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A perspective on the current state-of-the-art of quantum computing for drug discovery applications
Nick S. Blunt, Joan Camps, Ophelia Crawford, Róbert Izsák, Sebastian Leontica, Arjun Mirani, Alexandra E. Moylett, Sam A. Scivier, Christoph Sünderhauf, Patrick Schopf, Jacob M. Taylor, Nicole Holzmann
TL;DR
Classical electronic-structure calculations become intractable for chemically relevant systems beyond roughly 30 electrons, motivating quantum approaches for pharmaceutical chemistry. This perspective compares quantum algorithms and estimates error-corrected resources for Ibrutinib–protein simulations, finding that a (42e,42o) calculation could take over 1000 years with Trotterisation but around 7.6 days with qubitisation. The results frame algorithmic improvements as transformative for the potential of non-trivial quantum phase estimation calculations, while those calculations remain intractable at the present stage.
Problem
Chemically relevant electronic-structure problems become intractable beyond approximately 30 electrons, despite the desirability of exact or nearly exact quantum-mechanical solutions.
Method
The perspective compares quantum-algorithm scaling and estimates error-corrected quantum resources for quantum phase estimation applied to active spaces in an Ibrutinib protein-drug system.
Results
Over 1000 years with Trotterisation is reduced to around 7.6 days with qubitisation for ground-state energy estimation in a (42e,42o) active space.
Takeaways & Limitations
Algorithmic improvements reduce quantum-computing costs by several orders of magnitude and expand the potential for non-trivial quantum phase estimation calculations.
Takeaways & Limitations
The estimates require sufficiently large error-corrected quantum computers, and non-trivial quantum phase estimation calculations remain intractable at the present stage.
Abstract
from arXiv · showhide
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 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 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 Trotterisation approach to just a few days with sparse qubitisation, painting a picture of fast and exciting progress in this nascent field.
1 Introduction
Quantum computing may extend pharmaceutical quantum chemistry beyond classically tractable limits, but useful drug-design calculations require fault-tolerant, error-corrected hardware. This perspective compares quantum algorithms and estimates resources for progressively larger active spaces in an Ibrutinib–protein complex.
- Motivation: Chemically relevant electronic-structure problems become intractable classically for more than approximately 30 electrons, motivating quantum methods for exact or nearly exact solutions.Accurate quantum methods are presented as potentially useful for pharmaceutical research, where current drug-design methods rely mainly on statistical fitting or classical mechanics.
- Hardware progress: Quantum hardware progress includes error-correction experiments that suppress errors and keep a logical qubit operational across superconducting, trapped-ion, and diamond platforms.These results are described as groundwork for large-scale fault-tolerant quantum computation.
- Scope and approach: The perspective focuses on large complete-active-space configuration-interaction calculations enabled by near-future quantum computers.It frames these calculations as a possible disruption for pharmaceutical applications.
- Scope and approach: The authors illustrate the workflow with covalently bound Ibrutinib and Bruton’s tyrosine kinase, estimating resources for progressively larger binding-pocket clusters.The workflow covers quantum-memory mapping, algorithm selection, and an error-corrected architecture.
- Main result: Quantum algorithmic advances reduce estimated runtimes for fully quantum calculations in active spaces of around 50 orbitals to a few days on sufficiently large error-corrected computers.The paper attributes this progress to developments over the preceding five years.
- Algorithm comparison: Quantum phase estimation scales more favorably than the variational quantum eigensolver, so the remainder of the paper focuses on phase estimation.The paper compares the scaling of these two algorithms and examines Trotterisation and qubitisation for constructing the required unitary operators.
2 Chemistry on a quantum computer
Quantum chemistry maps molecular interactions to an electronic Hamiltonian, but accurate solutions remain difficult because exact methods scale exponentially with system size. Quantum computers are considered promising for active spaces and industrially relevant chemical problems where classical approximations remain limited.
- Electronic structure problem: 128? Exact first-principles equations are insoluble beyond the simplest cases, motivating efficient approximate quantum-chemistry methods.The passage attributes this difficulty to the resulting equations of quantum mechanics and special relativity.
- Electronic structure problem: The electronic Hamiltonian encodes electron kinetic energy and electron–electron, nuclear–electron, and nuclear–nuclear interactions.Its eigensolutions represent possible electronic states and their total energies.
- Classical approximations: Hartree–Fock is computationally tractable for molecules containing several hundred atoms but does not account for electron-correlation effects.This limitation motivates correlated methods and active-space treatments for strongly correlated systems.
- Classical approximations: Full configuration interaction provides the exact solution in a basis but scales exponentially with the number of electrons and orbitals.Polynomially scaling alternatives such as CCSD use less expensive wavefunction ansätze, while CASCI restricts the configuration-interaction solution to an active space.
- Motivation for quantum computing: Strongly correlated systems remain challenging because correctly describing them can require active spaces beyond the reach of classical quantum chemistry.The paper identifies this active-space bottleneck as an area where quantum computers may provide a breakthrough.
- Motivation for quantum computing: The perspective estimates quantum resources for a protein–drug system involving interactions such as weak hydrogen bonds and uses quantum phase estimation for pharmaceutically relevant calculations.Quantum benefit is framed as outperforming classical computers in an industrially relevant process, including obtaining better-than-DFT results at reasonable cost.
3 Algorithm choices
The paper compares VQE and QPE through scaling estimates and focuses on QPE for resource estimation. VQE resource requirements depend on ansatz depth, parameter optimization, Hamiltonian measurements, repetitions, and accuracy, while several assumptions limit the estimates.
- Algorithm choices: The analysis compares the scaling properties and resource requirements of variational quantum eigensolver and quantum phase estimation calculations.The paper presents resource-estimation calculations and then motivates its focus on QPE.
- VQE: UCCSD is the fixed chemically inspired ansatz used for VQE resource estimates, with parameters optimized during the VQE process.Its operators include single and double electron excitations from a Hartree–Fock state.
- VQE limitations: For strongly correlated systems, UCCSD may fail to prepare a state sufficiently close to the ground state because its excitations are limited.Alternative ansätze may reduce parameters or gate depth, but their behavior for larger chemical systems is difficult to predict.
- VQE resource estimates: The number of Hamiltonian expectations required by VQE is difficult to know in advance, and typical calculations require more evaluations than the favorable estimate assumes.The estimate assumes one evaluation per parameter direction, while measurement-reduction methods can lower the number of required measurements.
- Comparison and discussion: QPE becomes preferable once the chemical system is sufficiently large, although the crossover depends on the constant preceding the scaling.The paper uses this comparison to motivate choosing QPE for the remainder of the work.
- Comparison and discussion: The scaling analysis is not definitive because VQE improvements remain possible, and its estimates rely on assumptions that may not hold generally.The authors explicitly acknowledge that the analysis does not exhaust possible improvements to VQE.
4 Implementing error corrected quantum algorithms
Large-scale quantum algorithms require quantum error correction because useful circuits may contain over 10^10 logical gates. The section describes the surface-code architecture, magic-state distillation, and routing of distilled states to data qubits.
- Quantum error correction: Over 10^10 logical gates may make uncorrected execution impractical, so quantum error correction is required for large-scale applications.Gate errors would need to be unrealistically small for the full circuit to run without error.
- Quantum error correction: 2d^2 physical qubits represent each logical qubit in the surface-code accounting used here.The code uses a d × d grid plus d^2 syndrome qubits for stabiliser measurements.
- Quantum error correction: 1% is the surface-code error threshold below which increasing d decreases the logical-qubit error rate.The logical error probability is approximately 0.1(100p)^((d+1)/2) per logical operation.
- Magic-state factories: 225-to-1 distillation concatenates eleven 15-to-1 factories with a second 15-to-1 factory, producing failure probability 1500625p^9 in 15 time steps.The construction uses substantially more magic states and logical qubits than a single factory.
- QPU architecture: A fast-block architecture arranges data qubits and auxiliary qubits in a 2D grid so any data qubit can consume one magic state within one time step.Factories are arranged around the data block while unused logical qubits are minimised.
5 Trotterisation vs Qubitisation
Hamiltonian simulation approximates quantum time evolution while balancing accuracy against circuit cost. The section compares empirical Trotterisation with qubitisation-based methods and finds a major runtime advantage for the latter.
- Trotterisation: τ → 0 reduces Trotter error, but implementation cost increases as τ decreases.The method therefore requires a resource–accuracy trade-off when choosing the time-step size.
- Trotterisation: a = 1.51 ± 0.84 and b = −4.66 ± 0.27 parameterise the empirical Trotter-error law fitted across small molecules.The fit models the ground-state energy difference between the original and Trotterised operators as a function of molecule size.
- Qubitisation: Around 10^10 T gates with projected runtimes of a few days are achieved by modern qubitisation and linear-combination-of-unitaries methods.These methods implement a walk operator whose energies can be retrieved through quantum phase estimation.
- Qubitisation: ∼90% fewer Hamiltonian terms can result from sparse truncation, lowering the implementation cost of the walk operator.The sparse method applies the LCU decomposition to a truncated Hamiltonian under an allocated error budget.
6 Drug Design Methods and the Model System
Drug-design calculations require accurate treatment of protein–ligand interactions, but classical force fields and quantum-mechanical methods each have important scope limits. The paper therefore uses an embedded QM-cluster model of the covalent Ibrutinib–BTK system for resource estimation.
- Drug-design methods: Classical force fields omit or inadequately describe electronic effects such as polarisation, charge transfer, aromatic stacking, metal interactions, and covalent bond breaking.These limitations motivate higher-level quantum-mechanical treatment for selected drug-design problems.
- Drug-design methods: Routine steeply scaling quantum-mechanical methods remain mainly limited to small-molecule properties and conformations.Semiempirical methods reduce cost but are often less accurate than fully quantum-mechanical methods.
- Embedding methods: QM/MM and QM-cluster approaches generally remain restricted to a few hundred atoms, limiting treatment of allosteric and other large-scale mechanisms.Both approaches use a smaller high-level region embedded within a broader molecular environment.
- The model system: The QM-cluster size is selected from residues, ligand groups, water molecules, and ions contributing to binding or mechanism.The study estimates resources for progressively larger regions of the binding pocket and Ibrutinib cluster.
- The model system: The model system is Ibrutinib covalently bound to cysteine 481 of Bruton’s tyrosine kinase through a Michael addition reaction.Ibrutinib inhibits BTK and was approved for treatment of non-Hodgkin lymphoma in 2015.
7 Results
Resource estimates compare QPE with sparse qubitisation and Trotterisation across progressively larger active spaces, showing substantially more favourable runtimes for qubitisation. For sparse qubitisation, estimated runtimes range from hours for (14e,14o) to years for (100e,100o), while Trotterisation is far more expensive for comparable active spaces.
- Sparse qubitisation runtimes: 1.3 or 3.0 hours are estimated for sparse-qubitisation QPE on (14e,14o), using p = 10−4 or p = 10−3, respectively.The estimates use the CCSD(T) truncation criterion.
- Sparse qubitisation runtimes: 1.3 and 2.6 years are estimated for (100e,100o) sparse-qubitisation QPE at p = 10−4 and p = 10−3, respectively.Across the considered active spaces, runtime follows an approximate power law in the number of spatial orbitals, with exponent 4.6.
- Hamiltonian truncation: The CCSD(T) truncation criterion removes more Hamiltonian terms than the L2-norm criterion, producing fewer T gates while targeting truncation error of 0.3 mHa or less.For the studied active spaces, the estimated T-gate counts between the two qubitisation approaches are typically within a factor of 1.2 to 2.0.
- QPE algorithm comparison: The Trotterised approach has dramatically higher runtime and steeper scaling than sparse qubitisation; (32e,32o) takes 1.9 days with qubitisation but roughly 250 years with Trotterisation.The comparison uses textbook QPE with Trotterisation and no Hamiltonian truncation versus truncated sparse qubitisation.
- QPU resource trade-offs: Trotterisation also increases total physical-qubit requirements because its higher T-gate count necessitates larger surface-code distances and large magic-state factories.Although qubitisation has a substantial data-qubit overhead, the overall physical-qubit count is increased for Trotterisation in the comparison.
- Error correction: For (32e,32o) qubitisation, increasing p from 10−4 to 10−3 raises the code distance from d = 15 to d = 32, whereas changing QPE approaches at fixed p raises it from d = 15 to d = 20.The code distance is more sensitive to physical error rate than to the T-gate count in this example.
8 Conclusions
The paper estimates quantum resources for pharmaceutical quantum chemistry and finds that algorithmic advances can reduce runtimes by orders of magnitude. Practical use still requires fault-tolerant hardware, improved error correction, balanced embedding, and further algorithmic development.
- Resource estimates: The study estimates QPE resources for several active spaces in the Ibrutinib protein-drug system using Trotterisation and qubitisation.The two approaches use the full and truncated Hamiltonians, respectively.
- Resource estimates: Over 1000 years for a (42e,42o) active space with Trotterisation falls to around 7.6 days with sparse qubitisation.The estimate assumes a physical error rate of 0.01% and a 1 µs code cycle duration.
- Implications: Algorithmic improvements can reduce quantum-computing costs by several orders of magnitude and substantially change the potential of quantum computers.The paper identifies these reductions as transformative for quantum-computing capability.
- Remaining challenges: A (100e,100o) active space is still estimated to require over a year, showing that larger calculations remain costly.The authors therefore emphasize the importance of further algorithmic improvements.
- Remaining challenges: Current quantum computers have too few qubits for the resource estimates, and practical scaling remains distant because error rates must fall further.The paper notes that present systems remain some way from non-trivial QPE calculations.
- Pharmaceutical application: Quantum calculations require accurate treatment of the quantum region together with a balanced environment treatment and appropriate embedding.Otherwise, errors from the environment may overwhelm the potential improvements from quantum computation.
A Number of repetitions of QPE
The appendix specifies how many QPE repetitions to perform and how to combine their outcomes into an energy estimate with target accuracy and success probability. It uses a median of the lowest measurement outcomes to reduce outlier effects while accounting for state overlap and error-correction failure.
- Repetition and estimation: The repetition parameters are chosen to achieve the desired energy accuracy and overall success probability.The method selects the smallest l and corresponding k for which the median estimate reaches the specified success probability.
- Repetition and estimation: The procedure repeats QPE l times and takes the median of the lowest k outcomes to obtain the final energy estimate.The values of l and k depend on the chemical system and calculation, and the median reduces outlier effects.
- Probability model: The analysis incorporates QPE precision, initial-state overlap η, and the single-run error-correction failure probability Pf.Pf includes undetected magic-state-distillation errors or logical errors during phase estimation.
- Probability model: The probability model assumes excited-state measurements fall above the desired range, successful ground-state measurements fall within it with probability P0, and other outcomes fall below it.These assumptions determine how individual QPE outcomes contribute to the final estimate.
- Parameter choice: Choosing k from an estimated η does not guarantee higher overall success when the true η is larger, so l and/or k may need to increase.The appendix deliberately uses a conservative repetition choice to avoid underestimating the required number of repetitions.
A.1 QPE probabilities
This appendix analyzes the probability that QPE returns an eigenvalue estimate within a target distance of the true eigenvalue. It represents eigenvalues in binary form, derives the relevant probability expression, and examines how the probability changes with the precision parameter m.
- Precision target: The target estimation error is ϵ = 2^-t, corresponding to estimating the eigenvalue to t bits of precision.The appendix defines the probability of an estimate lying within this distance of the true eigenvalue.
- Eigenvalue representation: Each eigenvalue Ej is represented as a binary expansion with coefficients φjp ∈ {0,1} and residual 0 ≤ δj < 1.This representation supports the subsequent analysis of the probability distribution over QPE estimates.
- Probability analysis: The analysis defines pl as the probability of obtaining the desired eigenvalue index when that eigenvalue is measured.The probability is then used to calculate the chance that the estimate lies within the target distance.
- Probability analysis: The derived probability is a decreasing function of m, and its limiting behavior is examined as m approaches infinity.For larger values, the appendix proposes replacing an exponentially long sum with a bound that avoids the sum.
- Probability expression: The QPE probability expression is evaluated for an eigenvalue estimate whose precision is controlled by the number of measured bits.The appendix explicitly relates the desired distance 2^-t to the number of precision bits.