Quantum Chemistry: Universality of Givens Rotations (QHack 2022)

Overview

This repository contains a solution to the Quantum Chemistry – Universality of Givens Rotations coding challenge from QHack 2022.

Givens rotations are particle-conserving unitaries widely used in quantum chemistry. In this challenge, the goal is to compute the rotation angles required to prepare a specific six-qubit quantum state using a sequence of Givens rotations, starting from a given ground state.

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Problem Statement

Given a six-qubit quantum state of the form:

|ψ⟩ = a|110000⟩ + b|001100⟩ + c|000011⟩ + d|100100⟩

starting from the ground state |110000⟩, determine the three Givens rotation angles
θ₁, θ₂, θ₃ required to prepare |ψ⟩ using the circuit described in the challenge.

Constraints

• The coefficients a, b, c, d are real and normalized
• a > 0
• The angles θ₁, θ₂, θ₃ must lie in the interval [−π, π)
• Angles must be returned in the order they appear in the circuit

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Approach

The solution analytically computes the required angles using trigonometric relationships derived from the amplitudes of the target state:

• θ₂ = −2 · arctan(c / b)
• θ₃ = −2 · arctan(d / a)
• θ₁ = 2 · arcsin(c / sin(θ₂ / 2))

These angles uniquely parametrize the sequence of Givens rotations needed to generate the desired state.

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File Description

• qchem300.py
  Implements the givens_rotations function.

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Function Specification

givens_rotations(a, b, c, d)

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BY:

-Anushri Maheshwari

-Faaz Mohammed

-Vibha Patel