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Register a new userEfficient step-merged quantum imaginary time evolution algorithm for quantum chemistry
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We develop a resource efficient step-merged quantum imaginary time evolution approach (smQITE) to solve for the ground state of a Hamiltonian on quantum computers. This heuristic method features a fixed shallow quantum circuit depth along the state evolution path. We use this algorithm to determine binding energy curves of a set of molecules, including H$_2$, H$_4$, H$_6$, LiH, HF, H$_2$O and BeH$_2$, and find highly accurate results. The required quantum resources of smQITE calculations can be further reduced by adopting the circuit form of the variational quantum eigensolver (VQE) technique, such as the unitary coupled cluster ansatz. We demonstrate that smQITE achieves a similar computational accuracy as VQE at the same fixed-circuit ansatz, without requiring a generally complicated high-dimensional non-convex optimization. Finally, smQITE calculations are carried out on Rigetti quantum processing units (QPUs), demonstrating that the approach is readily applicable on current noisy intermediate-scale quantum (NISQ) devices.
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An adaptive variational quantum imaginary time evolution (AVQITE) approach is introduced that yields efficient representations of ground states for interacting Hamiltonians on near-term quantum computers. It is based on McLachlans variational principle applied to imaginary time evolution of variational wave functions. The variational parameters evolve deterministically according to equations of motions that minimize the difference to the exact imaginary time evolution, which is quantified by the McLachlan distance. Rather than working with a fixed variational ansatz, where the McLachlan distance is constrained by the quality of the ansatz, the AVQITE method iteratively expands the ansatz along the dynamical path to keep the McLachlan distance below a chosen threshold. This ensures the state is able to follow the quantum imaginary time evolution path in the system Hilbert space rather than in a restricted variational manifold set by a predefined fixed ansatz. AVQITE is used to prepare ground states of H$_4$, H$_2$O and BeH$_2$ molecules, where it yields compact variational ansatze and ground state energies within chemical accuracy. Polynomial scaling of circuit depth with system size is demonstrated through a set of AVQITE calculations of quantum spin models. Finally, it is shown that quantum Lanczos calculations can also be naturally performed alongside AVQITE without additional quantum resource costs.
Molecular dynamics is one of the most commonly used approaches for studying the dynamics and statistical distributions of many physical, chemical, and biological systems using atomistic or coarse-grained models. It is often the case, however, that the interparticle forces drive motion on many time scales, and the efficiency of a calculation is limited by the choice of time step, which must be sufficiently small that the fastest force components are accurately integrated. Multiple time-stepping algorithms partially alleviate this inefficiency by assigning to each time scale an appropriately chosen step-size. However, such approaches are limited by resonance phenomena, wherein motion on the fastest time scales limits the step sizes associated with slower time scales. In atomistic models of biomolecular systems, for example, resonances limit the largest time step to around 5-6 fs. In this paper, we introduce a set of stochastic isokinetic equations of motion that are shown to be rigorously ergodic and that can be integrated using a multiple time-stepping algorithm that can be easily implemented in existing molecular dynamics codes. The technique is applied to a simple, illustrative problem and then to a more realistic system, namely, a flexible water model. Using this approach outer time steps as large as 100 fs are shown to be possible.
We describe how to efficiently construct the quantum chemical Hamiltonian operator in matrix product form. We present its implementation as a density matrix renormalization group (DMRG) algorithm for quantum chemical applications in a purely matrix product based framework. Existing implementations of DMRG for quantum chemistry are based on the traditional formulation of the method, which was developed from a viewpoint of Hilbert space decimation and attained a higher performance compared to straightforward implementations of matrix product based DMRG. The latter variationally optimizes a class of ansatz states known as matrix product states (MPS), where operators are correspondingly represented as matrix product operators (MPO). The MPO construction scheme presented here eliminates the previous performance disadvantages while retaining the additional flexibility provided by a matrix product approach; for example, the specification of expectation values becomes an input parameter. In this way, MPOs for different symmetries - abelian and non-abelian - and different relativistic and non-relativistic models may be solved by an otherwise unmodified program.
As we begin to reach the limits of classical computing, quantum computing has emerged as a technology that has captured the imagination of the scientific world. While for many years, the ability to execute quantum algorithms was only a theoretical possibility, recent advances in hardware mean that quantum computing devices now exist that can carry out quantum computation on a limited scale. Thus it is now a real possibility, and of central importance at this time, to assess the potential impact of quantum computers on real problems of interest. One of the earliest and most compelling applications for quantum computers is Feynmans idea of simulating quantum systems with many degrees of freedom. Such systems are found across chemistry, physics, and materials science. The particular way in which quantum computing extends classical computing means that one cannot expect arbitrary simulations to be sped up by a quantum computer, thus one must carefully identify areas where quantum advantage may be achieved. In this review, we briefly describe central problems in chemistry and materials science, in areas of electronic structure, quantum statistical mechanics, and quantum dynamics, that are of potential interest for solution on a quantum computer. We then take a detailed snapshot of current progress in quantum algorithms for ground-state, dynamics, and thermal state simulation, and analyze their strengths and weaknesses for future developments.
Reliable and robust convergence to the electronic ground state within density functional theory (DFT) Kohn-Sham (KS) calculations remains a thorny issue in many systems of interest. In such cases, charge sloshing can delay or completely hinder the convergence. Here, we use an approach based on transforming the time-dependent DFT equations to imaginary time, followed by imaginary-time evolution, as a reliable alternative to the self-consistent field (SCF) procedure for determining the KS ground state. We discuss the theoretical and technical aspects of this approach and show that the KS ground state should be expected to be the long-imaginary-time output of the evolution, independent of the exchange-correlation functional or the level of theory used to simulate the system. By maintaining self-consistency between the single-particle wavefunctions and the electronic density throughout the determination of the stationary state, our method avoids the typical difficulties encountered in SCF. To demonstrate dependability of our approach, we apply it to selected systems which struggle to converge with SCF schemes. In addition, through the van Leeuwen theorem, we affirm the physical meaningfulness of imaginary time TDDFT, justifying its use in certain topics of statistical mechanics such as in computing imaginary time path integrals.
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