Goldman Sachs &co. LLC

International Business Machines Corporation

Nikitas Stamatopoulos

Stefan Woerner

Guglielmo Mazzola

William Joseph Zeng

Shouvanik Chakrabarti

Rajiv Krishnakumar

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.

Quantum advantage using quantum circuit for gradient estimation

Systems, computer-implemented methods, and computer program products to facilitate estimation of quantum resources to calculate an expectation value of a stochastic process using a re-parameterization method are provided. According to an embodiment, a system can comprise a processor that executes computer executable components stored in memory. The computer executable components can comprise a re-parameterization component that applies a quantum fault-tolerant operation to a variationally prepared quantum state corresponding to a probability distribution to produce a quantum state corresponding to a target probability distribution. The computer executable components can further comprise an estimation component that estimates at least one defined criterion of a quantum computer to be used to compute an expectation value of a stochastic process associated with the target probability distribution.

Quantum resource estimation using a re-parameterization method

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New York, NY, United States of America

Nikitas Stamatopoulos