There is provided a method for implementing an algorithm for forming, or synthesizing, quantum circuits on a system capable of performing the quantum circuit synthesis by using a deterministic walk (i.e. a pseudo-random walk with a random or pseudo-random starting point). In one implementation, the deterministic walk is performed using a parallel search algorithm. In an implementation of the parallel search algorithm, a user utilizes a programming language to write instructions for a compiler. Then, a meet in the middle approach is utilized to separate the circuit into two halves. Next, the parallel search technique is used to find a claw, or a pair, which satisfies the circuit analysis. Subsequently there is the production of a result and/or a synthesis of the circuit if the pair is found.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A method for implementing an algorithm for synthesizing quantum circuits, the method comprising: performing one or more deterministic walks on a search space; and performing a circuit synthesis according to results of the one or more deterministic walks. 2. The method of claim 1, wherein a starting point for the one or more deterministic walks is chosen randomly. 3. The method of claim 1, further comprising determining a plurality of search spaces. 4. The method of claim 3, wherein there are two search spaces. 5. The method of claim 4, wherein the two spaces are of equal size. 6. The method of claim 1, wherein a meet in the middle algorithm is used. 7. The method of claim 1, wherein the one or more deterministic walks are performed in parallel. 8. The method of claim 7, wherein the parallel search comprises a mapping from unitary matrices to binary strings. 9. The method of claim 7, wherein the parallel search comprises a step of generating a list of distinguished points. 10. The method of claim 1, wherein the circuit synthesis comprises a step of finding a list of unitary matrices having a product within an error tolerance of a given value. 11. The method of claim 10, wherein the error tolerance is less than a machine precision value. 12. The method of claim 11, wherein the error tolerance is 0. 13. The method of claim 1, wherein the circuit synthesis uses a gate set. 14. The method of claim 13, wherein the gate set is universal. 15. A method for synthesizing quantum circuits, the method comprising the steps of: generating a starting point; mapping the starting point to a candidate matrix; applying a hash function to the candidate matrix to generate a new point; determining if the new point is a distinguished point; creating a distinguished point structure; storing the distinguished point structure; and finding a merging of trails with matrices of two different types. 16. The method of claim 15, wherein a plurality of collectors, workers, and verifiers are used to perform the method. 17. The method of claim 16, wherein inter-processor communication is used. 18. A non-transitory computer readable medium comprising computer executable instructions for: performing one or more deterministic walks on a search space; and performing a circuit synthesis according to results of the one or more deterministic walks. 19. A quantum computing system comprising a processor and memory, the memory comprising computer executable instructions for synthesizing quantum circuits by: performing one or more deterministic walks on a search space; and performing a circuit synthesis according to results of the one or more deterministic walks.