Perspective on the Current State-of-the-Art of Quantum Computing for Drug Discovery Applications

Abstract

Computational chemistry is an essential tool in the pharmaceutical industry. Quantum computing is a fast evolving technology that promises to completely shift the computational capabilities in many areas of chemical research by bringing into reach currently impossible calculations. This perspective illustrates the near-future applicability of quantum computation of molecules to pharmaceutical problems. We briefly summarize and compare the scaling properties of state-of-the-art quantum algorithms and provide novel estimates of the quantum computational cost of simulating progressively larger embedding regions of a pharmaceutically relevant covalent protein-drug complex involving the drug Ibrutinib. Carrying out these calculations requires an error-corrected quantum architecture that we describe. Our estimates showcase that recent developments on quantum phase estimation algorithms have dramatically reduced the quantum resources needed to run fully quantum calculations in active spaces of around 50 orbitals and electrons, from estimated over 1000 years using the Trotterization approach to just a few days with sparse qubitization, painting a picture of fast and exciting progress in this nascent field.

Figure 1

Outline of the VQE algorithm, indicating which parts occur on the quantum computer and which parts on the classical.

Figure 2

Outline of the circuit used to perform QPE, as discussed in ref (61).

Figure 3

(a) Layouts for 15-to-1 (top) and 20-to-4 (bottom) magic-state factories. These consist of 11 and 14 logical qubits, respectively (green). The magic states produced are stored in the blue spaces. (b) Factory which distills 225 imperfect magic states to one higher quality magic state. Eleven first-level 15-to-1 factories (green) are used to produce 15 refined magic states, which are in turn used by the second-level 15-to-1 factory (orange) to produce one magic state of even higher quality (red). Blue lines are used to store and transport lower-quality magic states. White spaces are unused logical qubits.

Figure 4

Fit of empirical law for our set of molecules. The fit is done in two steps. In the first step (left), for each of the molecules, we generate δE₀ for τ/τ_max = [1.0, 0.5, 0.1, 0.05, 0.01, 0.005, 0.001] and do a one-parameter fit of . Note that, for larger molecules, ϵ₀ for small values of τ appear to deviate from the quadratic behavior. We attribute this to numerical error and exclude these values from the fits. In the second step (right), we plot a₁ for each molecule and fit a₁ = a(n_q)^b, obtaining the parameters of the empirical law in eq 38: a = 1.51 ± 0.84; b = −4.66 ± 0.27.

Figure 5

Cluster containing part of the binding pocket and the Ibrutinib inhibitor. The various fragments in which the active space orbitals were selected are indicated using various colors.

Figure 6

Runtime to perform QPE using sparse qubitization. Active spaces from (14e,14o) to (100e,100o) are considered. It is assumed that one time step takes 1 μs to perform. Physical error rates, p, of 0.01 and 0.1% are considered. The Hamiltonian is either truncated using an L₂-norm criterion or a CCSD(T) criterion. In each case, the runtime scales as approximately n_o^4.6 with the number of active orbitals.

Figure 7

Comparison of resources (runtime and total number of physical qubits) using two QPE algorithms. The first (orange) used qubitization, and the Hamiltonian was truncated to remove small terms up to an error budget. The second (green) used textbook QPE with Trotterization and no truncation of the Hamiltonian. The latter algorithm has a much steeper scaling in runtime. Even for a (14e,14o) active space the runtime is multiple orders of magnitude more expensive.

Figure 8

QPU layouts used to perform QPE experiments on the (32e,32o) active space example. Left: layout used for QPE with Trotterization. Right: Layout used for QPE with qubitization. Data block qubits are orange, magic-state factory qubits are green, and routing and storage qubits are blue. Qubitization uses many more data qubits such that the data block is much larger. However, the higher T-gate count in QPE with Trotterization necessitates larger magic-state factories (225-to-1) compared to those in qubitization (116-to-12). Axes are included to indicate the total number of logical qubits in both layouts, with each logical qubit having size 1-by-1. However, note that the code distance is higher in QPE with Trotterization (see Table 2) so that these are not to physical scale.