Abstract: This disclosure relates to protocols and systems for generating random bit strings by amplifying weak bit strings using certified quantum random bit strings generated by measuring a quantum state of entangled photons. Some disclosed systems include a quantum apparatus comprising one or more quantum systems configured to generate entangled photons and measure their quantum state. Certain disclosed systems include one or more security tests, wherein at least one security test evaluates the quantum nature of the measurements using a Bell inequality. A randomness extractor can amplify the randomness of weak random strings using random strings certified by the security tests. The generated random bit strings may be used as cryptographic keys.

Abstract: In some aspects, the techniques described herein relate to a quantum method for solving a second-order cone program (SOCP) instance, the method including: defining a Newton system for the SOCP instance by constructing matrix G and vector h based on the SOCP instance; preconditioning matrix G and vector h via row normalization to reduce a condition number of matrix G; iteratively determining u until a predetermined iteration condition is met, the iterations including: causing a quantum computing system to apply matrix G and vector h to a quantum linear system solver (QLSS) to generate a quantum state; causing the quantum computing system to perform quantum state tomography on the quantum state; and updating a value of u based on a current value of u and the output of the quantum state tomography; and determining a solution to the SOCP instance based on the updated value of u.

Abstract: This disclosure relates to protocols and systems for generating random bit strings by amplifying weak bit strings using certified quantum random bit strings generated by measuring a quantum state of entangled photons. Some disclosed systems include a quantum apparatus comprising one or more quantum systems configured to generate entangled photons and measure their quantum state. Certain disclosed systems include one or more security tests, wherein at least one security test evaluates the quantum nature of the measurements using a Bell inequality. A randomness extractor can amplify the randomness of weak random strings using random strings certified by the security tests. The generated random bit strings may be used as cryptographic keys.