17990473. QUANTUM ADVANTAGE USING QUANTUM CIRCUIT FOR GRADIENT ESTIMATION simplified abstract (INTERNATIONAL BUSINESS MACHINES CORPORATION)
QUANTUM ADVANTAGE USING QUANTUM CIRCUIT FOR GRADIENT ESTIMATION
Organization Name
INTERNATIONAL BUSINESS MACHINES CORPORATION
Inventor(s)
Nikitas Stamatopoulos of New York NY (US)
Guglielmo Mazzola of Zurich (CH)
William J. Zeng of New York NY (US)
QUANTUM ADVANTAGE USING QUANTUM CIRCUIT FOR GRADIENT ESTIMATION - A simplified explanation of the abstract
This abstract first appeared for US patent application 17990473 titled 'QUANTUM ADVANTAGE USING QUANTUM CIRCUIT FOR GRADIENT ESTIMATION
Simplified Explanation
The patent application describes quantum gradient algorithms that offer an advantage over conventional methods in quantum computing systems. These algorithms are implemented using a quantum circuit and involve a phase oracle O based on a finite difference approximation with an order greater than zero. The complexity of the algorithm scales as (√{square root over (k)}/ϵ), where k represents the dimensionality of the gradient and ϵ is the desired error tolerance.
- Quantum gradient algorithms provide a quantum advantage over conventional methods.
- The algorithms are implemented using a quantum circuit on qubits of a quantum computing system.
- A phase oracle O is used, which is based on a finite difference approximation with an order greater than zero.
- The complexity of the algorithm scales as (√{square root over (k)}/ϵ), where k is the dimensionality of the gradient and ϵ is the desired error tolerance.
- The quantum circuit is repeatedly executed to determine a k-dimensional gradient of a function ƒ(x) within an error ϵ at point x.
Potential Applications
- Optimization problems in various fields such as finance, logistics, and engineering can benefit from the improved efficiency of quantum gradient algorithms.
- Machine learning and artificial intelligence applications that involve gradient-based optimization can be enhanced using these algorithms.
- Quantum chemistry simulations and molecular modeling can be improved by leveraging the quantum advantage provided by these algorithms.
Problems Solved
- Conventional methods for gradient-based optimization can be computationally expensive and time-consuming, especially for high-dimensional problems.
- Quantum gradient algorithms offer a more efficient approach to compute gradients, reducing the computational burden and enabling faster optimization.
- These algorithms address the challenges faced in quantum computing systems by utilizing the unique properties of quantum circuits and qubits.
Benefits
- Quantum gradient algorithms provide a quantum advantage, enabling faster and more efficient optimization compared to conventional methods.
- The use of quantum circuits and qubits allows for parallel computation, leading to significant speedup in gradient calculations.
- By reducing the computational complexity, these algorithms pave the way for solving larger and more complex optimization problems in various domains.
Original Abstract Submitted
Described herein are quantum gradient algorithms that result in a quantum advantage over conventional methods. In an example, a quantum circuit is configured to implement a quantum gradient algorithm when executed on qubits of a quantum computing system. The quantum gradient algorithm includes a phase oracle Odefined by a finite difference approximation with an order greater than zero, and a complexity of the quantum gradient algorithm scales as (√{square root over (k)}/ϵ). The quantum circuit is repeatedly executed on qubits of a quantum computing system to determine a k-dimensional gradient of a function ƒ(x) within an error ϵ at point x.
