Quantum Algorithms for Photoreactivity in Cancer-Targeted Photosensitizers

TL;DR

Problem: improving PDT efficacy requires photosensitizers with strong near-IR absorption and high ISC rates, which are challenging to model classically. Approach: the authors develop fault-tolerant quantum algorithms—threshold projection via quantum signal processing for cumulative absorption, and an evolution-proxy method for ISC—applied to BODIPY derivatives with solvent embedding; a vibronic extension is discussed for strong vibronic coupling. Contributions: concrete end-to-end algorithms with explicit resource estimates across active spaces up to 45 spatial orbitals, demonstration on four BODIPY derivatives, and a pathway toward realistic fault-tolerant quantum workflows for PDT design. Significance: this work suggests quantum simulations can feasibly screen and optimize photosensitizers beyond classical capabilities, potentially accelerating the development of next-generation PDT agents and guiding future incorporation of Type I pathways and biologically realistic environments.

Abstract

Photodynamic therapy (PDT) is a targeted cancer treatment that uses light-activated photosensitizers to generate reactive oxygen species that selectively destroy tumor cells, generally causing less collateral damage than conventional treatments. However, its clinical success hinges on the availability of photosensitizers with strong optical sensitivity and high efficiency in generating reactive oxygen species. While classical computational methods have provided useful insights into photosensitizer design, they struggle to scale and often lack the accuracy needed for these simulations. In this work, we show how fault-tolerant quantum algorithms can be used to identify promising photosensitizer candidates for PDT. To predict photosensitizer performance, we assess two computational properties. First, we quantify light sensitivity by calculating the cumulative absorption in the therapeutic window with a threshold projection algorithm. Second, we determine the efficiency of reactive oxygen generation by estimating intersystem crossing (ISC) rates using the evolution-proxy approach, complemented by a vibronic dynamic treatment where appropriate. We apply these algorithms to a clinically relevant and actively pursued class of photosensitizers, BODIPY derivatives, including heavy-atom and transition-metal-substituted systems that are challenging for classical methods. Our resource estimates, obtained with PennyLane, suggest that systems with active spaces ranging from 11 to 45 spatial orbitals can be simulated using $180$-$350$ logical qubits and Toffoli gate depths between $10^7$ and $10^9$, placing our algorithms within reach of realistic fault-tolerant quantum devices. This paves the way to an efficient quantum-based workflow for designing photosensitizers that can accelerate the discovery of new PDT agents.

Figures (9)

• Figure 1: Workflow for quantum-guided photosensitizer design. Left (Hamiltonian): Select a chemically motivated active space and construct an effective Hamiltonian $H_\mathrm{eff}$ using low-rank factorization with solvent embedding. Center left (Target observables): Identify two key quantities that determine photosensitizer performance: (i) cumulative absorption within the therapeutic window ($700\text{--}850$ nm), which controls light penetration, and (ii) the intersystem crossing (ISC) rate, which governs population transfer into the reactive triplet manifold. Center right (Quantum simulations): Apply two quantum algorithms: (i) threshold projection (\ref{['ssec:TP_algo']}) to compute cumulative absorption within the therapeutic window; (ii) the evolution–proxy algorithm (\ref{['ssec:ISC_evo_proxy_algo']}) to rank candidates by their relative ISC rates ($\tilde{k}_{\text{ISC}}$), estimated from early-time singlet–triplet population transfer. Right (Guided drug design): Simulated observables guide molecular edits that red-shift absorption and enhance triplet yield and ISC rate, thereby increasing the efficacy of light-induced cancer therapy.
• Figure 2: Photophysical processes underlying the PDT application studied in this work. ① Upon absorbing a photon $h\nu$, the photosensitizer is promoted from its singlet ground state (with quantum numbers $n = 0; \ S = 0$) to excited singlet states (with $n = 1,...; \ S = 0$). ② The excited-state population may undergo intersystem crossing, a spin-forbidden transition, to the triplet manifold (with $S = 1$), typically to the lowest triplet state. ③ Photosensitizer in its triplet excited state can subsequently transfer energy to ground state oxygen $^3\text{O}_2$, converting it into singlet oxygen $^1\text{O}_2$, a reactive oxygen species (ROS) that drives local oxidative damage in cells. ④ Excited photosensitizer triggers an electron transfer to nearby oxygen, forming superoxide radicals $^{.}O_2^{-}$ as Type I ROS. ⑤ Vibrational relaxation occurs as a fast, nonradiative process within a given electronic manifold, dissipating excess vibrational energy and allowing the system to settle into its vibrational ground level before undergoing fluorescence, phosphorescence, or ISC.
• Figure 3: Assume $\bm{D}\ket{E_0}$ has support over the energy interval $[E_{\min}, E_{\max}]$, and we aim to project it into a narrower therapeutic energy window $[E_\text{lo}, E_\text{hi}]$. This can be achieved using a threshold projection approach: one projection from the left into $[E_{\min}, E_\text{hi}]$, and another from the right into $[E_\text{lo}, E_{\max}]$. In the Trotter setting (see \ref{['app:TP_w_trotter']}, the arc segments (blue and orange for (a), green and purple for (b)) are padded to equal lengths for symmetry. In qubitization, no padding is needed, the arcs are defined directly via the $\arccos(E/\lambda)$ map. With this construction, a single qubit measurement suffices to determine whether the state lies inside or outside the target energy window. This approach relies on an appropriate shifting of the Hamiltonian to position the threshold at 0.
• Figure 4: High-level threshold projection circuit for determining whether an excitation energy lies within the therapeutic window $[E_\text{lo},E_\text{hi}]$. The system register $\ket{\psi}=\hat{D}\ket{E_0}$ is prepared via PREP and entangled with single-ancilla projectors, which implement the conditions $E \leq E_\text{hi}$ (upper boundary) and $E \geq E_\text{lo}$ (lower boundary). Each ancilla undergoes a one-bit sign test using a sequence of controlled and uncontrolled walk operators. A Toffoli gate writes the logical AND of the left and right projection ancillas, $\ket{0}_\text{L}$ and $\ket{0}_\text{R}$, into a joint ancilla initialized to $\ket{0}$. This ancilla is then measured in the computational basis; the outcome is $1$ if and only if both tests pass (in-window), and $0$ otherwise. Additionally, afterward we apply PREP$^\dagger$ to the QSP output state and projected into $\ket{0}$, yielding a second independent measurement loaiza2025simulating. Together, these two readouts provide a $2$-fold reduction in sampling cost, as shown in \ref{['eq:outer_repetition_2']}. A detailed implementation of QSP is presented in \ref{['fig:QSP_double_phase_walk']}.
• Figure 5: The breakdown of the generalized QSP circuit used in \ref{['fig:algo_circs_dual_projection']} to evaluate the matrix element \ref{['eq:cumulative_absorption_sum']}. The bulk of the circuit represents the implementation via quantum signal processing of a threshold function that probabilistically projects into the therapeutic window. The threshold function comprises the product of two Heaviside functions of the form $1/2 + \text{sign}(H-E_{\text{th}})/2$. To reduce the cost as much as possible, we leverage generalized quantum signal processing motlagh2024generalized. As a further optimization, the application of $W$ or $W^\dagger$ are implemented sandwitching each $W$ by controlled reflections $\mathcal{R}$, see \ref{['eq:walk_identity']}babbush2018encoding. This can be combined with generalized QSP to halve the cost of QSP berry2024doubling.