Fast reconstruction algorithm based on HMC sampling.

Area of Science:

• Quantum Computing
• Computational Physics

Background:

• Noisy Intermediate-Scale Quantum (NISQ) devices have limited qubit resources, hindering the implementation of complex quantum algorithms.
• Circuit cutting is a technique to partition large quantum circuits for execution on smaller quantum hardware, but incurs significant classical post-processing overhead.
• The classical overhead of circuit cutting scales exponentially with the number of cuts and qubits, limiting its application to large-scale problems.

Purpose of the Study:

• To develop a computationally efficient algorithm for reconstructing quantum circuits after applying circuit cutting.
• To reduce the classical post-processing overhead associated with circuit cutting techniques.
• To enable the execution of larger quantum circuits on NISQ devices.

Main Methods:

• Proposed a novel reconstruction algorithm utilizing Hamiltonian Monte Carlo (HMC) sampling.
• Employed Hamiltonian dynamics to efficiently sample high-probability solutions in exponentially large state spaces.
• Demonstrated the algorithm's effectiveness in reconstructing the original quantum circuit's probability distribution.

Main Results:

• The proposed HMC-based algorithm significantly reduces the post-processing overhead of circuit cutting.
• The method avoids excessive computation by efficiently exploring the state space.
• The computational cost of reconstruction scales favorably compared to existing methods.

Conclusions:

• The developed fast reconstruction algorithm is crucial for overcoming the limitations of circuit cutting on NISQ devices.
• This advancement facilitates the application of circuit cutting to larger and more complex quantum circuits.
• The research paves the way for broader utilization of quantum resources in the NISQ era.