The ability of quantum computers to overcome the exponential memory scaling of many-body problems is expected to transform quantum chemistry. Quantum algorithms require accurate representations of electronic states on a quantum device, but current approximations struggle to combine chemical accuracy and gate efficiency while preserving physical symmetries, and rely on measurement-intensive adaptive methods that tailor the wave function to each molecule. In this contribution, we present a symmetry-preserving and gate-efficient that provides chemically accurate molecular energies with a well-defined circuit structure. Our approach exploits local qubit connectivity, orbital optimization, and connections with generalized valence bond theory to maximize the accuracy that is obtained with shallow quantum circuits. Numerical simulations for molecules with weak and strong electron correlation, including benzene, water, and the singlet-triplet gap in tetramethyleneethane, demonstrate that chemically accurate energies are achieved with as much as 84% fewer two-qubit gates compared to state-of-the-art adaptive techniques. Published by the American Physical Society 2024
The ability of quantum computers to overcome the exponential memory scaling of many-body problems is expected to transform quantum chemistry. Quantum algorithms require accurate representations of electronic states on a quantum device, but current approximations struggle to combine chemical accuracy and gate efficiency while preserving physical symmetries, and rely on measurement-intensive adaptive methods that tailor the wave function to each molecule. In this contribution, we present a symmetry-preserving and gate-efficient that provides chemically accurate molecular energies with a well-defined circuit structure. Our approach exploits local qubit connectivity, orbital optimization, and connections with generalized valence bond theory to maximize the accuracy that is obtained with shallow quantum circuits. Numerical simulations for molecules with weak and strong electron correlation, including benzene, water, and the singlet-triplet gap in tetramethyleneethane, demonstrate that chemically accurate energies are achieved with as much as 84% fewer two-qubit gates compared to state-of-the-art adaptive techniques. Published by the American Physical Society 2024
The ability of quantum computers to overcome the exponential memory scaling of many-body problems is expected to transform quantum chemistry. Quantum algorithms require accurate representations of electronic states on a quantum device, but current approximations struggle to combine chemical accuracy and gate-efficiency while preserving physical symmetries, and rely on measurement-intensive adaptive methods that tailor the wave function ansatz to each molecule. In this contribution, we present a symmetry-preserving and gate-efficient ansatz that provides chemically accurate molecular energies with a well-defined circuit structure. Our approach exploits local qubit connectivity, orbital optimisation, and connections with generalised valence bond theory to maximise the accuracy that is obtained with shallow quantum circuits. Numerical simulations for molecules with weak and strong electron correlation, including benzene, water, and the singlet-triplet gap in tetramethyleneethane, demonstrate that chemically accurate energies are achieved with as much as 84% fewer two-qubit gates compared to state-of-the-art adaptive ansatz techniques.
Abstract Quantum computers promise to revolutionise molecular electronic simulations by overcoming the exponential memory scaling. While electronic wave functions can be represented using a product of fermionic unitary operators, the best ansatz for strongly correlated electronic systems is far from clear. In this contribution, we construct universal wave functions from gate-efficient, spin symmetry-preserving fermionic operators by introducing an algorithm that globally optimises the wave function in the discrete ansatz design and continuous parameter spaces. Our approach maximises the accuracy that can be obtained with near-term quantum circuits and provides a practical route for designing ansätze in the future. Numerical simulations for strongly correlated molecules, including water and molecular nitrogen, and the condensed-matter Hubbard model, demonstrate the improved accuracy of gate-efficient quantum circuits for simulating strongly correlated chemistry.
Quantum computation is one of the most promising new paradigms for the simulation of physical systems composed of electrons and atomic nuclei, with applications in chemistry, solid-state physics, materials science, and molecular biology. This requires a truncated representation of the electronic structure Hamiltonian using a finite number of orbitals. While it is, in principle, obvious how to improve on the representation by including more orbitals, this is usually unfeasible in practice (e.g., because of the limited number of qubits available) and severely compromises the accuracy of the obtained results. Here, we propose a quantum algorithm that improves on the representation of the physical problem by virtue of second-order perturbation theory. In particular, our quantum algorithm evaluates the second-order energy correction through a series of time-evolution steps under the unperturbed Hamiltonian. An important application is to go beyond the active-space approximation, allowing to include corrections of virtual orbitals, known as multireference perturbation theory. Here, we exploit the fact that the unperturbed Hamiltonian is diagonal for virtual orbitals and show that the number of qubits is independent of the number of virtual orbitals. This gives rise to more accurate energy estimates without increasing the number of qubits. Moreover, we demonstrate numerically for realistic chemical systems that the total runtime has highly favorable scaling in the number of virtual orbitals compared to previous studies. Numerical calculations confirm the necessity of the multireference perturbation theory energy corrections to reach accurate ground-state energy estimates. Our perturbation theory quantum algorithm can also be applied to symmetry-adapted perturbation theory. As such, we demonstrate that perturbation theory can help to reduce the quantum hardware requirements for quantum chemistry. Published by the American Physical Society 2024
Quantum computers promise to revolutionise electronic simulations by overcoming the exponential scaling of many-electron problems. While electronic wave functions can be represented using a product of fermionic unitary operators, shallow quantum circuits for exact states have not yet been achieved. We construct universal wave functions from gate-efficient, symmetry-preserving fermionic operators by introducing an algorithm that globally optimises the wave function in the discrete ansatz design and the continuous parameter spaces. Our approach maximises the accuracy that can be obtained with near-term quantum circuits. Highly accurate numerical simulations on strongly correlated molecules, including water and molecular nitrogen, and the condensed-matter Hubbard model, demonstrate that our algorithm reliably advances the state-of-the-art, defining a new paradigm for quantum simulations featuring strong electron correlation.
Quantum computing is emerging as a new computational paradigm with the potential to transform several research fields, including quantum chemistry. However, current hardware limitations (including limited coherence times, gate infidelities, and limited connectivity) hamper the straightforward implementation of most quantum algorithms and call for more noise-resilient solutions. In quantum chemistry, the limited number of available qubits and gate operations is particularly restrictive since, for each molecular orbital, one needs, in general, two qubits. In this study, we propose an explicitly correlated Ansatz based on the transcorrelated (TC) approach, which transfers -- without any approximation -- correlation from the wavefunction directly into the Hamiltonian, thus reducing the number of resources needed to achieve accurate results with noisy, near-term quantum devices. In particular, we show that the exact transcorrelated approach not only allows for more shallow circuits but also improves the convergence towards the so-called basis set limit, providing energies within chemical accuracy to experiment with smaller basis sets and, therefore, fewer qubits. We demonstrate our method by computing bond lengths, dissociation energies, and vibrational frequencies close to experimental results for the hydrogen dimer and lithium hydride using just 4 and 6 qubits, respectively. Conventional methods require at least ten times more qubits for the same accuracy.
Simulation of electronic structure is one of the most promising applications on noisy intermediate-scale quantum (NISQ) era devices. However, NISQ devices suffer from a number of challenges like limited qubit connectivity, short coherence times, and sizable gate error rates. Thus, desired quantum algorithms should require shallow circuit depths and low qubit counts to take advantage of these devices. Here, we attempt to reduce quantum resource requirements for molecular simulations on a quantum computer while maintaining the desired accuracy with the help of classical quantum chemical theories of canonical transformation and explicit correlation. In this work, compact ab initio Hamiltonians are generated classically, in the second quantized form, through an approximate similarity transformation of the Hamiltonian with (a) an explicitly correlated two-body unitary operator with generalized pair excitations that remove the Coulombic electron-electron singularities from the Hamiltonian and (b) a unitary one-body operator to efficiently capture the orbital relaxation effects required for accurate description of the excited states. The resulting transcorrelated Hamiltonians are able to describe both the ground and the excited states of molecular systems in a balanced manner. Using the variational quantum eigensolver (VQE) method based on the unitary coupled cluster with singles and doubles (UCCSD) ansatz and only a minimal basis set (ANO-RCC-MB), we demonstrate that the transcorrelated Hamiltonians can produce ground state energies comparable to the reference CCSD energies with the much larger cc-pVTZ basis set. This leads to a reduction in the number of required CNOT gates by more than 3 orders of magnitude for the chemical species studied in this work. Furthermore, using the quantum equation of motion (qEOM) formalism in conjunction with the transcorrelated Hamiltonian, we are able to reduce the deviations in the excitation energies from the reference EOM-CCSD/cc-pVTZ values by an order of magnitude. The transcorrelated Hamiltonians developed here are Hermitian and contain only one- and two-body interaction terms and thus can be easily combined with any quantum algorithm for accurate electronic structure simulations.