Abstract The linear combination of unitaries (LCU) method has proven to scale better than existing product formulas in simulating long time Hamiltonian dynamics. However, given the number of multi-control gate operations in the standard prepare-select-unprepare architecture of LCU, it is still resource-intensive to implement on the current quantum computers. In this work, we demonstrate LCU implementations on an ion trap quantum computer for calculating squared overlaps | ⟨ ψ ( t = 0 ) | ψ ( t > 0 ) ⟩ | 2 of time-evolved states. This is achieved by an optimized LCU method, based on pre-selecting relevant unitaries, coupled with a compilation strategy which makes use of quantum multiplexor gates, leading to a significant reduction in the depth and number of two-qubit(2Q) gates in circuits. For L Pauli strings in a Taylor series expanded n -qubit-mapped time evolution operator, we find a 2Q gate count of 2 ⌈ log 2 ( L ) ⌉ ( 2 n + 1 ) − n − 2 . We test this approach by simulating a Rabi–Hubbard Hamiltonian.
Abstract The linear combination of unitaries (LCU) method has proven to scale better than existing product formulas in simulating long time Hamiltonian dynamics. However, given the number of multi-control gate operations in the standard prepare-select-unprepare architecture of LCU, it is still resource-intensive to implement on the current quantum computers. In this work, we demonstrate LCU implementations on an ion trap quantum computer for calculating squared overlaps | ⟨ ψ ( t = 0 ) | ψ ( t > 0 ) ⟩ | 2 of time-evolved states. This is achieved by an optimized LCU method, based on pre-selecting relevant unitaries, coupled with a compilation strategy which makes use of quantum multiplexor gates, leading to a significant reduction in the depth and number of two-qubit(2Q) gates in circuits. For L Pauli strings in a Taylor series expanded n -qubit-mapped time evolution operator, we find a 2Q gate count of 2 ⌈ log 2 ( L ) ⌉ ( 2 n + 1 ) − n − 2 . We test this approach by simulating a Rabi–Hubbard Hamiltonian.
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.
We develop three new methods to implement any Linear Combination of Unitaries (LCU), a powerful quantum algorithmic tool with diverse applications. While the standard LCU procedure requires several ancilla qubits and sophisticated multi-qubit controlled operations, our methods consume significantly fewer quantum resources. The first method ( Single-Ancilla LCU ) estimates expectation values of observables with respect to any quantum state prepared by an LCU procedure while requiring only a single ancilla qubit, and no multi-qubit controlled operations. The second approach ( Analog LCU ) is a simple, physically motivated, continuous-time analogue of LCU, tailored to hybrid qubit-qumode systems. The third method ( Ancilla-free LCU ) requires no ancilla qubit at all and is useful when we are interested in the projection of a quantum state (prepared by the LCU procedure) in some subspace of interest. We apply the first two techniques to develop new quantum algorithms for a wide range of practical problems, ranging from Hamiltonian simulation, ground state preparation and property estimation, and quantum linear systems. Remarkably, despite consuming fewer quantum resources they retain a provable quantum advantage. The third technique allows us to connect discrete and continuous-time quantum walks with their classical counterparts. It also unifies the recently developed optimal quantum spatial search algorithms in both these frameworks, and leads to the development of new ones that require fewer ancilla qubits. Overall, our results are quite generic and can be readily applied to other problems, even beyond those considered here.
We present a quantum algorithm for the dynamical simulation of time-dependent Hamiltonians.Our method involves expanding the interaction-picture Hamiltonian as a sum of generalized permutations, which leads to an integral-free Dyson series of the time-evolution operator.Under this representation, we perform a quantum simulation for the time-evolution operator by means of the linear combination of unitaries technique.We optimize the time steps of the evolution based on the Hamiltonian's dynamical characteristics, leading to a gate count that scales with an L 1 -norm-like scaling with respect only to the norm of the interaction Hamiltonian, rather than that of the total Hamiltonian.We demonstrate that the cost of the algorithm is independent of the Hamiltonian's frequencies, implying its advantage for systems with highly oscillating components, and for time-decaying systems the cost does not scale with the total evolution time asymptotically.In addition, our algorithm retains the near optimal log(1/ )/ log log(1/ ) scaling with simulation error .
Abstract Quantum computers can be used to simulate the evolution of quantum systems via the discretization of this evolution into unitary gate sequences. While Trotter-Suzuki (TS) methods stand as the most prevalent approach for quantum simulation, their effectiveness is contingent upon the sparsity of the Hamiltonian system. This is due to the precision and gate complexity of the TS method being dependent on the number of terms within the Hamiltonian. Despite attempts to mitigate this dependence through the random permutation of terms within TS methods, scalability issues persist. To address this, Campbell introduced the qDRIFT algorithm, leveraging random compilation to alleviate the reliance on the Hamiltonian’s term count. However, the initial implementation of this algorithm necessitated the involvement of classical computing resources for gate set compilation. Our study presents two novel quantum circuit implementations of the qDRIFT algorithm, eliminating the need for classical computing resources. We employ the Linear Combination of Unitaries (LCU) approach and the Quantum Forking (QF) procedure to construct efficient circuits to implement the qDRIFT algorithm. Furthermore, we conduct a comparative analysis of the gate complexities between our proposed circuits and TS methods, identifying the scenarios in which our circuits exhibit superior performance.
Trapped-ion quantum computers offer high-fidelity operations, long coherence times, and all-to-all connectivity within a single trap. However, scaling to large circuits is limited by the trap's ion capacity. The QCCD architecture addresses this by enabling ion shuttling across multiple traps, but excessive shuttling increases execution time and degrades fidelity. This paper presents an improved ion-shuttling approach targeting linear QCCD architectures. Building on a state-of-the-art approach [27] for linear trapped-ion devices, our approach introduces a front-layer-based scheduling method that dynamically prioritizes executable gates, along with a novel destination trap selection method for ion-shuttling, effectively reducing unnecessary ion movements. We also present a look-ahead gate selection strategy based on the gate dependency graph, avoiding the high runtime of the gate proximity approach used in the state-of-the-art approach, especially in circuits with all-to-all communication. Our approach achieves up to a 37.67% reduction in shuttle count and up to a 74.91% reduction in compilation time compared to the state-of-the-art approach for linear trapped-ion devices on actual NISQ benchmarks and synthetic circuits. On average, our approach achieves a 16.44% reduction in shuttle count and a 30.77% reduction in compilation time across all test cases. These improvements highlight the effectiveness of our approach, particularly for actual circuits.
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.