We study a hardware-efficient variational quantum algorithm ansatz tailored for the trapped-ion quantum simulator, HEA-TI. We leverage programmable single-qubit rotations and global spin-spin interactions among all ions, reducing the dependence on resource-intensive two-qubit gates in conventional gate-based methods. We apply HEA-TI to state engineering of cluster states and analyze the scaling of required quantum resources. We also apply HEA-TI to solve the ground state problem of chemical molecules $\mathrm{H_{2}}$, $\mathrm{LiH}$ and $\mathrm{F_{2}}$. We numerically analyze the quantum computing resources required to achieve chemical accuracy and examine the performance under realistic experimental noise and statistical fluctuation. The efficiency of this ansatz is shown to be comparable to other commonly used variational ansatzes like UCCSD, with the advantage of substantially easier implementation in the trapped-ion quantum simulator. This approach showcases the hardware-efficient ansatz as a powerful tool for the application of the near-term quantum computer.
We study a hardware-efficient variational quantum algorithm ansatz tailored for the trapped-ion quantum simulator, HEA-TI. We leverage programmable single-qubit rotations and global spin-spin interactions among all ions, reducing the dependence on resource-intensive two-qubit gates in conventional gate-based methods. We apply HEA-TI to state engineering of cluster states and analyze the scaling of required quantum resources. We also apply HEA-TI to solve the ground state problem of chemical molecules H2, LiH and F2. We numerically analyze the quantum computing resources required to achieve chemical accuracy and examine the performance under realistic experimental noise and statistical fluctuation. The efficiency of this ansatz is shown to be comparable to other commonly used variational ansatzes like UCCSD, with the advantage of substantially easier implementation in the trapped-ion quantum simulator. This approach showcases the hardware-efficient ansatz as a powerful tool for the application of the near-term quantum computer.
We study a hardware-efficient ansatz tailored for a trapped-ion quantum simulator (HEA-TI), utilizing single-qubit rotations and global spin-spin interactions to reduce the reliance on resource-intensive multiqubit gates typical of conventional gate-based approaches. This ansatz also allows streamlined experimental control sequences with continuous global interaction and insertions of single-qubit gates. We examine the scaling behavior of quantum resources required by HEA-TI. We also apply it to the ground-state calculation of chemical molecules and examine its performance under realistic experimental noise and statistical fluctuations. Our results demonstrate that HEA-TI achieves competitive efficiency with other commonly used variational ansatzes, such as UCCSD, while offering significant implementation advantages for trapped-ion platforms.
Abstract Variational quantum eigensolvers (VQE) are among the most promising approaches for solving electronic structure problems on near-term quantum computers. A critical challenge for VQE in practice is that one needs to strike a balance between the expressivity of the VQE ansatz versus the number of quantum gates required to implement the ansatz, given the reality of noisy quantum operations on near-term quantum computers. In this work, we consider an orbital-optimized pair-correlated approximation to the unitary coupled cluster with singles and doubles (uCCSD) ansatz and report a highly efficient quantum circuit implementation for trapped-ion architectures. We show that orbital optimization can recover significant additional electron correlation energy without sacrificing efficiency through measurements of low-order reduced density matrices (RDMs). In the dissociation of small molecules, the method gives qualitatively accurate predictions in the strongly-correlated regime when running on noise-free quantum simulators. On IonQ’s Harmony and Aria trapped-ion quantum computers, we run end-to-end VQE algorithms with up to 12 qubits and 72 variational parameters—the largest full VQE simulation with a correlated wave function on quantum hardware. We find that even without error mitigation techniques, the predicted relative energies across different molecular geometries are in excellent agreement with noise-free simulators.
Abstract Quantum computing leverages the quantum resources of superposition and entanglement to efficiently solve computational problems considered intractable for classical computers. Examples include calculating molecular and nuclear structure, simulating strongly interacting electron systems, and modeling aspects of material function. While substantial theoretical advances have been made in mapping these problems to quantum algorithms, there remains a large gap between the resource requirements for solving such problems and the capabilities of currently available quantum hardware. Bridging this gap will require a co-design approach, where the expression of algorithms is developed in conjunction with the hardware itself to optimize execution. Here we describe an extensible co-design framework for solving chemistry problems on a trapped-ion quantum computer and apply it to estimating the ground-state energy of the water molecule using the variational quantum eigensolver (VQE) method. The controllability of the trapped-ion quantum computer enables robust energy estimates using the prepared VQE ansatz states. The systematic and statistical errors are comparable to the chemical accuracy, which is the target threshold necessary for predicting the rates of chemical reaction dynamics, without resorting to any error mitigation techniques based on Richardson extrapolation.
Quantum algorithms are promising candidates for the enhancement of computational efficiency for a variety of computational tasks, allowing for the numerical study of physical systems intractable to classical computers. In the Noisy Intermediate Scale Quantum (NISQ) era of quantum computing, however, quantum resources are limited and thus quantum algorithms utilizing such resources efficiently are highly coveted. We present a resource-efficient quantum algorithm for bosonic ground and excited state computations using the Variational Quantum Eigensolver algorithm with the Unitary Coupled Cluster ansatz. The algorithm is based on two quantum resource reduction strategies, consisting of a selective Hamming truncation of the encoded qubit Hilbert space along with a qubit ground state encoding protocol. Our algorithm proves to significantly increase accuracy with a simultaneous reduction of required quantum resources compared to current approaches. Furthermore, the selective Hamming truncation of our algorithm presents a versatile method to tailor the utilized quantum resources of a quantum computer depending on the hardware parameters. Finally, our work may contribute to shortening the route to achieve a practical quantum advantage in bosonic quantum simulations. The study of vibrational properties of molecular systems is crucial in a variety of contexts, such as spectroscopy, fluorescence, chemical reaction dynamics and transport properties. Thus, our algorithm provides a resource-efficient flexible approach to study such applications in the context of quantum computational chemistry on quantum computers.
One of the most significant challenges in quantum chemistry simulations is the accurate and efficient treatment of strongly correlated systems using classical computers. Quantum computational chemistry is an emerging field that has grown alongside the development of quantum computers, aiming to tackle challenges beyond the reach of traditional computational chemistry methods. Given the current limitations of quantum hardware, hybrid quantum-classical algorithms have become the dominant approach in quantum computational chemistry, with the Variational Quantum Eigensolver (VQE) serving as a representative example. In the realm of variational quantum algorithms, the design of the ansatz plays a pivotal role, as it directly determines both the accuracy of the results and the optimization efficiency of the algorithm, making it a central component in achieving success in quantum computational chemistry. However, existing ansätze often fails to strike a balance between precision and hardware efficiency, posing a major bottleneck for practical applications. In our previous work, we proposed a novel strategy for designing hardware-efficient ansätze with built-in physical constraints (PCHEA). This approach demonstrated outstanding performance in simulating one-dimensional Heisenberg models and several typical molecular systems. By embedding physical insights into the design, PCHEA not only improved computational accuracy but also significantly enhanced hardware compatibility, making it a promising candidate for near-term quantum devices. Nevertheless, challenges remain. When applying the one-dimensional PCHEA to two-dimensional systems, the circuit costs increase significantly. To address this challenge, in this work, we simplify the implementation of the physics-constrained hardware-efficient ansatz, using fSim gates arranged in hardware-efficient linear and brickwall layouts to construct one-dimensional fSim linear and fSim brickwall ansätze. This modification substantially reduces both the number of two-qubit gates and the circuit depth. These ansätze ensure universality, systematic improvement, and size consistency within a particle-number-conserving Hilbert space, with significant improvements observed in the simulation of the one-dimensional Heisenberg model. Furthermore, building on the advancements in quantum hardware connectivity, we extend the one-dimensional PCHEA to a two-dimensional version by arranging it in a grid pattern. The two-dimensional PCHEA not only retains the physical constraints of the one-dimensional PCHEA but also exploits hardware connectivity to further reduce circuit costs. Simulations on two-dimensional Heisenberg models show that the two-dimensional PCHEA achieves chemical accuracy with considerably lower circuit depth, fewer parameters, and fewer two-qubit gates compared to the one-dimensional PCHEA. This work reinforces the effectiveness of designing hardware-efficient ansätze with embedded physical constraints, presenting a promising approach to advancing the practical application of quantum computers for simulating two-dimensional systems. Such progress brings us closer to achieving more efficient and scalable quantum simulations while addressing key challenges in quantum computational chemistry.
High Resolution Image Download MS PowerPoint Slide Quantum computers have the potential to efficiently solve the electronic structure problem but are currently limited by noise and shallow circuits. We present an enhanced Variational Quantum Eigensolver (VQE) ansatz based on the Qubit Coupled Cluster (QCC) approach that requires optimization of only n parameters, where n is the number of Pauli string generators, rather than the typical n + 2 m parameters, where m is the number of qubits. We evaluate the ground state energies and molecular dissociation curves of strongly correlated molecules, namely O 3 and Li 4, using active spaces of varying sizes in conjunction with our enhanced QCC ansatz, Unitary Coupled Cluster Single–Double (UCCSD) ansatz, and the classical Coupled Cluster Singles and Doubles (CCSD) method. Compared to UCCSD, our approach significantly reduces the number of parameters while maintaining high accuracy. Numerical simulations demonstrate the effectiveness of our approach, and experiments on superconducting and trapped-ion quantum computers showcase its practicality on real hardware. By eliminating the need for symmetry-restoring gates and reducing the number of parameters, our enhanced QCC ansatz enables accurate quantum chemistry calculations on near-term quantum devices for strongly correlated systems.