Accurate numerical simulations of open quantum systems using spectral tensor trains.

Area of Science:

• Quantum Information Science
• Computational Physics
• Quantum Computing

Background:

• Decoherence in qubits is a primary obstacle for reliable quantum computations.
• Noise from quantum/thermal fluctuations and external fields degrades qubit states.

Purpose of the Study:

• To introduce a novel numerical method, Q-ASPEN, for simulating quantum systems under realistic noise conditions.
• To enable accurate estimation of resources required for quantum error correction.

Main Methods:

• Developed Quantum Accelerated Stochastic Propagator Evaluation (Q-ASPEN) for time-dependent noise-averaged reduced density matrix.
• Employed spectral tensor trains, combining tensor networks and pseudospectral methods, as a variational ansatz.
• Utilized neural network training techniques for ansatz optimization.

Main Results:

• Q-ASPEN provides arbitrarily accurate solutions for quantum relaxation problems with intrinsic and extrinsic noise.
• Demonstrated feasibility of accurate calculations for systems with tens of quantum levels.
• Benchmarks on spin-boson models and quantum chains show polynomial memory scaling.

Conclusions:

• Q-ASPEN offers a powerful tool for simulating noisy quantum systems.
• The method significantly advances the potential for practical quantum error correction.
• Spectral tensor trains enable efficient and accurate quantum dynamics simulations.