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International Conference on Simulation of Semiconductor Processes and Devices

Quantum Algorithms for Simulating Quantum Transport via the Time-Dependent Open-System SchröDinger Equation

Satofumi Souma

Published Sep 24, 2025• 0 citations
Publisher

Abstract

We propose and demonstrate a quantum circuitbased framework for simulating quantum transport phenomena governed by the time-dependent Schrödinger equation for open quantum systems. While the theoretical formulation is compatible with large-scale classical simulations, its implementation as a quantum algorithm offers a promising path toward quantumaccelerated modeling of nanoscale devices. A key challenge in such simulations lies in incorporating dissipation and particle injection processes arising from coupling to external reservoirs. In this work, we present quantum circuit constructions that explicitly encode these effects using controlled rotations, measurementinduced decoherence, and reset operations. By comparing the results of our quantum simulations with those obtained from classical numerical solutions of the open-system Schrödinger equation, we confirm that the proposed quantum model can reproduce both transient dynamics and steady-state behavior. These results validate the physical fidelity of the approach and highlight the potential of quantum computing in electronic transport simulations.

DOI
10.1109/sispad66650.2025.11186024

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We propose and demonstrate a quantum circuitbased framework for simulating quantum transport phenomena governed by the time-dependent Schrödinger equation for open quantum systems. While the theoretical formulation is compatible with large-scale classical simulations, its implementation as a quantum algorithm offers a promising path toward quantumaccelerated modeling of nanoscale devices. A key challenge in such simulations lies in incorporating dissipation and particle injection processes arising from coupling to external reservoirs. In this work, we present quantum circuit constructions that explicitly encode these effects using controlled rotations, measurementinduced decoherence, and reset operations. By comparing the results of our quantum simulations with those obtained from classical numerical solutions of the open-system Schrödinger equation, we confirm that the proposed quantum model can reproduce both transient dynamics and steady-state behavior. These results validate the physical fidelity of the approach and highlight the potential of quantum computing in electronic transport simulations.
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Abstract The extent to which quantum computers can simulate physical phenomena and solve the partial differential equations (PDEs) that govern them remains a central open question. In this work, one of the most fundamental PDEs is addressed: the multidimensional transport equation with space- and time-dependent coefficients. We present a quantum numerical scheme based on three steps: quantum state preparation, evolution, and measurement of relevant observables. The evolution step combines a high-order centered finite difference with a time-splitting scheme based on product formula approximations, also known as Trotterization. We introduce a novel vector-norm analysis and prove that the number of time-steps can be reduced by a factor exponential in the number of qubits, compared with previously established operator-norm analysis. This new scaling significantly reduces the projected computational resources, independently of the circuit implementation of the trotterized evolution operator. We also present efficient quantum circuits based on (sparse) Walsh approximations along with numerical simulations that confirm the predicted vector-norm scaling. We report results on real quantum hardware for the one-dimensional convection equation, and solve a non-linear ordinary differential equation via its associated Liouville equation, a particular case of transport equations. This work provides a practical framework for efficiently simulating transport phenomena on quantum computers, with potential applications in plasma physics, molecular gas dynamics and non-linear dynamical systems, including chaotic systems.
Abstract Quantum simulation represents the most promising quantum application to demonstrate quantum advantage on near-term noisy intermediate-scale quantum (NISQ) computers, yet available quantum simulation algorithms are prone to errors and thus difficult to realize with limited circuit depth on nowadays quantum devices. Herein, we propose a novel scheme to utilize intrinsic gate errors of NISQ devices to enable controllable simulation of open quantum system dynamics without ancillary qubits or explicit bath engineering, thus turning unwanted quantum noises into useful quantum resources. Specifically, we simulate the energy transfer process in a photosynthetic dimer system on IBM-Q cloud. By employing tailored decoherence-inducing gates, we show that quantum dissipative dynamics can be simulated efficiently across coherent-to-incoherent regimes with results comparable to those of the numerically exact classical method. Moreover, we demonstrate a calibration routine that enables consistent and predictive simulations of open-quantum system dynamics in the intermediate coupling regime. This work provides a new direction for quantum advantage in the NISQ era.
Simulating large-scale coupled-oscillator systems presents substantial computational challenges for classical algorithms, particularly when pursuing first-principles analyses in the thermodynamic limit. Motivated by the quantum algorithm framework proposed by Babbush et al. (2023), we present and implement a detailed quantum circuit construction for simulating one-dimensional spring–mass systems. Our approach incorporates key quantum subroutines, including block encoding, quantum singular value transformation (QSVT), and amplitude amplification, to realize the unitary time-evolution operator associated with simulating classical oscillators dynamics. In the uniform mass–spring setting, our circuit construction requires a gate complexity ofO(log⁡22N log⁡2(1/ε))\mathcal {O}\bigl (\log _{2}^{2} N\,\log _{2}(1/\varepsilon )\bigr )O(log22​Nlog2​(1/ε)), where N is the number of oscillators and$\varepsilon isthetargetaccuracyoftheapproximation.Formoregeneral,heterogeneousmass–springsystems,thetotalgatecomplexityisis the target accuracy of the approximation. For more general, heterogeneous mass–spring systems, the total gate complexity isisthetargetaccuracyoftheapproximation.Formoregeneral,heterogeneousmass–springsystems,thetotalgatecomplexityis\mathcal {O}\bigl (N\log _{2} N\,\log _{2}(1/\varepsilon )\bigr ).Bothsettingsrequire. Both settings require.Bothsettingsrequire\mathcal {O}(\log _{2} N)$qubits. Numerical simulations agree with classical solvers across all tested configurations, indicating that this circuit-based Hamiltonian simulation approach can substantially reduce computational costs and potentially enable larger-scale many-body studies on future quantum hardware.
We develop an analog classical simulation algorithm of noiseless quantum dynamics. By formulating the Schrödinger equation into a linear system of real-valued ordinary differential equations (ODEs), the probability amplitudes of a complex state vector can be encoded in the continuous physical variables of an analog computer. Our algorithm reveals the full dynamics of complex probability amplitudes. Such real-time simulation is impossible in quantum simulation approaches without collapsing the state vector, and it is relatively computationally expensive for digital classical computers. For a real symmetric time-independent Hamiltonian, the ODEs may be solved by a simple analog mechanical device such as a one-dimensional spring-mass system. Since the underlying dynamics of quantum computers is governed by the Schrödinger equation, our findings imply that analog computers can also perform quantum algorithms. We illustrate how to simulate the Schrödinger equation in such a paradigm, with an application to quantum approximate optimization algorithm. This may pave the way to emulate quantum algorithms with physical computing devices, including analog, continuous-time circuits.
Abstract Quantum effects such as the environment assisted quantum transport (ENAQT) displayed in photosynthetic Fenna–Mathews–Olson (FMO) complex has been simulated on analog quantum simulators. Digital quantum simulations offer greater universality and flexibility over analog simulations. However, digital quantum simulations of open quantum systems face a theoretical challenge; one does not know the solutions of the continuous time master equation for developing quantum gate operators. We give a theoretical framework for digital quantum simulation of ENAQT by introducing new quantum evolution operators. We develop the dynamical equation for the operators and prove that it is an analytical solution of the master equation. As an example, using the dynamical equations, we simulate the FMO complex in the digital setting, reproducing theoretical and experimental evidence of the dynamics. The framework gives an optimal method for quantum circuit implementation, giving a log reduction in complexity over known methods. The generic framework can be extrapolated to study other open quantum systems.