qmm-benchmark

This is a benchmark for equivalence checking of quantum circuits using quantum Mealy machine [WLY21].

Basic Definitions

A quantum Mealy machine (QMM) is a 5-tuple , where:

• is a finite input alphabet;
• is a finite output alphabet;
• is a finite-dimensional Hilbert space;
• is a set of unitary operators. For each , is a unitary operator on ; and
• is a quantum measurement in , that is, is a linear operator on for each and .

See [WLY21] for more details.

The benchmark is for equivalence checking of two states in a QMM. That is, given a QMM and two states and , decide whether and for some .

Data Format

testXXX.data is a binary file, whose contents are listed below:

<dim, int>
<sigma, int>
<gamma, int>
<limit, int>
<eps, double>
for a in 0..sigma-1:
    for i in 0..dim-1:
        for j in 0..dim-1:
            <unitary[a][i][j].real, double>
            <unitary[a][i][j].imag, double>
for b in 0..sigma-1:
    for i in 0..dim-1:
        for j in 0..dim-1:
            <measure[b][i][j].real, double>
            <measure[b][i][j].imag, double>
for i in 0..dim-1:
    for j in 0..dim-1:
        <rho1[i][j].real, double>
        <rho1[i][j].imag, double>
for i in 0..dim-1:
    for j in 0..dim-1:
        <rho2[i][j].real, double>
        <rho2[i][j].imag, double>

The offsets of the first few data are shown below for calibration:

offset        <content, type>
 0000	        <dim, int>
 0004	        <sigma, int>
 0008	        <gamma, int>
 000c	        <limit, int>
 0010	        <eps, double>
 ....

Examples

We select test002 as an illustrative example, in which case:

• dim = 4.
• sigma = 2.
• gamma = 2.
• limit = -1.
• eps = 1e-8.
• 
• 
• 

“limit” denotes . It is noted that for the case “limit = -1”, it means that no such is required, or equivalently holds.

Source Code

The implementation of checking equivalence of QMM is the file "qmm.h".

The hard-coded data is seen in "datafactory.h".

References

[WLY21] Qisheng Wang, Junyi Liu and Mingsheng Ying. Equivalence checking of quantum finite-state machines. Journal of Computer and System Sciences, 116: 1-21, 2021. arXiv:1901.02173. doi:10.1016/j.jcss.2020.08.004.