The description of gene interactions that constantly occur in the cellular environment is an extremely challenging task due to an immense number of degrees of freedom and incomplete knowledge about microscopic details. Hence, a coarse-grained and rather powerful modeling of such dynamics is provided by Boolean Networks (BNs). BNs are dynamical systems composed of Boolean agents and a record of their possible interactions over time. Stable states in these systems are called attractors which are closely related to the cellular expression of biological phenotypes. Identifying the full set of attractors is, therefore, of substantial biological interest. However, for conventional high-performance computing, this problem is plagued by an exponential growth of the dynamic state space. Here, we demonstrate a novel quantum search algorithm inspired by Grover's algorithm to be implemented on quantum computing platforms. The algorithm performs an iterative suppression of states belonging to basins of previously discovered attractors from a uniform superposition, thus increasing the amplitudes of states in basins of yet unknown attractors. This approach guarantees that a new attractor state is measured with each iteration of the algorithm, an optimization not currently achieved by any other algorithm in the literature. Tests of its resistance to noise have also shown promising performance on devices from the current Noise Intermediate Scale Quantum Computing (NISQ) era.
The description of gene interactions that constantly occur in the cellular environment is an extremely challenging task due to an immense number of degrees of freedom and incomplete knowledge about microscopic details. Hence, a coarse-grained and rather powerful modeling of such dynamics is provided by Boolean Networks (BNs). BNs are dynamical systems composed of Boolean agents and a record of their possible interactions over time. Stable states in these systems are called attractors which are closely related to the cellular expression of biological phenotypes. Identifying the full set of attractors is, therefore, of substantial biological interest. However, for conventional high-performance computing, this problem is plagued by an exponential growth of the dynamic state space. Here, we demonstrate a novel quantum search algorithm inspired by Grover's algorithm to be implemented on quantum computing platforms. The algorithm performs an iterative suppression of states belonging to basins of previously discovered attractors from a uniform superposition, thus increasing the amplitudes of states in basins of yet unknown attractors. This approach guarantees that a new attractor state is measured with each iteration of the algorithm, an optimization not currently achieved by any other algorithm in the literature. Tests of its resistance to noise have also shown promising performance on devices from the current Noise Intermediate Scale Quantum Computing (NISQ) era.
Describing gene interactions in cells is challenging due to their complexity and the limited microscopic detail available. Boolean networks offer a powerful, coarse-grained approach to modeling these dynamics using binary agents and their interactions. In this context, attractors-stable states of the system-are associated with biological phenotypes, making their identification biologically important. However, traditional computing struggles with the exponential growth of the state space in such models. Here, we present a novel quantum search algorithm for identifying attractors in synchronous Boolean networks, specifically designed for use on quantum computers. The algorithm iteratively suppresses known attractor basins, increasing the probability of detecting new ones. Unlike classical methods, it guarantees the discovery of a new attractor in each run. Early tests demonstrate strong resilience to noise on current NISQ (noisy intermediate-scale quantum) devices, marking a promising advance toward practical quantum-enhanced biological modeling.
• Published in the international journal Patterns, successfully implementing the dynamics of biological Boolean networks (BNs) on a real quantum processing unit (QPU). • Demonstrated the efficiency of utilizing quantum superposition states to compute gene knockout and overexpression perturbation experiments in a single ensemble operation. • Traced back the predecessors of an attractor using Grover's search algorithm and successfully estimated the basin size through quantum counting techniques. [Quantum Biology Society] When analyzing complex biological mechanisms such as intracellular gene expression or metabolic pathways, classical computers face the limitation of exponentially expanding state spaces to compute as the number of components (nodes) increases. Recently, an empirical study that groundbreakingly resolved this fundamental computational bottleneck in systems biology through quantum computing has been published, drawing significant attention. A paper titled "Leveraging quantum computing for dynamic analyses of logical networks in systems biology" was published in Patterns, a data science journal published by Cell Press. A joint research team, including Felix M. Weidner and Professor Hans A. Kestler from Ulm University in Germany, presented a groundbreaking proof of principle for implementing the dynamics of biological logical networks using qubits. ■ 'Quantum Superposition' Taming Exponential Expansion In biological Boolean networks (BNs), when there are n components, the number of states the entire system can have increases exponentially to 2ⁿ. Focusing on the fact that the dimension of the computational space of an entangled system of qubits also expands exponentially, the research team successfully matched the exponential growth of network states to a system of multiple qubits. In a 5-gene network experiment (Emx2, Pax6, Coup-tfi, Sp8, Fgf8) modeling the development of the mammalian cerebral cortex, the research team created a uniform superposition of all possible initial states using Hadamard gates. With just a single run of the quantum state transition circuit, they were able to simultaneously evaluate multiple classical state transitions and ultimately converge the system into an attractor state, which signifies a stable phenotype. ■ 'Quantum Perturbation' Experiments Instead of Genetic Scissors In traditional biological research, an enormous number of classical simulations are required to understand the impact of specific gene knockouts or overexpression. However, in a quantum network model, biologically meaningful stable state information can be efficiently extracted through algorithms that utilize quantum properties such as superposition. The research team processed combinations of perturbations of multiple genes in a single ensemble operation using superposition states, and successfully derived a more realistic basin size by weighting specific genes to reflect prior biological knowledge. ■ Tracing the Origins of Disease with Grover's Algorithm What is particularly notable is that by combining the characteristics of quantum circuits with Grover's search algorithm, they traced back the initial predecessors that caused a specific final phenotype (attractor). Furthermore, they successfully estimated the total number of states leading to that attractor using quantum counting techniques. Such quantum backtracking techniques can serve as highly powerful and practical analytical tools for inversely identifying the pathogenic pathways of complex metabolic diseases at the molecular network level and selecting key target proteins. ■ Going Beyond Simulators to Successfully Run on Real Quantum Hardware (QPU) This research did not stop at a simple theoretical proposal. The research team directly ran and demonstrated this biological quantum circuit while comparing the performance of two real quantum computers with classical simulators. This is evaluated as a major breakthrough proving that algorithms impossible to implement on classical hardware can be introduced to real quantum computers for the dynamic analysis of biological systems.
Classical computational simulations of biological systems, particularly at the cellular level, face significant limitations due to the exponential growth in computational requirements with system complexity. This work proposes a novel approach to simulating cellular processes utilizing quantum-inspired algorithms, specifically tensor network methods, to overcome these limitations. These algorithms mimic key aspects of quantum computation – superposition and interference – to efficiently model intricate molecular interactions and resulting emergent phenomena. The core idea is to represent complex biological systems using tensor networks, enabling parallel processing and capturing correlations inherent in quantum systems. This approach provides a computationally feasible pathway for simulating dynamic cellular behavior, offering potential breakthroughs in areas such as drug discovery, disease modeling, and understanding fundamental biological mechanisms. The presented framework focuses on the theoretical foundations and algorithmic design, without necessitating access to quantum hardware, making it immediately applicable for high-performance computing environments. We explore the mathematical formalism underpinning the method, detailing the key equations and operations involved in simulating cellular processes. The ultimate goal is to establish a robust and scalable simulation technique capable of tackling the complexities of biological systems.
The dynamics of cellular mechanisms can be investigated through the analysis of networks. One of the simplest but most popular modeling strategies involves logic-based models. However, these models still face exponential growth in simulation complexity compared with a linear increase in nodes. We transfer this modeling approach to quantum computing and use the upcoming technique in the field to simulate the resulting networks. Leveraging logic modeling in quantum computing has many benefits, including complexity reduction and quantum algorithms for systems biology tasks. To showcase the applicability of our approach to systems biology tasks, we implemented a model of mammalian cortical development. Here, we applied a quantum algorithm to estimate the tendency of the model to reach particular stable conditions and further revert dynamics. Results from two actual quantum processing units and a noisy simulator are presented, and current technical challenges are discussed.
Quantum computing has noteworthy speedup over classical computing by taking advantage of quantum parallelism, i.e., the superposition of states. In particular, quantum search is widely used in various computationally hard problems. Grover's search algorithm finds the target element in an unsorted database with quadratic speedup than classical search and has been proved to be optimal in terms of the number of queries to the database. The challenge, however, is that Grover's search algorithm leads to high numbers of quantum gates, which make it infeasible for the Noise-Intermediate-Scale-Quantum (NISQ) computers. In this paper, we propose a novel hardware efficient quantum search algorithm to overcome this challenge. Our key idea is to replace the global diffusion operation with low-cost local diffusions. Our analysis shows that our algorithm has similar oracle complexity to the original Grover's search algorithm while significantly reduces the circuit depth and gate count. The circuit cost reduction leads to a remarkable improvement in the system success rates, paving the way for quantum search on NISQ machines.
Grover’s algorithm harnesses the power of quantum computing to swiftly locate specific elements in an unstructured database, outperforming classical computers in tasks like database searching. This algorithm capitalizes on the unique ability of qubits to be in both 0 and 1 states simultaneously (superposition), allowing it to scan the entire search space at once. It then boosts the probability of the target element, making it more prominent. While the foundational concepts of Grover’s algorithm are well-documented, practical implementation using quantum operators, especially for large search spaces, remains less explored beyond basic examples with a small number of qubits. Existing general synthesis techniques often involve numerous operators or are time-consuming. Our proposed methods specifically address the amplitude-amplification component of Grover’s algorithm for any size of search space. These methods detail the required types and quantities of qubits and operators, emphasizing minimal usage and efficient assembly. Developed and evaluated in Python, our methods consistently identified target elements with over 95% accuracy and achieved configurations comparably compact as those in the existing literature but at a faster pace. We anticipate that these methods facilitate practical implementations of Grover’s algorithm across various domains.