Near-term quantum computers may be able to significantly speed up complex computational tasks, but algorithms that make efficient use of quantum resources are needed. Quantum chemistry is widely regarded as a candidate for the first demonstration of quantum advantage with near-term quantum computers. In the present work, we demonstrate how taking advantage of the symmetries of a molecule leads to a reduction in the number of qubits required. This reduction in qubits also leads to a reduction in the number of variational parameters needed to reach chemical accuracy. Furthermore, we show how a simple modification of the hardware-efficient ansatz for the variational quantum eigensolver yields a factor of 3 reduction in the number of parameters with no loss in accuracy for most problems in quantum chemistry.
Near-term quantum computers may be able to significantly speed up complex computational tasks, but algorithms that make efficient use of quantum resources are needed. Quantum chemistry is widely regarded as a candidate for the first demonstration of quantum advantage with near-term quantum computers. In the present work, we demonstrate how taking advantage of the symmetries of a molecule leads to a reduction in the number of qubits required. This reduction in qubits also leads to a reduction in the number of variational parameters needed to reach chemical accuracy. Furthermore, we show how a simple modification of the hardware-efficient ansatz for the variational quantum eigensolver yields a factor of 3 reduction in the number of parameters with no loss in accuracy for most problems in quantum chemistry.
Quantum computing has the potential to significantly speed up complex computational tasks, and arguably the most promising application area for near-term quantum computers is the simulation of quantum mechanics. To make the most of our limited quantum computing resources, we need new and more compact algorithms and mappings. Whereas previous work, including recent demonstrations, has focused primarily on general mappings for fermionic systems, we propose instead to construct customized mappings tailored to the considered quantum mechanical systems. Specifically, we take advantage of existing symmetry, which we build into the mappings a priori to obtain optimal compactness. To demonstrate this approach, we have performed quantum computing calculations of the fluorine molecule, in which we have mapped 16 active spin-orbitals to 4 qubits. This is a four-fold reduction in the qubit requirement, as compared to the standard general mappings. Moreover, our compact system-to-qubits mappings are robust against noise that breaks symmetry, thereby reducing non-statistical errors in the computations. Furthermore, many systems, including F2, are described by real Hamiltonians, allowing us to also reduce the number of single-qubit operations in the hardware-efficient ansatz for the quantum variational eigensolver by roughly a factor of three.
Abstract A symmetry-adapted fermion-to-spin mapping or encoding that is able to store information about the occupancy of the n spin-orbitals of a molecular system into a lower number of n − k qubits in a quantum computer (where the number of reduced qubits k ranges from 2 to 5 depending on the symmetry of the system) is introduced. This mapping reduces the computational cost of a quantum computing simulation and at the same time enforces symmetry constraints. These symmetry-adapted encodings (SAEs) can be explicitly seen as a block-diagonalization of the Jordan–Wigner qubit Hamiltonian, followed by an orthogonal projection. We provide the form of the Clifford tableau for a general class of fermion-to-qubit encodings, and then use it to construct the map that block-diagonalizes the Hamiltonian in the SAEs. The algorithm proposed does not require any further computations to obtain this map, which is derived directly from the character table of the molecular point group. An implementation of the algorithm is presented as an open-source Python package, QuantumSymmetry, a user guide and code examples. QuantumSymmetry uses open-source quantum chemistry software PySCF for Hartree–Fock calculations, and is compatible with quantum computing toolsets OpenFermion and Qiskit. QuantumSymmetry takes arbitrary user input such as the molecular geometry and atomic basis set to construct the qubit operators that correspond in the appropriate SAE to fermionic operators on the molecular system, such as the second-quantized electronic structure Hamiltonian. QuantumSymmetry is used to produce numerical examples of variational quantum algorithm simulations to find the ground state energy for a number of example molecules, for both Unitary Coupled Clusters with Singles and Doubles and Adaptive Derivative Assembled Pseudo-Trotter Variational Quantum Eigensolver ansätze. We show that, beyond the advantage given by the lower qubit count, the proposed encodings consistently result in shallower and less complex circuits with a reduced number of variational parameters that are able to reach convergence faster and without any loss of computed accuracy.
One of the most important application areas of molecular quantum chemistry is the study and prediction of chemical reactivity. Large-scale, fully error-tolerant quantum computers could provide exact or near-exact solutions to the underlying electronic structure problem with exponentially less effort than a classical computer thus enabling highly accurate predictions for comparably large molecular systems. In the nearer future, however, only “noisy” devices with a limited number of qubits that are subject to decoherence will be available. For such near-term quantum computers the hybrid quantum-classical variational quantum eigensolver algorithm in combination with the unitary coupled-cluster ansatz (UCCSD-VQE) [Peruzzo et al. Nat. Commun. 2014, 5, 4213 and McClean et al. New J. Phys. 2016, 18, 023023] has become an intensively discussed approach that could provide accurate results before the dawn of error-tolerant quantum computing. In this work we present an implementation of UCCSD-VQE that allows for the first time to treat both open- and closed-shell molecules. We study the accuracy of the obtained energies for nine small molecular systems as well as for four exemplary chemical reactions by comparing to well-established electronic structure methods like (nonunitary) coupled-cluster and density functional theory. Finally, we roughly estimate the required quantum hardware resources to obtain “useful” results for practical purposes.
Computer simulation is central to understanding the behaviour of matter. Yet, more than a century after the development of quantum theory, first-principles simulation of chemistry remains a daunting challenge, owing to the exponential growth in memory required to represent interacting quantum particles such as electrons in molecules. Quantum computing offers, in principle, a fundamentally more efficient paradigm for simulating quantum systems, with quantum chemistry often cited as a flagship application. However, many quantum algorithms face intrinsic limitations, and any genuine quantum advantage must surpass the strong baseline set by decades of progress in classical algorithms and hardware. While classical methods often suffice for simulating weakly correlated systems, systems with many strongly correlated electrons remain a challenge for both classical and quantum approaches. In this thesis, we develop quantum algorithms for solving the time-independent Schrödinger equation, with a focus on molecular systems with strongly correlated electrons. We introduce a framework for identifying a compact set of states that parametrise the many-body wavefunction by capturing the correlation due to spin coupling between localised electrons. This representation requires very few variational parameters but incurs a very high memory cost on classical computers. To overcome this, we design quantum circuits that efficiently prepare such states by exploiting their symmetry, encoding the dominant entanglement structure of electronic wavefunctions into the initial qubit states. Through theoretical analysis and classical simulations of quantum computers, we show that this substantially reduces the quantum resources required to accurately compute ground- and excitedstate properties. Finally, we develop an approach for approximating the optimal ansatz within the variational quantum eigensolver, an algorithm designed for near-term quantum devices. Our method constructs wavefunctions from products of symmetrypreserving unitary operators and couples discrete and continuous optimisation to yield highly compact representations of strongly correlated electrons using shallow quantum circuits. Together, these results establish complementary directions for embedding problemspecific structure into quantum simulation algorithms, advancing the practical simulation of strongly correlated electrons.
The exact evaluation of the molecular ground state in quantum chemistry requires an exponentially increasing computational cost. Quantum computation is a promising way to overcome the exponential problem using polynomial-time quantum algorithms. A quantum-classical hybrid optimization scheme known as the variational quantum eigensolver is preferred for noisy intermediate-scale quantum devices. However, the circuit depth becomes one of the bottlenecks of its application to large molecules of more than 20 qubits. In this work, we employ point-group symmetry to reduce the number of operators in constructing ansatz so as to achieve a more compact quantum circuit. We illustrate this methodology with a series of molecules ranging from LiH (12 qubits) to C2H4 (28 qubits). A significant reduction of up to 82% of the operator numbers is reached on C2H4. This also sheds light onto further work in this direction to construct even shallower ansatz with enough expressive power and simulate even larger scale systems.
Abstract We present a quantum chemistry benchmark for noisy intermediate-scale quantum computers that leverages the variational quantum eigensolver, active-space reduction, a reduced unitary coupled cluster ansatz, and reduced density purification as error mitigation. We demonstrate this benchmark using 4 of the available qubits on the 20-qubit IBM Tokyo and 16-qubit Rigetti Aspen processors via the simulation of alkali metal hydrides (NaH, KH, RbH), with accuracy of the computed ground state energy serving as the primary benchmark metric. We further parameterize this benchmark suite on the trial circuit type, the level of symmetry reduction, and error mitigation strategies. Our results demonstrate the characteristically high noise level present in near-term superconducting hardware, but provide a relevant baseline for future improvement of the underlying hardware, and a means for comparison across near-term hardware types. We also demonstrate how to reduce the noise in post processing with specific error mitigation techniques. Particularly, the adaptation of McWeeny purification of noisy density matrices dramatically improves accuracy of quantum computations, which, along with adjustable active space, significantly extends the range of accessible molecular systems. We demonstrate that for specific benchmark settings and a selected range of problems, the accuracy metric can reach chemical accuracy when computing over the cloud on certain quantum computers.