A quantum algorithm for obtaining the energy spectrum of a physical system without guessing its eigenstates

Area of Science:

• Quantum Computing
• Quantum Physics
• Computational Chemistry

Background:

• Determining the energy spectrum of quantum systems is crucial for understanding their behavior.
• Existing methods often require prior knowledge or approximations of system eigenstates.

Purpose of the Study:

• To develop a general quantum algorithm for obtaining energy spectra and eigenstates.
• To provide a method that does not require guessing initial eigenstates.

Main Methods:

• A quantum algorithm coupling a probe qubit to a quantum register (R).
• Register R includes an ancilla qubit and an n-qubit system register.
• Preparation of R in a general reference state and construction of an excitation operator.
• Utilizing the probe qubit's resonant dynamical response to transitions within R.

Main Results:

• The probe qubit's frequency directly correlates with energy transitions.
• Successful acquisition of the system's energy spectrum.
• Identification of the system's eigenstates through resonant frequencies.

Conclusions:

• The presented quantum algorithm offers a general and robust approach for spectral analysis.
• This method eliminates the need for initial eigenstate guesses, simplifying quantum system characterization.
• Potential applications in quantum chemistry and condensed matter physics.