Probing Critical States of Matter on a Digital Quantum Computer.

Area of Science:

• Quantum Physics
• Condensed Matter Physics
• Computational Science

Background:

• Quantum mechanics governs microscopic behavior, but thermal fluctuations obscure its effects at the macroscopic level.
• Zero-temperature phase transitions are exceptions where quantum correlations drive emergent macroscopic phenomena.
• Classical simulations struggle to accurately describe quantum critical states due to computational complexity.

Purpose of the Study:

• To address the challenges of simulating quantum critical states on quantum computers.
• To explore the use of quantum simulation for studying quantum phase transitions.
• To demonstrate the capability of current quantum hardware for complex quantum many-body problems.

Main Methods:

• Utilized Quantinuum's H1-1 quantum computer.
• Employed hierarchical quantum tensor-network techniques.
• Encoded entanglement for a 128-site critical transverse-field Ising chain's ground state.

Main Results:

• Achieved high-fidelity ground state representation of the quantum critical Ising chain.
• Successfully extracted accurate critical properties of the model.
• Demonstrated the feasibility of quantum-assisted tensor-network contraction.

Conclusions:

• Quantum simulations offer a viable path for studying quantum critical phenomena beyond classical computational limits.
• Hierarchical quantum tensor-network methods are effective for representing complex quantum states.
• This work advances the application of quantum computing in condensed matter physics.