Skip to content

Explanation of config values

The following config values to emu-mps relate to the functioning of the currently available algorithms (TDVP and DMRG) used to evolve the quantum state in time, and will be explained in more detail below:

  • dt
  • precision
  • max_bond_dim
  • max_krylov_dim
  • extra_krylov_tolerance
  • num_gpus_to_use
  • autosave_dt
  • optimize_qubit_ordering
  • solver

dt

Note that emu-mps assumes the Hamiltonian is piece-wise constant in time for intervals of dt. It then constructs the Hamiltonian by sampling the amplitude, detuning and phase of the pulse midway through the interval, and making a single Hamiltonian. The TDVP or DMRG algorithms are then used to evolve the state by dt. There are two sources of error related to dt.

  • The discretization of the pulse
  • TDVP

Both sources of error dictate that dt shall not be too small, but the functioning of TDVP also dictates that a very small dt requires improving the precision, as described in the next section.

precision

The 2-site TDVP and DMRG algorithms used in emu-mps work by repeatedly time-evolving two neighbouring qubits in the MPS, and then truncating the result. Truncation is done by applying an SVD to the matrix representing the 2-qubit subsystem. The singular values give much information about the state. Denote the singular values by \(d_i\), and assume they are ordered in decreasing magnitude. Then the norm of the state will be \(\sum_i d_i^2\) and the entanglement entropy between the left and right parts of the state will be \(\sum_i d_i \log_2(d_i)\), for example.

The truncation mentioned above functions by throwing away the smallest singular values, until their squared sum exceeds \(precision^2\). The result is that the truncation procedure finds the smallest MPS whose distance is less than precision away from the original state. As described on the page of errors in TDVP, the error in TDVP increases with the number of timesteps, so for long sequences or small dt, improving the precision might be required.

max_bond_dim

In addition to the above procedure, at each truncation step, no more than max_bond_dim singular values are kept. This parameter will impose a hard cap on the memory consumed by the quantum state, at the cost of losing control over the magnitude of the truncation errors.

max_krylov_dim

Time evolution of each qubit pair is done by the Lanczos algorithm. This algorithm works by iteratively constructing a basis in which the Hamiltonian is close to diagonal. In this basis, the time-evolution of the state can efficiently be approximated by exponentiating a truncated Hamiltonian in the case of TDVP, or minimizing the truncated Hamiltonian in the DMRG case. The algorithm will never construct more than max_krylov_dim basis vectors, limiting the runtime and memory consumption of the time-evolution.

Note that the number of iterations the Lanczos algorithm needs to converge to the required tolerance depends on the dt parameter also present in the config (see the api specification). The default value of max_krylov_dim should work for most reasonable values of dt, so if you get a recursion error out of the Lanczos algorithm, ensure you understand how the errors in TDVP depend on dt.

extra_krylov_tolerance

In addition to the above hard cap on the number of basis vectors, the algorithm will also attempt to estimate the error incurred by computing the matrix exponential using only the current basis vectors. In principle, it is not needed to compute the time-evolution more precisely than precision since extra precision will be lost in the truncation. However, in practice it turns out that existing error estimates tend to underestimate the error. extra_krylov_tolerance is a fudge factor for how big the desired precision should be compared to precision. Its default value is 1e-3.

num_gpus_to_use

The num_gpus_to_use parameter sets the number of GPUs over which the MPS tensors are distributed during the simulation. Setting num_gpus_to_use = 0 runs the entire computation on the CPU. Using multiple GPUs can reduce memory usage per GPU, though the overall runtime remains similar.

Example: num_gpus_to_use = 2 # use 2 GPUs if available, otherwise fallback to 1 or CPU

optimize_qubit_ordering

The optimize_qubit_ordering parameter enables the reordering of qubits in the register. This can be useful in cases where the initial qubit ordering (chosen by the user) is not optimal. In such cases, setting optimize_qubit_ordering = True re-orders the qubits more efficiently, and that has been shown to improve performance and accuracy. The default value is False.

Note: enabling this option is not compatible with certain features, such as reading a user-provided initial state.

autosave_dt

The autosave_dt parameter defines the minimum time interval between two automatic saves of the MPS state. It is given in seconds with a default value 600 (\(10\) minutes). Saving the quantum state for later use (for e.g. to resume the simulation) will only occur at times that are multiples of autosave_dt.

solver

The solver parameter selects the algorithm used to evolve the system using a Pulser sequence. The Solver class is then defined with two possible values:

  • TDVP — the default value, used to perform real-time evolution of the MPS using the two-site TDVP algorithm.
  • DMRG is an alternative solver that variationally minimizes the effective Hamiltonian using the two-site DMRG algorithm, typically applied for simulating adiabatic sequences.

For a detailed description of the currently available solvers, please refer to the current algorithms.