic the system-environment interaction under study. Lastly, we present two studies on state preparation and phase classification: first, a hybrid algorithm to prepare ground states of electron-phonon systems; second, a quantum machine learning-based approach to distinguish phases in previously prepared quantum states.
Quantum simulation of molecular electronic structure is one of the most promising applications of quantum computing. However, achieving chemically accurate predictions for strongly correlated systems requires quantum phase estimation (QPE) on fault-tolerant quantum computing (FTQC) devices. Existing resource estimates for typical FTQC architectures suggest that such calculations demand millions of physical qubits, thereby placing them beyond the reach of near-term devices. Here, we investigate the feasibility of performing QPE for chemically relevant molecular systems in an early-FTQC regime, characterized by partial fault tolerance, constrained qubit budgets, and limited circuit depth. Our framework is based on single-ancilla, Trotter-based QPE implementations combined with partially randomized time evolution. Within this framework, we develop a novel Hamiltonian optimization strategy, termed unitary weight concentration, that reduces algorithmic cost by reshaping linear-combination-of-unitaries representations. Applying this framework to active-space models of iron-sulfur clusters, cytochrome P450 active sites, and CO2-utilization catalysts, we perform end-to-end resource estimation using the latest version of the space-time efficient analog rotation (STAR) architecture. Our results indicate that ground-state energy estimation for active spaces of approximately 20 to 50 spatial orbitals, well beyond the reach of classical full configuration interaction, is achievable using ∼105 physical qubits, with runtimes on the order of days to weeks. These findings demonstrate that while full-fledged fault-tolerant quantum computers will be required for even larger molecular simulations, chemically meaningful quantum chemistry problems are already within reach in an experimentally relevant, early-FTQC regime.
Simulating quantum dynamics beyond the reach of classical computers is one of the main envisioned applications of quantum computers. The most promising quantum algorithms to this end in the near term are the simplest, which use the Trotter formula and its higher-order variants to approximate the dynamics of interest. The approximation error of these algorithms is often poorly understood, even in the most basic and topical cases where the target Hamiltonian decomposes into two realizable terms: H=H_{1}+H_{2}. Recent studies have reported anomalously low approximation error with unexpected scaling in such cases, which they attribute to quantum interference between the errors from different steps of the algorithm. Here, we provide a simpler picture of these effects by relating the Trotter formula to its second-order variant for such H=H_{1}+H_{2} cases. Our method generalizes state-of-the-art error bounds without the technical caveats of prior studies, and elucidates how each part of the total error arises from the underlying quantum circuit. We compare our bound to the true error numerically, and find a close match over many orders of magnitude in the simulation parameters. Our findings further reduce the required circuit depth for the least experimentally demanding quantum simulation algorithms, and illustrate a useful method for bounding simulation error more broadly.