Goldman Sachs &co. LLC

International Business Machines Corporation

William Joseph Zeng

Stefan Woerner

Guglielmo Mazzola

Nikitas Stamatopoulos

Iordanis Kerenidis

Farrokh Labib

Anupam Prakash

Rajiv Krishnakumar

Shouvanik Chakrabarti

Tudor Giurgica-Tiron

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

An asynchronous approach to implementing a quantum algorithm can reduce dead time of a quantum information processing unit (QIPU). Multiple parameter sets are determined for a quantum program by a controller and the QIPU is instructed to execute the quantum program for the parameter sets. Results from each program execution are returned to the controller. After one or more results are received, the controller determines an updated parameter set while the QIPU continues executing the quantum program for the remaining parameter sets. The QIPU is instructed to execute the quantum program for the updated parameter set (e.g., immediately, after a current program execution, or after the remaining parameter sets are processed). This asynchronous approach can result in the QIPU having little or no dead time, and thus can make more efficient use of the QIPU.

Asynchronous quantum information processing

This disclosure relates to enhanced methods of operating quantum computing systems to perform amplitude estimation. More than that, the methods may be tuned to accommodate for specific noise levels (e.g., in given a quantum device). Embodiments also enable quantum computing systems to perform amplitude estimation faster than amplitude estimation algorithms performed using a classical (non-quantum) computer.

Methods of operating quantum computing systems for amplitude estimation

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William Joseph Zeng