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In the quest to accurately simulate the behavior of chemical entities, quantum computers are expected to offer a significant advantage over their classical counterparts. But to that end, algorithms and the hardware architectures themselves need to be tailored to the specific task at hand. In a collaboration with a co-author affiliated with both Forschungszentrum Juelich and RWTH Aachen University, our team at IBM Research-Zurich now lays out how exchange-type two-qubit gates constitute a very promising avenue to calculate molecular properties.

*A new hardware based on transmon qubits linked together by a tunable coupler for solving efficiently quantum chemistry problems, in this case a hydrogen molecule. Credit: Simon Hoenl.*

Breakthroughs in materials science are among the main drivers of technological change in the modern world. Understanding the inner workings of the molecules making up those materials is key to designing better drugs, healthier foods or more energy-efficient batteries, to name a few examples. Although the quantum mechanical equations governing the behavior of molecular entities have been known for many decades, solving them still represents a serious challenge even for our best current computers.

With the advent of quantum computing, the solution to this challenge could be within grasp. The very fact that quantum computers rely on manipulating the quantum states of their smallest units, known as qubits, makes them naturally better suited to simulate quantum mechanical systems like molecules.

But with near-term, noisy quantum computers, the approaches put forward so far to simulate large, complex molecules lack the efficiency needed for a successful implementation. The problem resides in the relatively long circuit depth of previous quantum algorithms, meaning that the computations take longer than allowed by the limited coherence time of the available qubits. Shortening the circuit depth by using quantum gates specifically tailored to the task at hand would mitigate those hardware imperfections. And that’s exactly what our team has achieved.

**A shorter path to deciphering the energy spectra of molecules**

In “Gate-Efficient Simulation of Molecular Eigenstates on a Quantum Computer“, published in the peer-reviewed journal Physical Review Applied, we propose and experimentally demonstrate a gate-efficient method to compute the eigenstate energies of molecules using superconducting qubit hardware and Qiskit Aqua that allows us to reduce the length of relevant algorithms by up to an order of magnitude. That improvement is roughly equivalent to increasing the coherence time of the qubits by the same factor.

Our approach is based on exchange-type quantum gates which we implement using a tunable-coupler architecture. Exchange-type gates have the property of preserving the number of excitations (number of qubits in the excited state ‘1’ as opposed to the ground state ‘0’). This feature, in turn, can be used to map onto the quantum hardware the fact that molecular systems conserve the number of electrons. The ability to naturally mirror this constraint of molecular systems is a key reason behind the greater efficiency of our architecture compared to previous schemes.

While exchange-type gates had been proposed before, our work represents the first time such gates are made tunable in both amplitude and phase. In our experimental implementation, each exchange-type gate comprises two fixed-frequency (transmon) qubits linked together by a tunable coupler. By modulating the frequency of the coupler through an external magnetic field, the excitations can be switched from one qubit to the other much like an electron jumping between molecular orbitals.

**Computing the spectrum of hydrogen**

In order to show how this architecture can be used to study the energy spectra of molecules, we compute the ground state and three excited states of molecular hydrogen using a hybrid, classical-quantum algorithm. To calculate the ground state, we resorted to the variational quantum eigensolver (VQE) algorithm. Once the ground state is known, we derived the three excited states by means of an equation-of-motion (EOM) approach. The accuracy of the calculations is primarily affected by the relatively short coherence time (20 nanoseconds) of the tunable coupler. Our analysis leads us to conclude that increasing the coherence time of the tunable coupler to around 500 nanoseconds would enable our architecture to reach chemical accuracy, the gold standard in quantum chemistry, for the hydrogen molecule.

Our research demonstrates a gate-efficient way to simulate molecular spectra on a tailor-made superconducting qubit processor using exchange-type two-qubit gates. By choosing excitation-preserving exchange-type gates, tunable in both amplitude and phase, we are able to efficiently computate the molecular ground state, which is subsequently used to efficiently calculate the molecule’s excited states. In the present case, the accuracy of the computation is still limited by the coherence time of the tunable coupling element. However, error mitigation schemes or minor improvements to the coherence of the coupler will allow us to reach chemical accuracy. Our findings show that adapting quantum algorithms and hardware to the problem at hand is a key requirement to perform quantum simulation on a larger scale. In particular, exchange-type gates are a promising choice to compute the energy spectra of larger molecules like water on near-term quantum hardware.