Constant depth, near constant depth, and subcubic size threshold circuits for linear algebraic calculations

A neuromorphic computer comprising:

• a plurality of threshold gates or spiking neurons configured to compute a specific linear algebraic calculation having a dominant size of N in a manner that is simultaneously efficient and at a near constant depth, wherein “efficient” is defined as a calculation algorithm that uses fewer of the plurality of threshold gates than a naïve algorithm, wherein the naïve algorithm is a straightforward algorithm for solving the specific linear algebraic calculation, wherein “constant depth” is defined as an algorithm that has an execution time that is independent of a size of an input to the specific linear algebraic calculation, and wherein the near constant depth comprises a computing depth equal to or between O(log(log(N)) and the constant depth.

A method of manufacturing a neuromorphic computer tailored to perform a specific linear algebraic calculation, the method comprising:

• manufacturing a plurality of threshold gates or spiking neurons;
• and
• arranging the plurality of threshold gates or spiking neurons to compute the linear algebraic calculation having a dominant size N in a manner that is simultaneously efficient and at a near constant depth, wherein “efficient” is defined as a calculation algorithm that uses fewer of the plurality of threshold gates than a naïve algorithm, wherein the naïve algorithm is a straightforward algorithm for solving the linear algebraic calculation, wherein “constant depth” is defined as an algorithm that has an execution time that is independent of a size of an input to the linear algebraic calculation, and wherein the near constant depth comprises a computing depth equal to or between O(log(log(N)) and the constant depth.