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arXiv:2410.19903

General, efficient, and robust Hamiltonian engineering

Pascal Baßler, Heinrich, Markus, Martin Kliesch

Published Oct 25, 2024• 0 citations
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Abstract

Implementing the time evolution under a desired target Hamiltonian is critical for various applications in quantum science. Due to the exponential increase in the number of parameters with system size and experimental imperfections, this task can be challenging in quantum many-body settings. We introduce an efficient and robust scheme to engineer arbitrary local many-body Hamiltonians. To this end, our scheme applies single-qubit $π$ or $π/2$ pulses to an always-on system Hamiltonian, which we assume to be native to a given platform. These sequences are constructed by efficiently solving a linear program (LP) which minimizes the total evolution time. In this way, we can engineer target Hamiltonians that are only limited by the locality of the interactions in the system Hamiltonian. Based on average Hamiltonian theory and using robust composite pulses, we make our schemes robust against errors, including finite pulse time errors and various control errors. To demonstrate the performance of our scheme, we provide numerical simulations. In particular, we solve the Hamiltonian engineering problem on a laptop for arbitrary two-local Hamiltonians on a 2D square lattice with $196$ qubits in only $60$ seconds. Moreover, we simulate the engineering of general Heisenberg Hamiltonians from Ising Hamiltonians using imperfect single-qubit pulses for smaller system sizes and achieve a fidelity exceeding $99.9\%$, which is orders of magnitude better than non-robust implementations.

DOI
10.48550/arxiv.2410.19903

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Implementing the time evolution under a desired target Hamiltonian is critical for various applications in quantum science. Due to the exponential increase in the number of parameters with system size and experimental imperfections, this task can be challenging in quantum many-body settings. We introduce an efficient and robust scheme to engineer arbitrary local many-body Hamiltonians. To this end, our scheme applies single-qubit πππ or π/2π/2π/2 pulses to an always-on system Hamiltonian, which we assume to be native to a given platform. These sequences are constructed by efficiently solving a linear program (LP) which minimizes the total evolution time. In this way, we can engineer target Hamiltonians that are only limited by the locality of the interactions in the system Hamiltonian. Based on average Hamiltonian theory and using robust composite pulses, we make our schemes robust against errors, including finite pulse time errors and various control errors. To demonstrate the performance of our scheme, we provide numerical simulations. In particular, we solve the Hamiltonian engineering problem on a laptop for arbitrary two-local Hamiltonians on a 2D square lattice with 196196196 qubits in only 606060 seconds. Moreover, we simulate the engineering of general Heisenberg Hamiltonians from Ising Hamiltonians using imperfect single-qubit pulses for smaller system sizes and achieve a fidelity exceeding 99.9%99.9\%99.9%, which is orders of magnitude better than non-robust implementations.
Implementing the time evolution under a desired target Hamiltonian is critical for various applications in quantum science. Due to the exponential increase of parameters in the system size and due to experimental imperfections, this task can be challenging in quantum many-body settings. We introduce an efficient and robust scheme to engineer arbitrary local many-body Hamiltonians. To this end, our scheme applies single-qubit π or π/2 pulses to an always-on system Hamiltonian, which we assume to be native to a given platform. These sequences are constructed by efficiently solving a linear program (LP) which minimizes the total evolution time. In this way, we can engineer target Hamiltonians that are only limited by the locality of the interactions in the system Hamiltonian. Based on average Hamiltonian theory and by using robust composite pulses, we make our schemes robust against errors, including finite-pulse-time errors and various control errors. To demonstrate the performance of our scheme, we provide numerical simulations. In particular, we solve the Hamiltonian-engineering problem on a laptop for arbitrary two-local Hamiltonians on a two-dimensional square lattice with 196 qubits in only 60 s. Moreover, we simulate the engineering of general Heisenberg Hamiltonians from Ising Hamiltonians with imperfect single-qubit pulses for smaller system sizes, and achieve a fidelity larger than 99.9%, which is orders of magnitude better than nonrobust implementations.
Implementing the time evolution under a desired target Hamiltonian is critical for various applications in quantum science. Due to the exponential increase of parameters in the system size and due to experimental imperfections, this task can be challenging in quantum many-body settings. We introduce an efficient and robust scheme to engineer arbitrary local many-body Hamiltonians. To this end, our scheme applies single-qubit π or π / 2 pulses to an always-on system Hamiltonian, which we assume to be native to a given platform. These sequences are constructed by efficiently solving a linear program (LP) which minimizes the total evolution time. In this way, we can engineer target Hamiltonians that are only limited by the locality of the interactions in the system Hamiltonian. Based on average Hamiltonian theory and by using robust composite pulses, we make our schemes robust against errors, including finite-pulse-time errors and various control errors. To demonstrate the performance of our scheme, we provide numerical simulations. In particular, we solve the Hamiltonian-engineering problem on a laptop for arbitrary two-local Hamiltonians on a two-dimensional square lattice with 196 qubits in only 60 s. Moreover, we simulate the engineering of general Heisenberg Hamiltonians from Ising Hamiltonians with imperfect single-qubit pulses for smaller system sizes, and achieve a fidelity larger than 99.9%, which is orders of magnitude better than nonrobust implementations.
Quantum simulators enable the exploration of complex quantum phenomena in condensed-matter systems by reproducing their dynamics on controllable quantum devices. However, experimental constraints often restrict the class of Hamiltonians that can be realized natively. Hamiltonian engineering addresses this limitation by expanding the set of accessible Hamiltonians beyond the fixed system Hamiltonian provided by the hardware. We introduce a framework for fermionic Hamiltonian engineering based on interleaving free evolution under the system Hamiltonian with a sequence of experimentally feasible local fermionic unitaries. The required sequences and free-evolution times are obtained efficiently through a linear program, enabling effective time evolution under a broad class of target Hamiltonians. In particular, our method realizes arbitrary complex tunnelling coefficients, constrained only by the connectivity of the underlying system Hamiltonian. We further show that symmetries of the Hamiltonian engineering task can be exploited to drastically reduce the cost of computing the control parameters, and that errors arising from finite pulse times can be compensated within the same framework through a simple modification of the linear program. To our knowledge, this is the first automated method to realize locally tunable artificial gauge fields in interacting fermionic lattice models using only site-resolved energy shifts as control. We demonstrate the method by engineering the dynamics of interacting Fermi-Hubbard chains with complex tunnelling coefficients and of the Harper-Hofstadter model on a 1088-mode lattice. For the latter, we exploit the translation symmetry of the model to determine a provably optimal six-pulse sequence that produces the desired dynamics independent of the lattice size.
Quantum computers hold the promise of solving certain computational problems significantly faster than classical computers. Unlocking the full potential of quantum hardware depends on our ability to efficiently translate high-level quantum algorithms into executable sequences of quantum operations tailored to the specific constraints of a given device, a task known as quantum compilation. Among the most promising applications is the simulation of quantum systems, such as in quantum chemistry, where scalable, error resilient, and experimentally feasible Hamiltonian simulation techniques are essential. In the first part of this thesis, we present recent advances in the field of quantum compilation, emphasizing on efficient gate decomposition and circuit optimization. In particular, we analyze compilation techniques for Clifford circuits and general single-qubit rotations. Clifford operations play a central role in quantum error correction, the characterization of quantum devices and quantum cryptography. We explore asymptotically optimal decomposition methods, including constructions using either two-qubit gates or global entangling operations, the latter being especially well-suited for platforms like trapped ions. For single-qubit unitaries, we discuss approximation schemes that achieve the theoretically optimal scaling of gate count with respect to the desired precision. Beyond gate synthesis, we examine various hardware-aware optimization strategies aimed at reducing circuit depth and gate overhead. These include techniques for qubit routing in systems with limited connectivity, as well as methods for removing redundant operations. The second and primary, scientific contribution of this thesis focuses on implementation of effective many-body interactions on quantum hardware by combining the system’s native dynamics with control operations, which we call Hamiltonian engineering. Motivated by the central role of Hamiltonian simulation in quantum science, we introduce a general and efficient framework for synthesizing arbitrary target Hamiltonians under mild locality constraints. We propose a novel linear programming (LP) approach that computes pulse sequences consisting of single-qubit π or π/2 rotations applied at certain times during free evolution under the system’s native Hamiltonian. Our LP-based framework offers multiple advantages. First, its classical runtime depends only on the number and locality of the interactions in the system Hamiltonian, not directly on the overall system size. Second, we extend the method to include robustness against common error sources such as finite pulse time effects and systematic control errors, leveraging tools from average Hamiltonian theory and robust composite pulses. Our approach enables the efficient realization of high-fidelity Hamiltonian dynamics with minimal experimental overhead. The scalability of the approach are demonstrated through simulations, including the engineering of a random two-body Hamiltonian on a 225 qubit lattice in under a minute of classical preprocessing. In conclusion, this thesis contributes both theoretical insights and practical tools that bridge the gap between algorithm design and experimental implementation in quantum computing. The techniques developed here are directly applicable to a variety of platforms, including trapped ions, neutral atoms, and superconducting circuits. By advancing the frontiers of Hamiltonian engineering, this work enables more efficient, robust, and scalable quantum simulations on nearterm devices. Finally, it brings us closer to realizing quantum technologies, which are possibly capable of solving meaningful problems.
We present a robust protocol to reshape interactions in a spin ensemble based on global control pulse sequences applied to multiple subensembles in parallel. This setting arises naturally from ensembles of solid-state defects or multi-species atomic arrays. We show that it is provably computationally hard to find pulse sequences that simultaneously engineer interactions both within and between subensembles. Despite its formal hardness, we identify a set of necessary or sufficient conditions under which one can synthesize a target Hamiltonian from the native one. Moreover, we introduce efficient numerical strategies for designing pulse sequences that engineer target Hamiltonians robust against common control imperfections. As a specific application, we discuss the robust generation of two-mode spin squeezing in dual-species atomic ensembles, which is a challenging task without subensemble control. Our results provide a practical toolbox to design novel quantum simulation and sensing experiments with minimal control overhead.
Quantum simulators enable the exploration of complex quantum phenomena in condensed-matter systems by reproducing their dynamics on controllable quantum devices. However, experimental constraints often restrict the class of Hamiltonians that can be realized natively. Hamiltonian engineering addresses this limitation by expanding the set of accessible target Hamiltonians from a fixed system Hamiltonian defined by the hardware. We introduce a new framework for fermionic Hamiltonian engineering based on conjugating free evolution under the system Hamiltonian with sequences of experimentally feasible local fermionic unitaries. The required sequences and free-evolution times are obtained efficiently via a linear program. By interleaving system evolution with these local unitaries, our method realizes effective time evolution under a broad class of target Hamiltonians, with intrinsic robustness to finite-pulse-time errors. In particular, we demonstrate that arbitrary complex tunnelling coefficients can be realized, constrained only by the connectivity of the underlying system Hamiltonian. We illustrate this capability by engineering the dynamics of the non-interacting Harper-Hofstadter model on a 1088-mode lattice and an interacting Fermi-Hubbard chain with complex tunnelling coefficients. By construction, our approach avoids the continuous energy absorption inherent to Floquet engineering.