Simulation of Quantum Circuits Using the Big-Batch Tensor Network Method.

Area of Science:

• Quantum Computing
• Computational Physics
• Tensor Networks

Background:

• Simulating large quantum circuits is computationally intensive.
• Google's Sycamore circuits demonstrated quantum supremacy, challenging classical simulation capabilities.

Purpose of the Study:

• To develop a tensor network approach for computing amplitudes and probabilities of correlated bitstrings in quantum circuits.
• To apply this method to Google's Sycamore circuits and assess its efficiency.

Main Methods:

• Utilized a tensor network approach to compute exact amplitudes and probabilities for a large number of correlated bitstrings.
• Employed a computational cluster with 60 GPUs for simulating the Sycamore circuit (53 qubits, 20 cycles).
• Extended the method for full-amplitude simulation, comparing efficiency with existing Schrödinger and Schrödinger-Feynman methods.

Main Results:

• Successfully computed exact amplitudes and probabilities for 2x10^6 correlated bitstrings of the Sycamore circuit.
• Verified the Porter-Thomas distribution for Google's quantum circuits.
• Achieved full-amplitude simulation for circuits with up to 50 qubits, setting a new record.
• Demonstrated improved efficiency over existing methods for shallow and general quantum circuits.

Conclusions:

• The tensor network approach is effective for simulating large quantum circuits and verifying quantum supremacy claims.
• The method provides valuable datasets and benchmarks for developing approximate simulation techniques.
• This work advances the capability to simulate complex quantum systems and aids in quantum computer verification.