Quantum computers have the potential to advance material design and drug discovery by performing costly electronic structure calculations. A critical aspect of this application requires optimizing the limited resources of the quantum hardware. Here, we experimentally demonstrate an end-to-end pipeline that focuses on minimizing quantum resources while maintaining accuracy. Using density matrix embedding theory as a problem decomposition technique, and an ion-trap quantum computer, we simulate a ring of 10 hydrogen atoms without freezing any electrons. The originally 20-qubit system is decomposed into 10 two-qubit problems, making it amenable to currently available hardware. Combining this decomposition with a qubit coupled cluster circuit ansatz, circuit optimization, and density matrix purification, we accurately reproduce the potential energy curve in agreement with the full configuration interaction energy in the minimal basis set. Our experimental results are an early demonstration of the potential for problem decomposition to accurately simulate large molecules on quantum hardware.

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Quantum computers have the potential to perform accurate and efficient electronic structure calculations, enabling the simulation of properties of materials. However, today’s noisy, intermediate-scale quantum (NISQ) devices have a limited number of qubits and gate operations due to the presence of errors. Here, we propose a systematically improvable end-to-end pipeline to alleviate these limitations. Our proposed resource-efficient pipeline combines problem decomposition techniques for compact molecular representations, circuit optimization methods for compilation, solving the eigenvalue problem on advanced quantum hardware, and error-mitigation techniques in post-processing the results. Using the density matrix embedding theory for compact representation, and an ion-trap quantum computer, we simulate a ring of 10 hydrogen atoms taking into account all electrons equally and explicitly in the electronic structure calculation. In our experiment, we simulated the largest molecular system on a quantum computer within chemical accuracy with respect to total molecular energy calculated by the full CI method. Our methods reduce the number of qubits required for high-accuracy quantum simulations by an order of magnitude in the present work, enabling the simulation of larger, more industrially relevant molecules using NISQ devices. They are further systematically improvable as devices’ computational capacity continues to grow.

We investigate many-body localization in the chain of interacting spins with a transverse powerlaw interaction, J0/r α , and random on-site potentials, φi ∈ (−W/2, W/2), in the long-range limit, α < 3/2, which has been recently examined experimentally on trapped ions. The many-body localization threshold is characterized by the critical disordering, Wc, which separates localized (W > Wc) and chaotic (W < Wc) phases. Using the analysis of the instability of localized states with respect to resonant interactions complemented by numerical finite size scaling, we show that the critical disordering scales with the number of spins, N , as Wc ≈ [1.37J0/(4/3 − α)]N 4/3−α ln N for 0 < α ≤ 1, and as Wc ≈ [J0/(1 − 2α/3)]N 1−2α/3 ln 2/3 N for 1 < α < 3/2 while the transition width scales as σW ∝ Wc/N . We use this result to predict the spin long-term evolution for a very large number of spins (N = 50), inaccessible for exact diagonalization, and to suggest the rescaling of hopping interaction with the system size to attain the localization transition at finite disordering in the thermodynamic limit of infinite number of spins.

Transport of vibrational energy via linear alkyl molecular chains can occur efficiently and with a high speed. This study addresses the question of how such transport is changed if an amide group is incorporated in the middle of such chain. A set of four compounds, Amn-4, was synthesized such that an amide group is connected to two alkyl chains. The alkyl chain on one side of the amide, featuring 4, 7, 11, or 15 CH2 units, is terminated by an azido group, while the alkyl chain on another side is of fixed length with four methylene groups terminated with a methyl ester group. The energy transport in Amn-4 in CD3CN solution, measured by relaxation-assisted two-dimensional infrared spectroscopy, was initiated and recorded using various combinations of tags and reporters, which included N3 and CO stretching modes of the end groups and amide-I and amide-II modes at the amide. It was found that the transport initiated by the amide-I mode in the alkyl chain attached to CO side of the amide proceeds with a constant speed of 4.2 Å/ps, supported by the CH2 rocking band of the chain. The end group-to-end group energy transport times for compounds with uneven alkyl chain length fragments appears to be additive. The transport from either end group of the molecule started as ballistic transport. The passage through the amide was found to be governed by intramolecular vibrational relaxation steps. After it passed the amide group, the transport was found to occur with constant but different speeds, dependent on the passage direction. The transport toward the ester was found to occur with the speed of 4.2 Å/ps, similar to that for the amide-I mode initiation and supported by the CH2 rocking band. The transport toward the azido group occurred with the speed of 8.0 Å/ps, which matches the speed supported by the CC stretching band. The results suggest that, after the CO group initiation, the excess energy reaches the amide group ballistically, redistributes at the amide, and reforms a wavepacket, which propagates further with a high speed of 8 Å/ps. This observation opens opportunities of controlling the energy transport process in molecules by affecting the alien group via specific interactions, including hydrogen bonding.