Gate-Based Quantum Simulation of Gaussian Bosonic Circuits on Exponentially Many Modes

Area of Science:

• Quantum Information Science
• Quantum Computing
• Quantum Simulation

Background:

• Gaussian Bosonic (GB) circuits are crucial for modeling various quantum systems.
• Efficient simulation of GB circuits on large-scale quantum computers remains a challenge.
• Existing methods struggle with the exponential scaling of modes in GB systems.

Purpose of the Study:

• To develop a novel quantum computing framework for simulating GB circuits.
• To encode bosonic states and GB operations into a qubit-based quantum computer.
• To explore the computational power of simulating Gaussian states on quantum hardware.

Main Methods:

• Encoding initial bosonic state expectation values and covariance matrix into qubit states.
• Developing a quantum circuit to implement symplectic propagators of GB gates.
• Mapping GB gates to qubit gates, distinguishing particle-preserving and non-particle-preserving operations.

Main Results:

• Identified efficient quantum simulation strategies for specific GB circuits and initial states.
• Established a dictionary for GB-to-qubit gate mapping, enabling real/imaginary time evolution simulation.
• Demonstrated a Bounded-Error Quantum Polynomial time (BQP)-complete GB decision problem for particle-preserving circuits.
• Showcased the framework's capability through numerical simulations of large-scale interferometers (∼8×10⁹ modes).

Conclusions:

• The proposed framework enables efficient quantum simulation of Gaussian states and circuits.
• Gaussian Bosonic evolutions on exponentially many modes are computationally equivalent to universal quantum computers.
• The framework provides a powerful tool for exploring complex quantum systems and their dynamics.