Chat with Bing

I want to simulate a noisy quantum dynamics. how to simulate a correlated error, such as correlated damping, in a numerical simulation? I expect the correlated error behaves differently from independent case.

Simulating a correlated error, such as correlated damping, in a numerical simulation of quantum dynamics is a challenging task that requires sophisticated techniques and algorithms. According to some recent papers, some possible methods are:

• Using tensor networks to compress the data required to describe quantum systems and implement an optimal dynamical quantum simulation protocol on a trapped-ion processor1.
• Using error mitigation techniques such as noise tailoring, zero-noise extrapolation, dynamical decoupling, and physically motivated postselection of measurement results to protect nonlocal quantum correlations in correlated squeezed generalized amplitude damping channels2.
• Using SchWARMA models to parametrize and simulate temporally correlated noise in quantum circuits by generalizing ARMA models to the space of completely positive trace preserving maps3.
• Using adaptive variational quantum dynamics simulation to capture both finite-rate and sudden post-quench dynamics with high fidelity by optimizing the time-dependent variational parameters on a quantum processor4.
• Using ultracold atoms in optical lattices to realize and simulate many-body phases of strongly correlated condensed matter systems, such as the Hubbard model5.

—

How can I perform this simulation on Qiskit? I used amplitude damping channel and phase damping channel to simulate a single qubit noisy dynamics. Are there any other approaches?

Qiskit provides a noise module that allows you to build custom noise models for noisy simulations. You can use the AerSimulator class to create a simulator with a noise model that mimics a real device or a custom noise model that you define. Some possible approaches to simulate correlated noise are:

• Using the NoiseModel class to specify quantum errors and readout errors for different gates and qubits. You can use the from_backend method to automatically generate a noise model based on the calibration information of a real device, or you can use the add_all_qubit_quantum_error and add_all_qubit_readout_error methods to add correlated errors to all qubits1.
• Using the kraus_error function to create a general n-qubit CPTP error channel given as a list of Kraus matrices. You can use this function to define correlated damping errors by specifying the appropriate Kraus operators1.
• Using the phase_amplitude_damping_error function to create a single-qubit generalized combined phase and amplitude damping error channel given by an amplitude damping parameter λ, a phase damping parameter γ, and an excited state thermal population p 1. You can use this function to define correlated damping errors by specifying the same parameters for different qubits1.
• Using the compose, tensor, and expand methods of the QuantumError class to combine different quantum errors into a single error. You can use these methods to create correlated errors by composing or tensoring errors that affect different qubits1.
• Using the set_density_matrix method of the AerSimulator class to initialize the simulator with a custom density matrix that represents a correlated state of the qubits. You can use this method to simulate correlated noise by preparing a mixed state that has non-zero off-diagonal elements2.

For more details and examples, you can refer to the Qiskit documentation and tutorials**12**.

—