Claude independently redesigned quantum circuits and in seven of the eight tasks reduced two scarce resources at once: the number of qubits and Toffoli valves. For the eighth task, the model found a new reversible architecture, and one of its variants required 12% more qubits than the most compact previous scheme, but reduced the number of valves 17 times. The authors of the work claim that Claude found new ways to build calculations, rather than limited to small optimization of ready-made solutions.
The quantum scheme consists of a sequence of operations over qubits. The fewer qubits the algorithm needs, the more modest the requirements for the future computer, and the reduction in the number of valves usually allows you to finish the calculation faster. Toffoli valves are particularly expensive, so researchers often consider their number when they estimate the resources of the quantum algorithm.
Claude Mythos 5 received text descriptions of eight tasks from chemistry, optimization, modeling, numerical computing and number theory. The model wrote the code of the scheme, after which a separate program checked the correctness of the solution and calculated the costs. The score was returning Claude, and the model tried the following option. During normal cycles, the person did not intervene, although the researchers set the initial conditions and sometimes asked to expand the search for possible solutions.
The most unusual result appeared when working with the addition of points on the elliptic curve. The operation is necessary for quantum algorithms that can solve the problem of discrete logarithming, on the complexity of which is held part of modern cryptography. Most of the resources here are taken by modular circulation, a mathematical operation, remotely resembling a division with numbers that cycle through a given limit.
Conventional computers can perform modular circulation by divsteps. For the quantum scheme, there was a problem: the calculation should remain reversible, so you can not just erase the information about which path the program chose in the previous step. If you keep the whole story, you will need additional qubits.
Claude proposed to restore the necessary information from current numerical values instead of storing a full history. The first rules worked only on small examples, after which the model turned to mathematical analysis, brought out new algebraic ratios and received a formula for restoring past steps. Claude checked it on numerical models and then formalized the proof at Lean. It took 53 hours to find a solution for a problem with an elliptical curve with minimal participation of people, follows from the description of the experiment.
In the second revealing task, Claude took up the Reed-Solomon decoder inside the quantum DQI optimization algorithm. The previous diagram relied on the extended Euclid algorithm, where the sequence of actions depends on the input data. Claude chose the Berlecamp-Massey algorithm, which repeats the same type of steps fixed number times and is better suited for quantum circuit. After additional changes, the number of valves in the most expensive part of the decoder decreased by about 12 times.
The model also tried to remove the extra storage of memory. Claude performed 403 million simulations and found that it is almost always enough to retain only one exceptional intermediate value. For him, the scheme reserves 19 qubits instead of the hundreds that would be needed when calculating for the worst case scenario. Approximately one launch of 10 000 requires more memory and ends with an error, but the conditions of the task allow such a frequency of failures.
The resulting circuits do not in themselves solve the hardware problems of quantum computers. Qubits are still easily lost due to interference, and practical machines need error correction, quick decoders and sophisticated control electronics. The work shows a narrower but more important result: the language model is able to look for new mathematical ways to reduce the cost of quantum computing and independently check the solutions found.
The quantum scheme consists of a sequence of operations over qubits. The fewer qubits the algorithm needs, the more modest the requirements for the future computer, and the reduction in the number of valves usually allows you to finish the calculation faster. Toffoli valves are particularly expensive, so researchers often consider their number when they estimate the resources of the quantum algorithm.
Claude Mythos 5 received text descriptions of eight tasks from chemistry, optimization, modeling, numerical computing and number theory. The model wrote the code of the scheme, after which a separate program checked the correctness of the solution and calculated the costs. The score was returning Claude, and the model tried the following option. During normal cycles, the person did not intervene, although the researchers set the initial conditions and sometimes asked to expand the search for possible solutions.
The most unusual result appeared when working with the addition of points on the elliptic curve. The operation is necessary for quantum algorithms that can solve the problem of discrete logarithming, on the complexity of which is held part of modern cryptography. Most of the resources here are taken by modular circulation, a mathematical operation, remotely resembling a division with numbers that cycle through a given limit.
Conventional computers can perform modular circulation by divsteps. For the quantum scheme, there was a problem: the calculation should remain reversible, so you can not just erase the information about which path the program chose in the previous step. If you keep the whole story, you will need additional qubits.
Claude proposed to restore the necessary information from current numerical values instead of storing a full history. The first rules worked only on small examples, after which the model turned to mathematical analysis, brought out new algebraic ratios and received a formula for restoring past steps. Claude checked it on numerical models and then formalized the proof at Lean. It took 53 hours to find a solution for a problem with an elliptical curve with minimal participation of people, follows from the description of the experiment.
In the second revealing task, Claude took up the Reed-Solomon decoder inside the quantum DQI optimization algorithm. The previous diagram relied on the extended Euclid algorithm, where the sequence of actions depends on the input data. Claude chose the Berlecamp-Massey algorithm, which repeats the same type of steps fixed number times and is better suited for quantum circuit. After additional changes, the number of valves in the most expensive part of the decoder decreased by about 12 times.
The model also tried to remove the extra storage of memory. Claude performed 403 million simulations and found that it is almost always enough to retain only one exceptional intermediate value. For him, the scheme reserves 19 qubits instead of the hundreds that would be needed when calculating for the worst case scenario. Approximately one launch of 10 000 requires more memory and ends with an error, but the conditions of the task allow such a frequency of failures.
The resulting circuits do not in themselves solve the hardware problems of quantum computers. Qubits are still easily lost due to interference, and practical machines need error correction, quick decoders and sophisticated control electronics. The work shows a narrower but more important result: the language model is able to look for new mathematical ways to reduce the cost of quantum computing and independently check the solutions found.
