Optimizing quantum operations in systems that are strongly coupled to their environment using tensor networks
ORAL · Invited
Abstract
In order to model realistic quantum devices it is necessary to simulate quantum systems strongly coupled to their environment. To date, most understanding of open quantum systems is restricted either to weak system-bath couplings, or to special cases amenable to particular techniques. Here, I present a general and yet exact numerical method that enables simulations even when coupling is strong.
To do this, the system equations of motion are expressed as a tensor network [1]. In fact, the structure of this network is such that the environment parts can be pre-contracted efficiently, independent of the system Hamiltonian [2]. The resulting object is a process tensor matrix product operator (PT-MPO); a process tensor is a multi-linear map that is the most general description of the influence of an environment over a system [3]. It enables, for example, the calculation of dynamics for a collection of time-dependent system Hamiltonians while only calculating the PT-MPO once. It also allows the efficient calculation of any system multi-time correlation function [4].
I show that this approach enables the optimization of a control pulse for creating excitons in quantum dots [5]. Here, a series of system Hamiltonians is contracted with the PT-MPO to build a map of operation fidelity against a set of control parameters. Further developing this idea, I show how the process tensor can be used directly to generate a gradient of an objective function, and thus find optimal control parameters more efficiently [6].
Finally, I discuss how to combine PT-MPOs with standard tensor network methods to treat a register of coupled qubits interacting with independent environments [7]. I show how such a chain thermalizes when coupled to one or two heat reservoirs.
Our codes are publicly available [8] and we would be happy to support colleagues who would like to try them out on other problems.
[1] A. Strathearn et al., Nat. Commun. 9 3322 (2018)
[2] M. R. Jørgensen and F. A. Pollock, Phys. Rev. Lett. 123 240602 (2019)
[3] F. A. Pollock, et al., Phys. Rev. A 97 012127 (2018)
[4] R. de Wit et al., J. Phys. Chem. Lett. 16 6594 (2025)
[5] G. E. Fux et al., Phys. Rev. Lett. 126 200401 (2021)
[6] E. P. Butler et al. Phys. Rev. Lett. 132 060401 (2024)
[7] G. E. Fux et al., Phys. Rev. Research 5 033078 (2023)
[8] OQuPy oqupy.readthedocs.io; G. E. Fux et al., J. Chem. Phys. 161 124108 (2024)
To do this, the system equations of motion are expressed as a tensor network [1]. In fact, the structure of this network is such that the environment parts can be pre-contracted efficiently, independent of the system Hamiltonian [2]. The resulting object is a process tensor matrix product operator (PT-MPO); a process tensor is a multi-linear map that is the most general description of the influence of an environment over a system [3]. It enables, for example, the calculation of dynamics for a collection of time-dependent system Hamiltonians while only calculating the PT-MPO once. It also allows the efficient calculation of any system multi-time correlation function [4].
I show that this approach enables the optimization of a control pulse for creating excitons in quantum dots [5]. Here, a series of system Hamiltonians is contracted with the PT-MPO to build a map of operation fidelity against a set of control parameters. Further developing this idea, I show how the process tensor can be used directly to generate a gradient of an objective function, and thus find optimal control parameters more efficiently [6].
Finally, I discuss how to combine PT-MPOs with standard tensor network methods to treat a register of coupled qubits interacting with independent environments [7]. I show how such a chain thermalizes when coupled to one or two heat reservoirs.
Our codes are publicly available [8] and we would be happy to support colleagues who would like to try them out on other problems.
[1] A. Strathearn et al., Nat. Commun. 9 3322 (2018)
[2] M. R. Jørgensen and F. A. Pollock, Phys. Rev. Lett. 123 240602 (2019)
[3] F. A. Pollock, et al., Phys. Rev. A 97 012127 (2018)
[4] R. de Wit et al., J. Phys. Chem. Lett. 16 6594 (2025)
[5] G. E. Fux et al., Phys. Rev. Lett. 126 200401 (2021)
[6] E. P. Butler et al. Phys. Rev. Lett. 132 060401 (2024)
[7] G. E. Fux et al., Phys. Rev. Research 5 033078 (2023)
[8] OQuPy oqupy.readthedocs.io; G. E. Fux et al., J. Chem. Phys. 161 124108 (2024)
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Publication: A. Strathearn et al., Nat. Commun. 9 3322 (2018)
R. de Wit et al., J. Phys. Chem. Lett. 16 6594 (2025)
G. E. Fux et al., Phys. Rev. Lett. 126 200401 (2021)
E. P. Butler et al., Phys. Rev. Lett. 132 060401 (2024)
G. E. Fux et al., Phys. Rev. Research 5 033078 (2023)
G. E. Fux et al., J. Chem. Phys. 161 124108 (2024)
Presenters
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Brendon Lovett
- St Andrews