MBQS: Many-Body Quantum Score – A scalable benchmark for digital and analog quantum processors

This packages provides a set of tools to compute the Many-Body Quantum Score (MBQS), which is designed to benchmark the performance of quantum processors in simulating many-body quantum systems [arXiv:2601.03461]¹. The score is obtained by comparing a given metric, called $P_2(L)$, with a threshold $\epsilon$.

The MBQS metric is parametrized by an initial state $\psi$ and computed according to the following protocol:

1. Setup a spin chain with $L$ spin $\frac{1}{2}$ equally spaced on a $1d$ ring.
2. Initialize the register with the state $\ket{\psi}$.
3. Evolve the system (quench) with the Ising Hamiltonian at the critical point $g = 1$ for a duration $t_*(L)$ (“surge time”).
4. Perform measurements ${ \sigma^z_i }$ and compute the connected 2-point functions:

$$ g^{(2)}\ell(t) := \Braket{\sigma^z_1 \sigma^z\ell}c := \Braket{\sigma^z_1 \sigma^z\ell} - \Braket{\sigma^z_1} \Braket{\sigma^z_\ell}. $$

5. Compute the metric (average relative error with respect to the theoretical values in Ising model):

$$ P_2(L) := \frac{1}{\lfloor L/2 \rfloor - 1} \sum_{\ell = 2}^{\lfloor L/2 \rfloor} \left| \frac{g^{(2) \text{th}}{\ell}(t\ast) - g^{(2) \text{exp}}{\ell}(t\ast)}{g^{(2) \text{th}}{\ell}(t\ast)} \right|. $$

The MBQS score S with the initial state $\psi$ corresponds to the largest problem size $L$ reached before failing the test with a threshold $\epsilon$, but excluding system sizes below some cut-off:

$$ S = L \quad \Longrightarrow \quad \forall L' \le L: \quad P_2(L') \le \epsilon. $$

In this package, we provide the evaluation for the folloling initial states:

• $\ket{+ \cdots +}$
• $\ket{\downarrow \cdots \downarrow}$

The surge time is defined to be the time at which the antipodal connected 2-point function is maximum. The only exception is for $L = 3$ and with the down state: it is defined to be the time for which the 1-point function is maximum (because the 2-point function has a large plateau).

Usage

We provide the computations of the surge time and correlation functions at that time using three different methods:

1. Exact simulation with qutip (for $L \lesssim 20$ on a laptop).
2. Exact solution with free fermions (for any $L$; not yet implemented).
3. Tabulated data from free fermions (for $L \le 50$).

The qutip method is provided as a way to check the results for low L but it is not scalable to large systems. The free fermions method is exact and can be used for any $L$. The tabulated data method is taken from the free fermions: for larger $L$, it falls back to free fermions.

We also provide utilities to map the critical Ising model on a neutral atom QPU.

As a Python package

You can use mbqs as a package. The most important classes are available as top-level imports: MBQS, MBQSProtocol, RydbergMapping. You can check the unit tests and CLI actions to find how to use them.

Command-line interface

• Display in console the parameters needed to run the protocol for a given system size:

mbqs protocol -J 1. -L 4

• Display in console the parameters needed to run the protocol for several system sizes:

mbqs protocol -J 1. -L {4..6}

• Parameters for running the protocol on an neutral atom analog quantum simulator can be added using the --include-rydberg flag or using the interatomic distance as a parameter instead of the coupling constant:

mbqs protocol -J 1. -L 4 --include-rydberg
mbqs protocol -a 7.75 -L 4

• Save a json file with the protocol parameters (use --verbose to also display in the console):

mbqs protocol -J 1. -L {4..6} --json protocol.json

• Compute the theoretical correlations at the surge time:

mbqs correlations -L 3

• Compute the correlations from a file of samples:

mbqs correlations -i samples.json

• Evaluate the metric from correlations functions in a file:

# without parameters in file
mbqs scorer -i examples/correlations_samples.json -L 3 --threshold 0.3
# with parameters
mbqs scorer -i examples/correlations_exact.json

• Evaluate the metric from samples in a file:

mbqs scorer -i examples/samples.json

• Evaluate the score for a file containing correlations functions for different system sizes:

mbqs scorer -i examples/correlations_sequence.json

Examples of json files can be found in the examples directory.

Autocompletion can be enabled for the mbqs command by running the following command (only for the current session):

eval "$(register-python-argcomplete mbqs)"

To make it persistent (for example, for bash on Linux), you can execute the following commands:

mkdir -p ~/.local/share/bash-completion/completions
register-python-argcomplete mbqs > ~/.local/share/bash-completion/completions/mbqs

Contributing

To install all the dependencies including the development tools, run:

uv venv
make install-dev

Before performing a commit, ensure that the following returns no error or warning:

make check
make test