Symmetries

The Symmetries class in QDK/Chemistry is a general container for symmetry information that quantum algorithms can exploit to reduce resource requirements. As a core data class, it follows QDK/Chemistry’s immutable data pattern.

Overview

Many quantum algorithms can reduce circuit depth, qubit count, or classical post-processing cost when the symmetries of the target quantum state are known in advance. The Symmetries class encapsulates this symmetry information so that it can be passed to any algorithm that exploits it, such as the symmetry-conserving Bravyi-Kitaev qubit mapping.

Conserved quantum numbers

From the alpha and beta electron counts, several derived quantities are available as read-only properties.

Properties

n_alpha: Number of alpha (spin-up) electrons in the active space.
n_beta: Number of beta (spin-down) electrons in the active space.
n_particles: Total number of active electrons, \(n_\alpha + n_\beta\).
sz: Spin projection quantum number, \(S_z = (n_\alpha - n_\beta) / 2\).
spin_multiplicity: Spin multiplicity, \(2S + 1 = |n_\alpha - n_\beta| + 1\).

Creating a Symmetries object

A Symmetries object can be created by specifying electron counts directly, or by using a factory method to extract them from an existing Wavefunction or Ansatz.

Direct construction

Provide the alpha and beta electron counts explicitly:

from qdk_chemistry.data import Symmetries

# Closed-shell singlet with 4 active electrons
sym = Symmetries(n_alpha=2, n_beta=2)
print(sym.n_particles)       # 4
print(sym.sz)                # 0.0
print(sym.spin_multiplicity) # 1

# Open-shell doublet
sym = Symmetries(n_alpha=3, n_beta=2)
print(sym.sz)                # 0.5
print(sym.spin_multiplicity) # 2

From a wavefunction

If a Wavefunction is available, for example from an ScfSolver or MCCalculator calculation, the factory method from_wavefunction() extracts the active-space electron counts automatically:

from qdk_chemistry.data import Symmetries

symmetries = Symmetries.from_wavefunction(wavefunction)

From an ansatz

When an Ansatz is available, for example after a multi-configuration calculation, the electron counts can be derived from the ansatz’s wavefunction:

from qdk_chemistry.data import Symmetries

symmetries = Symmetries.from_ansatz(ansatz)

Note

Symmetries.from_ansatz(ansatz) is equivalent to Symmetries.from_wavefunction(ansatz.get_wavefunction()).