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arXiv:2203.14210 · Physical Review A

Quantum annealing with pairs of 2Σ molecules as qubits

Kasra Asnaashari, Roman V. Krems

Published Aug 8, 2022• 5 citations
arXivHTMLPDF

Abstract

The rotational and fine structure of open-shell molecules in a $\mathrm{\ensuremath{\Sigma}}$ electronic state gives rise to crossings between Zeeman states of different parity. These crossings become avoided in the presence of an electric field. We propose an algorithm that encodes Ising models into qubits defined by pairs of ${}^{2}\mathrm{\ensuremath{\Sigma}}$ molecules sharing an excitation near these avoided crossings. This can be used to realize a transverse field Ising model tunable by an external electric or magnetic field, suitable for quantum annealing applications. We perform dynamical calculations for several examples with one- and two-dimensional connectivities. Our results demonstrate that the probability of obtaining valid annealing solutions is high and can be optimized by varying the annealing times.

DOI
10.1103/physreva.106.022801

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The rotational and fine structure of open-shell molecules in a \ensuremathΣ\mathrm{\ensuremath{\Sigma}}\ensuremathΣ electronic state gives rise to crossings between Zeeman states of different parity. These crossings become avoided in the presence of an electric field. We propose an algorithm that encodes Ising models into qubits defined by pairs of 2\ensuremathΣ{}^{2}\mathrm{\ensuremath{\Sigma}}2\ensuremathΣ molecules sharing an excitation near these avoided crossings. This can be used to realize a transverse field Ising model tunable by an external electric or magnetic field, suitable for quantum annealing applications. We perform dynamical calculations for several examples with one- and two-dimensional connectivities. Our results demonstrate that the probability of obtaining valid annealing solutions is high and can be optimized by varying the annealing times.
We examine the rotational states of a pair of polar (2)Σ molecules subject to a uniform magnetic field. The electric dipole-dipole interaction between the molecules creates entangled pair-eigenstates of two types. In one type, the Zeeman interaction between the inherently paramagnetic molecules and the magnetic field destroys the entanglement of the pair-eigenstates, whereas in the other type it does not. The pair-eigenstates exhibit numerous intersections, which become avoided for pair-eigenstates comprised of individual states that meet the selection rules ΔJi = 0, ± 1, ΔNi = 2n (n = 0, ±1, ±2,…), and ΔMi = 0, ± 1 imposed by the electric dipole-dipole operator. Here Ji, Ni and Mi are the total, rotational and projection angular momentum quantum numbers of molecules i = 1, 2 in the absence of the electric dipole-dipole interaction. We evaluate the mutual alignment of the pair-eigenstates and find it to be independent of the magnetic field, except for states that undergo avoided crossings, in which case the alignment of the interacting states is interchanged at the magnetic field corresponding to the crossing point. We present an analytic model which provides ready estimates of the pairwise alignment cosine that characterises the mutual alignment of the pair of coupled rotors.
Inspired by simulated annealing algorithm, we propose a quantum cooling protocol which includes an annealing process. This protocol can be universally and efficiently applied to various quantum simulators, driving the system from an arbitrary initial state to the ground state with high fidelity. We have described the cooling process based on perturbation theory, validated the advantages of bath under time-modulated Zeeman field compared to bath under static one, and provided a justification for the necessity of an annealing process when the system to be cooled is unknown. We applied tensor network methods to numerically simulate our cooling protocol, using the transverse field Ising model (TFIM) as an example to verify the effectiveness of the protocol in cooling one-dimensional systems, two-dimensional systems, and systems with quantum noise. We compared the overall performance of cooling protocols with and without the annealing process on a test set generated with random parameters gPg_PgP​. The results indicate that the cooling protocol with annealing process can achieve both accuracy and efficiency. Our results also show that the cooling protocol's resistance to noise depends on the type of quantum noise.
A shorter processing time is desirable for quantum computation to minimize the effects of noise. We propose a simple procedure to variationally determine a set of parameters in the transverse-field Ising model for quantum annealing (QA) appended with a field along the [Formula: see text]-axis. The method consists of greedy optimization of the signs of coefficients of the [Formula: see text]-field term based on the outputs of short annealing processes. We test the idea in the ferromagnetic system with all-to-all couplings and spin-glass problems, and find that the method outperforms the traditional form of QA and simulated annealing in terms of the success probability and the time to solution, in particular, in the case of shorter annealing times, achieving the goal of improved performance while avoiding noise. The non-stoquastic [Formula: see text] term can be eliminated by a rotation in the spin space, resulting in a non-trivial diabatic control of the coefficients in the stoquastic transverse-field Ising model, which may be feasible for experimental realization. This article is part of the theme issue 'Quantum annealing and computation: challenges and perspectives'.
Calculating the molecular ground-state energy is a central challenge in computational chemistry. Conventional methods such as the Complete Active Space Configuration Interaction scale exponentially with molecular size, limiting their applicability to large molecules. Quantum computing offers a promising alternative by mapping molecular Hamiltonians by qubits, enabling cheaper computational scaling. Previous studies have shown that it is possible to formulate molecular ground state calculations as discrete optimization problems, addressable by quantum annealing. However, these efforts have been limited by previous generations of hardware and suboptimal annealing techniques. Here, the H2OH_{2}OH2​O ground-state problem is mapped to an Ising Hamiltonian using the Xian-Bias-Kas (XBK) method. By taking advantage of enhanced qubit connectivity and shorter embedding chains, it is solved with a more than doubled probability of achieving Hartree-Fock-level solutions with respect to the most advanced predecessor. Advanced annealing strategies extend Hartree-Fock-level accuracy to significantly larger problem instances, enabling solutions that use nearly 2.5 times more physically embedded qubits than the largest cases previously reported and allowing to improve annealing results by two orders of magnitude, reaching an energy difference of 0.120~Hartree relative to Hartree-Fock. These results show tangible progress toward practical quantum annealing applications in NISQ era.
The performance of open-system quantum annealing is adversely affected by thermal excitations out of the ground state. While the presence of energy gaps between the ground and excited states suppresses such excitations, error correction techniques are required to ensure full scalability of quantum annealing. Quantum annealing correction (QAC) is a method that aims to improve the performance of quantum annealers when control over only the problem (final) Hamiltonian is possible, along with decoding. Building on our earlier work [S. Matsuura et al., Phys. Rev. Lett. 116, 220501 (2016)], we study QAC using analytical tools of statistical physics by considering the effects of temperature and a transverse field on the penalty qubits in the ferromagnetic ppp-body infinite-range transverse-field Ising model. We analyze the effect of QAC on second (p=2p=2p=2) and first ($p\ensuremath{\ge}3$) order phase transitions, and construct the phase diagram as a function of temperature and penalty strength. Our analysis reveals that for sufficiently low temperatures and in the absence of a transverse field on the penalty qubit, QAC breaks up a single, large free-energy barrier into multiple smaller ones. We find theoretical evidence for an optimal penalty strength in the case of a transverse field on the penalty qubit, a feature observed in QAC experiments. Our results provide further compelling evidence that QAC provides an advantage over unencoded quantum annealing.
We propose a nonadiabatic approach to quantum annealing, in which we repeat quantum annealing in nonadiabatic time scales, and collect the final states of many realizations to find the ground state among them. In this way, we replace the diffculty of long annealing time in adiabatic quantum annealing by another problem of the number of nonsidabatic (short-time) trials. The one-dimensional transverse-field Ising model is used to test this idea, and it is shown that nonadiabatic quantum annealing has the same computational complexity to find the ground state as the conventional adiabatic annealing does. This result implies that the nonadiabatic method may be used to replace adiabatic annealing to avoid the effects of external disturbances, to which the adiabatic method is more prone than the nonadiabatic counterpart.