Chemically Motivated Simulation Problems are Efficiently Solvable by a Quantum Computer

TL;DR

This work reframes quantum chemistry from a ground-state‑centric paradigm to a dynamics‑driven one, arguing that many chemically relevant quantities are amenable to polynomial‑size quantum circuits via efficient Hamiltonian dynamics rather than exact ground-state preparation. Central to the proposal is mergo‑association, a hierarchically staged, scattering-based method to construct molecular input states from atomic fragments with heralded success, embedded in an open‑system framework. The authors detail a concrete first‑quantized implementation, analyze the Landau‑Zener bounds governing success probabilities, and propose weak measurement oracles that preserve exchange symmetry while certifying reactions. They then outline how a broad suite of dynamical observables—reaction rates, correlation functions, spectra, and S‑matrix elements—can be measured using clock‑register encodings and Hadamard tests, highlighting potential quantum advantages in simulating time‑dependent chemical processes. The framework points to a scalable path toward quantum simulations of chemistry that leverage dynamics, open-system effects, and photonic couplings, with future work focusing on numerical benchmarks and broader modeling capabilities (thermostats, non‑BO dynamics, and non-Markovian baths).

Abstract

Simulating chemical systems is highly sought after and computationally challenging, as the number of degrees of freedom increases exponentially with the size of the system. Quantum computers have been proposed as a computational means to overcome this bottleneck , thanks to their capability of representing this amount of information efficiently. Most efforts so far have been centered around determining the ground states of chemical systems. However, hardness results and the lack of theoretical guarantees for efficient heuristics for initial-state generation shed doubt on the feasibility. Here, we propose a heuristically guided approach that is based on inherently efficient routines to solve chemical simulation problems, requiring quantum circuits of size scaling polynomially in relevant system parameters. If a set of assumptions can be satisfied, our approach finds good initial states for dynamics simulation by assembling them in a scattering tree. In particular, we investigate a scattering-based state preparation approach within the context of mergo-association. We discuss a variety of quantities of chemical interest that can be measured after the quantum simulation of a process, e.g., a reaction, following its corresponding initial state preparation.

Figures (6)

• Figure 1: Complexity of solving chemical problems. We target the set of computational problems, ChemPoly, consisting of problems within chemistry with polynomial complexity when solved on a quantum computer. These problems have unknown overlap with those that correspond to observables in a laboratory; the sets Lab and ChemPoly may also coincide.
• Figure 2: Computational framework. Our simulation framework can be separated into a state preparation procedure (“molecule factory”), the evolution of the reaction of interest, and a measurement step that extracts usable information. The molecule factory prepares a set of molecular input states for the reaction, which may resemble thermal or ground states. These states are produced in a tree-like fashion equipped with a weak measurement scheme to ensure that the target states are prepared with sufficient probability in a heralded way. A photonic field serves as a source of energy for reactions, and an external bath, either explicit or implicit, serves as an energy sink. Furthermore, we utilize external potentials in the spirit of optical tweezers tailored to the different Hamiltonians along the procedure to ensure sufficient success probability and to control positions in space.
• Figure 3: Procedure of a single scattering step. Evolution through the simulation channel $\mathcal{E}(\cdot)$ produces states overlapping successful and not successful spaces. To project the state onto one of these subspaces, a weak measurement is performed, yielding either success or failure. In the case of success, proceed and potentially apply another step of time evolution to ensure the state represents a natural state. If unsuccessful, perform an additional, possibly modified, time evolution, which again produces overlap in the successful subspace, then measure again. Repeat this until success, the expected number of repetitions scaling inversely in the lower bound $P$ on the success probability per step. Success can be quantified by a weak measurement of an observable ${\mathbb O}_\text{suc}$ that, e.g., signifies the success of forming a bond by capturing spatial proximity.
• Figure 4: Scheduling of interactions. Inter-species interaction is described by $f(s)$ so that $f(0)=0, f(s\ge s_0)=1$ and is monotonically increasing until $s_0$ and then constant. The harmonic trap follows $g(s)$ with $g(0)=0, g(s_0)=1, g(s_1)=0$. It is monotonically increasing until $s_0$ and then decreasing until $s_1$. Following adiabatic evolution, there is a 'point of contact' of states at $s^*$ a little earlier than $s_0$, which is the evolution parameter (with corresponding effective distance) used to evaluate the diabatic transition probability. Here, we assume the scenario that the constituents are already placed at closed distance and we 'slowly turn on' the Coulomb interaction, where with the trajectory of $f(s)$, we aim to mimick an evolution of interaction strength that is Coulomb-like if they were to approach each other. To that end, let $z_{0,1},z_{0,2}$ be the centers of the traps. Then, in order to follow $V^{\rm int}(R_1(s), R_2(s)) = \frac{q_1 q_2}{\left| \Delta R_{12}(s)\right|}$ with nuclear charge $q_j$, let the implemented interaction be $V^{\rm int}(s)=f(s)H_{AB} = f(s) \frac{q_1 q_2}{\left| z_{0,1}-z_{0,2}\right|}$ where via $f(s)= \frac{|z_{0,1}-z_{0,2}|}{|\Delta R_{12}(s)|}$, the desired motion of the nuclei can be emulated. Towards $s \to s_0$, the fixed-strength potential assuming trap centers needs to be replaced by the actual strengths to account for fluctuations in the positions which will matter at that stage.
• Figure 5: Classifying chemical problems related to their hardness and space complexity. Dynamical properties are quantumly efficient, whereas static properties are generally hard. As quantum computers do not suffer from the curse of dimensionality, one can expect the sweet spot of quantum simulations, up to constant factors in the cost, to lie in the evaluation of dynamic properties.