As quantum computing scales up, circuits relying on sequential two-qubit gates face severe challenges from excessive depth and decoherence. In trapped-ion systems, global entangling gates offer a highly parallel alternative but are hindered by complex numerical optimization. We propose an efficient numerical framework for piecewise-constant amplitude-modulated global gates. Based on the Mølmer-Sørensen protocol, we utilize null-space projection for linear constraints of spin-motion coupling and tangent-space gradient descent to minimize laser power, while achieving high-order robustness against frequency drifts. At the application level, we identify a structural correspondence between hardware-native global interactions and Pauli strings in Hamiltonian simulation and propose an efficient compilation scheme. By reducing common physical models to fundamental X X interactions and formulating interaction graph partitioning as a Set Cover problem, we leverage global gates to significantly optimize the compilation process. Explicit pulse-level benchmarks further show that, for the tested weighted interaction graphs, the reduction in entangling-gate count can translate into a substantial reduction in total entangling duration. These results demonstrate that integrating hardware-native operations with tailored compilation strategies can substantially reduce circuit overhead, providing a practical roadmap for the codesign of near-term quantum simulators.
As quantum computing scales up, circuits relying on sequential two-qubit gates face severe challenges from excessive depth and decoherence. In trapped-ion systems, global entangling gates offer a highly parallel alternative but are hindered by complex numerical optimization. We propose an efficient numerical framework for piecewise-constant amplitude-modulated global gates. Based on the Mølmer-Sørensen protocol, we utilize null-space projection for linear constraints of spin-motion coupling and tangent-space gradient descent to minimize laser power, while achieving high-order robustness against frequency drifts. At the application level, we identify a structural correspondence between hardware-native global interactions and Pauli strings in Hamiltonian simulation and propose an efficient compilation scheme. By reducing common physical models to fundamental X X interactions and formulating interaction graph partitioning as a Set Cover problem, we leverage global gates to significantly optimize the compilation process. Explicit pulse-level benchmarks further show that, for the tested weighted interaction graphs, the reduction in entangling-gate count can translate into a substantial reduction in total entangling duration. These results demonstrate that integrating hardware-native operations with tailored compilation strategies can substantially reduce circuit overhead, providing a practical roadmap for the codesign of near-term quantum simulators.
Abstract Quantum simulation on noisy intermediate-scale quantum (NISQ) hardware is limited by short coherence time and gate errors. We present a universal variational compilation optimization method (VCOM) that directly leverages the native gate set of trapped-ion processors, namely single-qubit rotations and global Ising-type XX interactions, to construct shallow circuits for simulating molecular Hamiltonians. Specifically, VCOM employs a hybrid optimization strategy combining genetic algorithms with gradient-based refinement to compile Pauli string evolution operators e −i Pt , thereby substantially reducing circuit depth and multi-qubit gate overhead in Hamiltonian simulation. Applied to hydrogen chains, the compiled circuits achieve fidelities comparable to standard decompositions while reducing the proportion of two-qubit operations to only 1.9%–4.6% of the total native gates, a significant improvement over the standard second-order Trotter–Suzuki product formula. Under experimentally motivated laser-intensity and phase-noise models, the proposed scheme maintains high fidelity and exhibits significantly slower degradation than direct native gate decompositions of conventional circuits. These results establish native-gate-based variational compilation as a scalable and practical approach for digital quantum simulation on trapped-ion platforms, with potential extensions to strongly correlated systems and non-equilibrium dynamics.
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.
Almost every quantum circuit is built with two-qubit gates in the current stage, which are crucial to the quantum computing in any platform. The entangling gates based on Mølmer-Sørensen schemes are widely exploited in the trapped-ion system, with the utilization of the collective motional modes of ions and two laser-controlled internal states, which are served as qubits. The key to realize high-fidelity and robust gates is the minimization of the entanglement between the qubits and the motional modes under various sources of errors after the gate operation. In this work, we propose an efficient numerical method to search high-quality solutions for phase-modulated pulses. Instead of directly optimizing a cost function, which contains the fidelity and the robustness of the gates, we convert the problem to the combination of linear algebra and the solution to quadratic equations. Once a solution with the gate fidelity of 1 is found, the laser power can be further reduced while searching on the manifold where the fidelity remains 1. Our method largely overcomes the problem of the convergence and is shown to be effective up to 60 ions, which suffices the need of the gate design in current trapped-ion experiments.
High-fidelity and parallel realization in scalable platforms of the two-qubit entangling gates fundamental to universal quantum computing constitutes one of the largest challenges in implementing fault-tolerant quantum computation. Integrated optical addressing of trapped-ion qubits offers routes to scaling the high-fidelity optical control demonstrated to date in small systems. Here we show that in addition to scaling, capabilities practically enabled by integrated optics can substantially alleviate laser powers required for both light-shift (LS) and Molmer-Sorensen (MS) geometric phase gates acting on long-lived ground-state qubit encodings in a broad range of ion species. In the proposed gate schemes utilizing carrier nulling via ion positioning at phase-stable standing-wave (SW) nodes, our calculations suggest that suppressed spontaneous photon scattering at the SW node allows for gate drives operating at smaller Raman detunings, resulting in approximately an order-of-magnitude reduction in power requirement (and significantly larger in certain parameter regimes) for gates of a given duration and scattering-limited fidelity as compared to conventional running wave (RW)-based approaches. The SW schemes have the additional benefit of simultaneously eliminating undesired coherent couplings that typically limit gate speeds. Our work quantifies power requirements for multiple ion species and enhancements to be expected from carrier-nulled configurations practically enabled by integrated delivery, and informs experiments and systems for realization of fast and power-efficient laser-based entangling gates in scalable platforms.
Abstract Compiling quantum circuits to account for hardware restrictions is an essential part of the quantum computing stack. Circuit compilation allows us to adapt algorithm descriptions into a sequence of operations supported by real quantum hardware, and has the potential to significantly improve their performance when optimisation techniques are added to the process. One such optimisation technique is reducing the number of quantum gates that are needed to execute a circuit. For instance, methods for reducing the number of non-Clifford gates or CNOT gates from a circuit are an extensive research area that has gathered significant interest over the years. For certain hardware platforms such as trapped-ion quantum computers, we can leverage some of their special properties to further reduce the cost of executing a quantum circuit in them. In this work we use global interactions, such as the Global Mølmer–Sørensen (MS) gate present in trapped-ion hardware, to optimise and synthesise quantum circuits. We design and implement an algorithm that is able to compile an arbitrary quantum circuit into another circuit that uses global gates as the entangling operation, while optimising the number of global interactions needed. The algorithm is based on the ZX -calculus and uses a specialised circuit extraction routine that groups entangling gates into Global MS gates. We benchmark the algorithm in a variety of circuits, and show how it improves their performance under state-of-the-art hardware considerations in comparison to a naive algorithm and the Qiskit optimiser.
Abstract Trapped-ion quantum computing can utilize all motional modes of the ion-crystal, to entangle multiple qubits simultaneously, enabling universal computation with multi-qubit gates supplemented by single-qubit rotations. Using multiple tones to drive each ion individually induces Ising-type interactions, forming a multi-qubit gate, where the coupling matrix of all ion pairs is fully controllable. This reduces the total gate count while maintaining high fidelity, as opposed to traditional methods that rely on a single type of two-qubit gate, such as the well-known Mølmer–Sørensen gate. However, scaling to large ion chains, individual addressing can be technically challenging in terms of optical delivery and signal generation. We explore global and semi-global drives combined with single-qubit flips and show that these can reproduce the full set of multi-qubit gates. Although optimizing the combination of single-qubit flips is a computationally hard problem, we propose an efficient scheme to implement any desired couplings in large ion chains, yielding a concatenation scheme that uses at most N / 2 multi-qubit gates, with N being the number of ions. In addition, we show that by using B < N independent semi-global fields, each driving a set of N / B ions, the number of maximal multi-qubit gates is reduced to approximately N 2 B 2 ( N − 1 ) . We show how to design the driving fields that support these schemes and investigate their properties. Our results pave the way for efficient implementations of quantum algorithms in large-scale trapped-ion quantum systems.