Understanding the intricate quantum spin dynamics of radical pair reactions is crucial for unraveling the underlying nature of chemical processes across diverse scientific domains. In this work, we leverage Trotterization to map coherent radical pair spin dynamics onto a digital gate-based quantum simulation. Our results demonstrated an agreement between the idealized noiseless quantum circuit simulations and established master equation approaches for homogeneous radical pair recombination, identifying ∼15 Trotter steps to be sufficient for faithfully reproducing the coupled spin dynamics of a prototypical system. By utilizing this computational technique to study the dynamics of spin systems of biological relevance, our findings underscore the potential of digital quantum simulation (DQS) of complex radical pair reactions and builds the groundwork toward more utilitarian investigations into their intricate reaction dynamics. We further investigate the effect of realistic error models on our DQS approach and provide an upper limit for the number of Trotter steps that can currently be applied in the absence of error mitigation techniques before losing simulation accuracy to deleterious noise effects.
Understanding the intricate quantum spin dynamics of radical pair reactions is crucial for unraveling the underlying nature of chemical processes across diverse scientific domains. In this work, we leverage Trotterization to map coherent radical pair spin dynamics onto a digital gate-based quantum simulation. Our results demonstrated an agreement between the idealized noiseless quantum circuit simulations and established master equation approaches for homogeneous radical pair recombination, identifying ∼15 Trotter steps to be sufficient for faithfully reproducing the coupled spin dynamics of a prototypical system. By utilizing this computational technique to study the dynamics of spin systems of biological relevance, our findings underscore the potential of digital quantum simulation (DQS) of complex radical pair reactions and builds the groundwork toward more utilitarian investigations into their intricate reaction dynamics. We further investigate the effect of realistic error models on our DQS approach and provide an upper limit for the number of Trotter steps that can currently be applied in the absence of error mitigation techniques before losing simulation accuracy to deleterious noise effects.
• Published in AIP Publishing's APL Quantum, fully applying digital quantum simulation (DQS) to spin biology. • Successfully implemented the quantum spin dynamics of the radical pair mechanism utilizing the 'Trotterization' technique. • Analyzed the noise limits of actual quantum hardware and demonstrated the potential of utilizing quantum computing for the future development of new drugs targeting complex biomolecules. [Quantum Biology Society] In the emerging field of quantum biology, simulating spin-chemistry systems with actual biological complexity has posed computational limitations that are difficult to overcome with conventional classical computers. This is because as the number of elements constituting the spin system increases, the dimension of the Hilbert space required for computation grows exponentially. Recently, a study simulating biological phenomena using an actual digital quantum computer was published to resolve this problem, drawing the attention of the academic community. A paper titled "Simulating spin biology using a digital quantum computer: Prospects on a near-term quantum hardware emulator" was published on August 19 in APL Quantum, a journal of AIP Publishing. This research was led by a multinational joint research team including Pedro H. Alvarez and Clarice D. Aiello. ■ Mapping the Radical Pair Mechanism via Trotterization The radical pair mechanism (RPM), represented by the magnetic field sensing (magnetoreception) ability of migratory birds, centers on the quantum entanglement and coherence phenomena of electron spins in vivo. The research team introduced the Trotterization technique to directly apply gate-based digital quantum simulation (DQS) to biological systems. Through this technique, they successfully mapped the coherent spin dynamics of radical pairs onto quantum circuits. In ideal, noise-free quantum circuit simulations, they obtained accurate spin dynamics results consistent with the conventional classical Haberkorn master equation approach using only about 15 Trotter steps. ■ Analysis of Quantum Hardware Noise Limits and Future Prospects Furthermore, going beyond ideal environments, the research team conducted an in-depth analysis of the impact of realistic error models on simulations using a near-term (NISQ) quantum hardware emulator that mimics the noise profile of an IBM quantum device (e.g., ibmq_jakarta). The analysis revealed that realistic limitations were observed due to the constrained performance and noise (such as phase damping and amplitude damping) of current quantum hardware, including a shift in singlet yield and a decreased ability to sense magnetic field anisotropy. However, the researchers showed that by fitting an analytical model to the measured noisy data, the overall dynamical shape depending on the magnetic field angle could be successfully derived. In addition, they presented a practical upper limit for the number of Trotter steps that can be directly run on quantum devices if error mitigation techniques are introduced in the future. Unlike conventional classical computing methods that face exponential limits, the DQS approach possesses the potential to efficiently model biological spin systems simply through linear resource scaling by adding qubits. This study is evaluated as a groundbreaking first step demonstrating that digital quantum simulation can be utilized as an innovative tool for new drug development targeting complex biomolecules and ultra-precise biosensing modeling by directly calculating the entanglement and coherence of biological phenomena.
The Radical Pair Mechanism, a process by which magnetic fields modulate the kinetics of chemical reactions by influencing spin dynamics, is thought to underlie a variety of biological mechanisms and is inherently both quantum and noisy. Model simulations with limited electron-nuclear interactions have been conducted on classical devices resulting in experimentally verified final state results, however these simulations become too complex to simulate as the systems scale in size. This motivates us to propound the simulation of the relevant spin dynamics in a noisy quantum device to probe the currently unexplored open quantum systems aspects of the radical pair mechanism and to provide a novel theoretical tool for us to be able to tackle bottlenecks in simulating larger and more physically relevant biological spin systems. We employ a hybrid quantum machine learning approach where we evaluate a parametrized quantum circuit representing the evolution of the system on the quantum device and then update the parameters according to our objective cost function on a classical computer using a gradient optimizer and a noisy gradient free (SPSA) optimizer. We show that a 3 qubit circuit with a series of parametrized rotation gates representing the Hyperfine and Zeeman interactions can be optimized, resulting in a circuit that evolves a singlet state under different magnetic field angles. Moreover, we show that the noisy gradient free optimizer is better suited for optimizing on a noisy quantum device. However, the precision in the quantum circuit outputs is only sub-par at present, leaving room for further improvements.
A higher-order Suzuki-Trotter decomposition or Trotterization can be exploited to mitigate the Trotter error in digital quantum simulation. This work revisits the second-order symmetric Trotterization in terms of the Trotter error, where quantum many-body spin dynamics of the transverse-field Ising model is simulated. While the work presents a pedagogical way to exploit a real quantum computer, the effectiveness of the symmetric Trotterization is evaluated in a prototype superconducting quantum device on IBM Quantum Experience. It turns out that the symmetric Trotterization does not provide higher accuracy than the first-order Trotterization in the testbed using the transverse-field Ising model. The result indicates that apart from the quantum errors, such as logical gate error and readout error, the use of a higher-order Trotterization should be circumspect, and the Trotter error would play an insignificant role in particular applications in an early stage of realized noisy intermediate-scale quantum (NISQ) devices.
This work aims at giving Trotter errors in digital quantum simulation (DQS) of collective spin systems an interpretation in terms of quantum chaos of the kicked top. In particular, for DQS of such systems, regular dynamics of the kicked top ensures convergence of the Trotterized time evolution, while chaos in the top, which sets in above a sharp threshold value of the Trotter step size, corresponds to the proliferation of Trotter errors. We show the possibility to analyze this phenomenology in a wide variety of experimental realizations of the kicked top, ranging from single atomic spins to trapped-ion quantum simulators which implement DQS of all-to-all interacting spin-1/2 systems. These platforms thus enable in-depth studies of Trotter errors and their relation to signatures of quantum chaos, including the growth of out-of-time-ordered correlators.
Abstract This work aims at giving Trotter errors in digital quantum simulation (DQS) of collective spin systems an interpretation in terms of quantum chaos of the kicked top. In particular, for DQS of such systems, regular dynamics of the kicked top ensures convergence of the Trotterized time evolution, while chaos in the top, which sets in above a sharp threshold value of the Trotter step size, corresponds to the proliferation of Trotter errors. We show the possibility to analyze this phenomenology in a wide variety of experimental realizations of the kicked top, ranging from single atomic spins to trapped-ion quantum simulators which implement DQS of all-to-all interacting spin-1/2 systems. These platforms thus enable in-depth studies of Trotter errors and their relation to signatures of quantum chaos, including the growth of out-of-time-ordered correlators.
Digital quantum simulation (DQS) is one of the most promising applications of quantum computing. Trotterised DQS models quantum dynamics by decomposing the evolution into a sequence of gate-based Trotter steps. Using larger Trotter steps reduces the required gate count, but it is now understood that the Trotterisation step size cannot be increased beyond a certain threshold value, beyond which there is a sudden breakdown in simulation accuracy, due to the onset of quantum chaos. To date, this behaviour has only been studied for closed systems not subjected to the environmental noise and decoherence to which real-world quantum computers are highly sensitive. In this work, we study a range of experimentally relevant open-system quantum simulator models and show that Trotterisation thresholds persist even when open-system effects are included, even in the long-time, steady-state limit, once all coherence has been lost. We show that open DQS can accurately reproduce the dynamics of open target systems prior to the threshold, but still exhibits a sudden performance breakdown beyond it. We introduce new, statistical techniques to rigorously characterise the onset of quantum chaos beyond the Trotterisation threshold for both approximately unitary and genuine dissipative quantum chaos, based on random matrix theory (RMT), building on techniques developed for closed systems. Finally, we demonstrate that dissipative quantum chaos emerges when the dissipation is in balance with the presence of underlying unitary quantum chaos; the dissipation must be strong enough to induce genuinely dissipative behaviour, yet not so strong as to suppress the underlying chaotic structure.