Using multiple copies of the same quantum program makes the extra cost disappear proportionally.

A finite physical quantum computer cannot perfectly run an infinite family of different quantum operations. The researchers studied what happens when you store a target operation inside a quantum state, called a normalized Choi stateChoi stateA mathematical representation of a quantum channel as a quantum state, used for analysis and sampling., and reconstruct its results. To make this work, they ran real physical operations, measured them, and processed the data on a regular computer. They built a single method that exactly reconstructs any $d$-dimensional operation. They found that the extra sampling cost for one copy scales quadratically with the system dimension. If you add more identical program copies, this extra cost shrinks inversely with the number of copies. Essentially, having more quantum memory directly reduces the amount of classical sampling you need to do.

Why it matters

This quantifies a fundamental limit for quantum computing, showing how to exactly control quantum operations by trading between quantum memory and classical sampling. It affects engineers designing quantum systems, potentially reducing the resources needed for precise program execution.

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