Schrödinger-Heisenberg Variational Quantum Algorithms.

Area of Science:

• Quantum Computing
• Computational Physics
• Quantum Chemistry

Background:

• Intermediate-scale quantum computing (tens to hundreds of qubits) shows promise for complex problems in chemistry and physics.
• High accuracy requirements for quantum advantage are limited by gate infidelity (0.1%-1%) and restricted circuit depth.
• Current variational quantum algorithms (VQAs) struggle to explore complex quantum states due to circuit depth limitations.

Purpose of the Study:

• To propose a new paradigm, Schrödinger-Heisenberg variational quantum algorithms (SHVQA), to address the limitations of current VQAs.
• To enable efficient measurement of expectation values for states requiring deep circuits using shallower circuits.
• To enhance the expressivity and accuracy of quantum computations on near-term quantum hardware.

Main Methods:

• Implementation of SHVQA by integrating a virtual Heisenberg circuit with a real shallow Schrödinger circuit.
• Utilizing a Clifford virtual circuit for efficient classical processing of Hamiltonian effects.
• Leveraging the virtual circuit to enlarge state expressivity and achieve larger unitary designs.

Main Results:

• SHVQA allows efficient measurement of expectation values with shallower circuits compared to conventional methods.
• Numerical experiments demonstrate improved approximation of random states and higher-fidelity solutions for models like XXZ.
• Accurate quantum simulation of electronic structure Hamiltonians for small molecules was achieved.

Conclusions:

• SHVQA significantly enhances the accuracy and capability of quantum computations, overcoming depth limitations imposed by gate infidelity.
• The proposed method enables achieving results comparable to deeper circuits or more accurate operations with current hardware.
• SHVQA, combined with quantum error mitigation, offers a viable path towards accurate quantum computing on near-term devices.