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 chemistry simulations offer a cost-effective way for computational design of BODIPY photosensitizers with potential use in photodynamic therapy (PDT). However, accurate predictions of photophysical properties, such as excitation energies, pose a challenge for the popular time-dependent density functional theory (TDDFT) and equation-of-motion coupled cluster with singles and doubles (EOM-CCSD) methods. By contrast, reliable descriptions can be achieved by multi-reference quantum chemistry methods, though unfortunately, their computational cost grows exponentially with the number of correlated electrons. Alternatively, quantum computing holds a great potential for exact simulation of photophysical properties in a computationally more efficient way. To this end, we introduce the state-specific
ΔUCCSD-VQE (unitary coupled cluster with singles and doubles variational quantum eigensolver) and
ΔADAPT-VQE methods in which the electronically excited state is calculated via a non-Aufbau electronic configuration. The accuracy and capability of the developed methods are assessed against experimentally determined excitation energies for six BODIPY-derivatives. We show that the proposed methods predict accurate vertical excitation energies that are not only in good agreement with experimental reference data but also outperform popular quantum chemistry methods, such as TDDFT and EOM-CCSD. Spurred by its impressive performance and simplicity, we are confident that
ΔADAPT will emerge as the method of choice for guiding the rational design of photosensitizers for PDT and photocatalysis in the era of near-term quantum computing.
Estimating molecular ground-state energies is a central application of quantum computing, requiring both the preparation of accurate quantum states and efficient energy readout. Understanding the effect of hardware noise on these experiments is crucial to distinguish errors that have low impact, errors that can be mitigated, and errors that must be reduced at the hardware level. We ran a state preparation and energy measurement protocol on an ion-trap quantum computer, without any non-scalable off-loading of computational tasks to classical computers, and show that leakage errors are the main obstacle to chemical accuracy. More specifically, we apply adiabatic state preparation to prepare the ground state of a six-qubit encoding of the H3+ molecule and extract its energy using a noise-resilient variant of iterative quantum phase estimation. Our results improve upon the classical Hartree-Fock energy. Analyzing the effect of hardware noise on the result, we find that while coherent and incoherent noise have little influence, the hardware results are mainly impacted by leakage errors. Absent leakage errors, noisy numerical simulations show that with our experimental settings we would have achieved close to chemical accuracy, even shot noise included. These insights highlight the importance of targeting leakage suppression in future algorithm and hardware development.
Accurate ground-state energies are essential for understanding molecular structure, chemical bonding, and reaction energetics in quantum chemistry. In this work, we investigate the ground-state properties of the molecular systems HeH
+, ArH
+, and H
2O using Sample-Based Quantum Diagonalization (SQD), a hybrid quantum-classical framework designed for near-term quantum devices. Unlike variational approaches such as VQE, which require deep parameterized circuits and repeated expectation-value measurements, SQD reconstructs a low-energy determinant subspace directly from measured bitstrings. For the present calculations, bitstrings were generated on IBM quantum hardware using shallow local unitary cluster Jastrow (LUCJ) circuits whose parameters were constructed from the
t1 and
t2 amplitudes of coupled-cluster singles and doubles (CCSD) calculations based on restricted Hartree--Fock (RHF) references. From these samples, we compute ground-state potential-energy curves of HeH
+, ArH
+, and H
2O with the 6-31G and cc-pVDZ basis sets. For all three systems, the SQD results obtained with the cc-pVDZ basis closely follow the corresponding same-basis CCSD energies and reproduce the equilibrium-region trends of the potential-energy curves. HeH
+ and ArH
+ were chosen as simple yet astrophysically important molecular-ion benchmarks, while H
2O was included as a representative polyatomic molecule to assess the applicability of SQD beyond diatomic ionic systems. At the adopted equilibrium geometries, the deviations from the same-active-space CASCI references are 0.00, 2.51, and 6.34 mHa for HeH
+, ArH
+, and H
2O, respectively. These results demonstrate the feasibility of hardware-assisted SQD for the present benchmark systems and motivate further studies of its accuracy and computational scaling for larger molecular active spaces.
Measuring expectation values of observables is an essential ingredient in variational quantum algorithms. A practical obstacle is the necessity of a large number of measurements for statistical convergence to meet requirements of precision, such as chemical accuracy in the application to quantum chemistry computations. Here we propose an algorithm to estimate the expectation value based on its approximate expression as a weighted sum of classically tractable matrix elements with some modulation, where the weight and modulation factors are evaluated by sampling appropriately prepared quantum states in the computational basis on quantum computers. Each of those states is prepared by applying a unitary transformation consisting of at most
N CNOT gates, where
N is the number of qubits, to a target quantum state whose expectation value is evaluated. Our algorithm is expected to require fewer measurements than conventional methods for a required statistical precision of the expectation value when the target quantum state is concentrated in particular computational basis states. We provide numerical comparisons of our method with existing ones for measuring electronic ground-state energies (expectation values of electronic Hamiltonians for the lowest-energy states) of various small molecules. Numerical results show that our method can reduce the numbers of measurements to obtain the ground-state energies for a targeted precision by several orders of magnitudes for molecules whose ground states are concentrated. Our results provide another route to measure expectation values of observables, which could accelerate the variational quantum algorithms.
Abstract Quantum chemical calculations are among the most promising applications for quantum computing. Implementations of dedicated quantum algorithms on available quantum hardware were so far, however, mostly limited to comparatively simple systems without strong correlations. As such, they can also be addressed by classically efficient single-reference methods. Here we calculate the lowest energy eigenvalue of active space Hamiltonians of industrially relevant and strongly correlated metal chelates on trapped ion quantum hardware, and integrate the results into a typical industrial quantum chemical workflow to arrive at chemically meaningful properties. We are able to achieve chemical accuracy by training a variational quantum algorithm on quantum hardware, followed by a classical diagonalization in the subspace of states measured as outputs of the quantum circuit. This approach is particularly measurement-efficient, requiring 600 single-shot measurements per cost function evaluation on a ten qubit system, and allows for efficient post-processing to handle erroneous runs.