Memory-saving optimization of quadratic forms

One or more non-transitory computer-readable storage media configured to store instructions that, in response to being executed, cause a system to perform operations, the operations comprising:

• obtaining a first copy of a quantum state and a second copy of the quantum state, the first copy and the second copy of the quantum state representing a convex optimization problem in which the first copy of the quantum state and the second copy of the quantum state include respective index quantum registers that each hold a plurality of indices and respective mixing state quantum registers that each hold one or more quantum mixing states;
• amplifying and measuring an amplitude corresponding to the index quantum register associated with the first copy of the quantum state, the measured amplified amplitude of the index quantum register corresponding to a particular index of the plurality of indices;
• determining a final quantum mixing state corresponding to the mixing state quantum register of the second copy of the quantum state based on the measured amplified amplitude and the particular index of the index quantum register associated with the first copy of the quantum state;
• and
• determining a solution to the convex optimization problem based on the final quantum mixing state.

A system comprising:

• one or more processors;
• and
• one or more non-transitory computer-readable storage media configured to store instructions that, in response to being executed, cause the system to perform operations, the operations comprising:
• obtaining a first copy of a quantum state and a second copy of the quantum state, the first copy and the second copy of the quantum state representing a convex optimization problem in which the first copy of the quantum state and the second copy of the quantum state include respective index quantum registers that each hold a plurality of indices and respective mixing state quantum registers that each hold one or more quantum mixing states;
• amplifying and measuring an amplitude corresponding to the index quantum register associated with the first copy of the quantum state, the measured amplified amplitude of the index quantum register corresponding to a particular index of the plurality of indices;
• determining a final quantum mixing state corresponding to the mixing state quantum register of the second copy of the quantum state based on the measured amplified amplitude and the particular index of the index quantum register associated with the first copy of the quantum state;
• and
• determining a solution to the convex optimization problem based on the final quantum mixing state.