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Quantum Computer Solves Math Problem from 1978 Olympiad
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In Short: A new study demonstrates that a quantum computer can perform logical mathematical reasoning, proving two theorems, including one from the 1978 International Mathematical Olympiad.
A new study has shown that quantum computers can transition from being advanced number crunchers to systems capable of executing logical mathematical reasoning. Researchers from Zhejiang University and Tsinghua University in China used a 121-qubit superconducting quantum processor to prove two theorems, including one from the 1978 International Mathematical Olympiad.
The researchers employed a hybrid implementation of Wu's method and symbolic proof search, where quantum circuits were used to propose, apply, and evaluate logical steps to reach the right deduction. This experiment marks a significant step forward in the field of math and quantum computing.
The study, published in Nature Communications, highlights that the quantum system consistently outperformed classical systems, with the advantage increasing exponentially as the complexity of the problems grew. While classical computers can solve these problems very quickly, the quantum system's performance was closer to the optimal quantum strategy.
This breakthrough demonstrates the potential of quantum computers to handle abstract concepts, algebraic formulas, and chains of logical arguments, which were previously challenging for quantum hardware. The researchers believe this could lead to significant advancements in automated theorem proving and other complex mathematical tasks.
What's still developing
- Quantum computers already exist and are advancing quickly, but scientists predict there's much, much more to come from them – and a new study points the way to another significant step forward in the field of math.
- "Here we report the experimental realization of automated geometry theorem proving on a fully programmable superconducting quantum processor," write the researchers in their paper.
- "As illustrative examples, we prove two theorems on a superconducting quantum processor: the perpendicularity of the diagonals of a square and a 1978 International Mathematical Olympiad geometry problem." The first theorem mentioned there was a test of quantum algebra.
- Next came the IMO theorem, a more complex geometry problem involving intersecting triangles and circles.
- Researchers had not previously demonstrated experimentally whether quantum circuits could be encoded this way, given the noise and instability usually associated with qubits.
- This is the quantum verification problem, and a new experiment has found an ingenious workaround – a game that puts each type of system to the test.
- And as the test became more difficult, the chasm between the quantum system's performance and the best possible classical performance yawned ever wider, according to their paper published in Nature Communications.
- As the experiments grew larger and required more quantum operations, hardware noise increasingly degraded their performance.