Quantum computing solves biodiversity.

Ecologists rapidly adopt new techniques and technologies to improve our understanding of the natural world. Two decades ago, Schneider [1] documented the rise of mathematically based theories, computer-supported models, and quantitative methods to explain ecologically complex relationships that were replacing more descriptive approaches. This trajectory has continued, with quantitative ecology firmly entrenched as fundamental to the modern discipline [2]. We believe that the application of quantum computing (see Glossary) will drive the next paradigm shift for numerical ecology. Quantum computing has the potential to enable increased accuracy and precision of complex ecological models and outperform classical computers in solving complex problems [3].

Conventional (classical) computational capability has increased significantly according to Moore’s law [4], enabling more complex statistical and mathematical approaches. As an example, 50 years ago Hastings [5] described the computational challenges of sampling from high-dimensional probability distributions using Monte Carlo methods. At the time, Hastings was pressing the boundaries of both statistical methodology and the capability limits of classical computing. Fast forward to today, quantum computing has the potential to overcome computational bottlenecks associated with optimisation, machine learning and simulations, and enable the development of a new suite of algorithms to better understand the natural world. Here, we explore the role quantum computing may have in ecology.

Basis of quantum computing

Quantum computers exploit the properties of quantum mechanics [6], generally using an encoding in quantum binary objects – qubits. Two key principles of quantum computing are superposition and entanglement. Superposition is where a quantum object is in a linear combination of states (binary states in the case of a qubit), but when observed the system collapses into a single binary state (Figure 1) according to a probability distribution determined by the complex amplitudes in the superposition itself (see [7] for an extreme case of a virus-superposition proposal). Entanglement is a property of a quantum system comprising two or more qubits where the measurement outcome of one part of the state is correlated to the outcome of the previous measurement of another part of the state [8]. In a quantum computer of n-qubits, with each qubit accessing two states f g j0 , j1 , superposition and entanglement over the full set of 2n binary combinations can be created through quantum-logic operations enabling the quantum computer to approach problems in a completely different way compared with the classical computing system, which can only operate on a single binary state in any one logical step.

In the past decade, multi-qubit systems have been developed in a rapid and accessible wayi [9,10]. In the next decade, it is predicted that the quantum computers will be solving problems that continue to challenge classical computing, leading to new discoveries across multiple disciplinesi [11]. We propose that this should also include ecology.

Let’s not focus on the hardware

Much of the global research effort in quantum computing is directed towards hardware development. Current hardware candidates include superconductors, ion traps, photonics, quantum dots, and cold atoms [11]. These different hardware approaches all exploit the same quantum mechanics, each with their different strengths and weaknesses, but the common feature of the candidates is the control of the quantum state (Figure 1). The race is on to increase the number of qubits and reduce the level of uncertainty or quantum noise in the logic operations [12]. Arute and colleagues [9] demonstrated quantum supremacy, where a quantum processor (Google’s 53 qubit Sycamore quantum computer using a superconductor-qubit platform) obtained output probability distributions for random programmes faster than a classical computer could simulate. This result was broadened to quantum advantage by Zhong et al. [10] for the Gaussian Boson Sampling problem using a photonic quantum computer where the equivalent task on the Fugaku supercomputer was estimated to require 600 million years. This means that the transition where quantum computers can do things that classical computers may struggle to do may be upon us sooner than previously anticipated. Quantum hardware developments are rapid. IBM have so far followed their predicted hardware trajectory with a 127-qubit quantum computer deployed in 2021, and a 433-qubit system announced in 2022i . In the near term, the number of qubits is expected to rise, and Noisy Intermediate Scale Quantum (NISQ) technologies are expected to improve the control of the qubits and therefore reduce the errors in the logical processing of information encoded in quantum states [12]. In the long term, a high level of redundancy over millions of qubits will provide strong suppression of errors in a fault-tolerant universal quantum computer. Whether quantum advantage is achieved in the near or long term, the transition between hardware development and testing quantum computing in a variety of research environments across broader scales and applications is upon us now.

It is important to note that most users of classical computers do not necessarily understand how the silicon technologies in computer chips work. Nonetheless, these silicon technologies have transformed the world [13]. A similar paradigm will exist for quantum hardware. Users will not necessarily need to understand quantum mechanics. Instead, they will need to understand how a quantum solution can solve a problem using the accessible hardware.

Potential applications

Potential applications of quantum computing in ecology can be demonstrated by focussing on statistical methodologies, which have already been used in quantum computing. Anderson and colleagues [2] examined eight decades of ecology and conservation data and observed that Monte Carlo, Markov Chain Monte Carlo (MCMC), least-squares, maximum likelihood, Akaike information criterion (AIC), and Bayesian statistical approaches were the most used statistical paradigms. Here, we focus on Monte Carlo, MCMC, AIC, and Bayesian statistical approaches, which are also being adapted in quantum applications in other scientific fields. At their heart, these statistical approaches cover probability, uncertainty, and stochasticity, which are principally observed in ecological systems. These are just a selection of approaches that are quantumready, which we believe could transition to ecological analyses. Undoubtedly there will be further advances by researchers who will adapt, develop, and apply new quantum techniques relevant for ecology such as data classification using quantum machine learning [14].

Monte Carlo and MCMC

Ecologists have long used Monte Carlo simulations as a method of modelling real phenomena [15]. The addition of MCMC approaches has improved sampling methods [5], which have then been used to make ecological Bayesian inference more workable [16]. Moreover, increases in computing power made Monte Carlo and MCMC methods more accessible and used more broadly in ecology [2].

Monte Carlo methods have long been associated with quantum mechanics. Monte Carlo simulations have been used on classical computers to solve Schrödinger’s equation for many interacting particles [17], termed Quantum Monte Carlo (QMC) [18]. Quantum computers are well suited to Monte Carlo methods, because the probability distribution in question can be encoded into a superposition state of the quantum computer enabling a projective measurement in a way that is predicted to be faster than traditional methods [19]. The ability to overcome slow, sequential sampling will be of interest to quantitative ecologists (Box 1). QMC is already being used in the physical sciences using quantum computers [20], but there is potential for it to be applied to ecology. Borrowing heavily on the lexicon of ecology, Cleland et al. [21] use the terms ‘survival of the fittest’ and ‘stochastic population dynamics’ which will resonate strongly with ecologists. We believe that quantum computing will enable ecologists to stretch what is possible with both Monte Carlo simulations and MCMC. Rapidly advancing the use of quantum computing in ecology will be enhanced by multidisciplined collaboration and a shared understanding of concepts.

Akaike information criterion

Burnham and Anderson [22] recognised how information criteria [23] could be used as an estimator of prediction error for hypotheses in a model set [24]. The AIC has since been widely used by ecologists as an information-theoretic alternative to more traditional statistical approaches such as analysis of variance (ANOVA) [25].

The ability to rank different models using AIC to estimate expected prediction error has proven applicability to quantum environments [25]. Indeed, Schwartz and van Enk [26] state that AIC will outperform the Bayesian information criterion in a quantum state. Our experience with AIC applications with classical computing and ecological data suggests the method tends to select overparameterised models, which is also observed in other disciplines [27]. Despite the promise of quantum computing approaches to speed up cross-validation of the models, we do suggest some caution. Ferrie [28] suggests that AIC is useful if ‘all future measurements will be the same as those used to perform the data analysis’, which may be difficult to satisfy.

Bayesian model averaging approaches

Bayesian data analysis is currently the most widely used statistical paradigm in ecology, rapidly rising in prominence in the 1990s [2]. The advantage of applying Bayes theorem is that it combines prior knowledge with sample data and treats model parameters as random variables [29]. The two standard approaches to Bayesian model averaging in quantitative ecology are: (i) fit separate models and then use Bayes factors as model weights, and (ii) treat the probabilities of each possible model as parameters to be estimated and consider all possible models using MCMC. The second approach is perhaps more useful and makes model-averaging coefficients easier. However, it is a computational intensive approach because the number of posterior samples needed scales with the number of models. Quantum computing has the potential to increase the speed of these calculations.

Bayesian approaches are not without challenges. Models may not necessarily reduce prediction errors or perform as well as nonparametric methods in some circumstances [30]. A perceived advantage of Bayesian data analysis over frequentist approaches is that it is well suited to large datasets [31]. However, large datasets can pose a problem because the likelihood for each parameter sampled must be calculated. Again, a quantum computing approach may overcome these challenges, recognising that large data sets in a quantum computing state remains to be developed.

Quantum computation theorists are attracted to a Bayesian approach because: (i) it is based on a state of knowledge; (ii) it is based on a probability which is used as a statement of confidence; and (iii) it can be updated or improved as more information is acquired [32]. In physics, statistical approaches are being challenged using concepts from quantum information. For example, Bayesian approaches have been used to improve model predictions using exponentially fewer experiments for phase estimation in a quantum setting [33]. This approach of adapting statistical approaches to improve efficiencies will be particularly enticing for ecologists where field observations can be costly in both collecting data and time.