A quantum circuit and method for Schur transform includes: a first quantum register including n quantum systems initialized to an initial state of “0”, where n is an integer and represents a number of quantum systems; a second quantum register including m quantum systems initialized to the initial state of “0”, where m is an integer and represents a required workspace; a first quantum circuit that operates on only the first register and performs a block diagonalization of the n quantum systems into permutation modules; a second quantum circuit that operates on both registers and block diagonalizes each of the permutation modules using a QFTPermMod operation; and one or more quantum output registers coupled to the second quantum circuit for holding a basis for the Schur transform.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A quantum circuit for Schur transform comprising: a first quantum register including n quantum systems initialized to an initial state of “0”, where n is an integer and represents a number of quantum systems; a second quantum register including m quantum systems initialized to the initial state of “0”, where m is an integer and represents a required workspace; a first quantum circuit that operates on only the first register and performs a block diagonalization of the n quantum systems into permutation modules; a second quantum circuit that operates on both registers and block diagonalizes each of the permutation modules using a QFTPermMod operation; and one or more quantum output registers coupled to the second quantum circuit for holding a basis for the Schur transform. 2. The quantum circuit of claim 1, wherein m is equal to n. 3. The quantum circuit of claim 1, wherein the QFTPermMod operation comprises: providing a first quantum register including a computational basis given by elements of the transversal of G0 in Sn where G0 is a Young subgroup, and Sn is a subgroup tower; providing a second quantum register that is an ancilla register of log |G0| qubits and is initialized to |0>; performing an inverse quantum Fourier Transform (QFT−1(G0)) on the second quantum register; performing a generalized phase estimation (GPER) on the inverse QFT−1(G0) of the second quantum register and the first register, where R is the right regular representation of Sn; and performing a quantum Fourier Transform (QFT(Sn)) on the first and second quantum registers. 4. The quantum circuit of claim 1, wherein the quantum circuit performs the Schur transform using a representation theory of symmetric groups. 5. The quantum circuit of claim 1, wherein the quantum circuit performs the Schur transform using a Schur-Weyl duality. 6. A quantum method for performing Schur transform, the method comprising: providing a first quantum register including n quantum systems initialized to an initial state of “0”, where n is an integer and represents a number of quantum systems; providing a second quantum register including m quantum systems initialized to the initial state of “0”, where m is an integer and represents a required workspace; performing a block diagonalization on the first register into permutation modules; performing block diagonalizing on each of the permutation modules using a QFTPermMod operation; and holding outputs of the block diagonalization of each of the permutation modules as a basis for the Schur transform. 7. The quantum method of claim 6, wherein m is equal to n. 8. The quantum method of claim 6, wherein the QFTPermMod operation comprises: providing a first quantum register including a computational basis given by elements of the transversal of G0 in Sn, where G0 is a Young subgroup, and Sn is a subgroup tower; providing a second quantum register that is an ancilla register of log |G0| qubits and is initialized to |0>; performing an inverse quantum Fourier Transform (QFT−1(G0)) on the second quantum register; performing a generalized phase estimation (GPER) on the inverse QFT−1(G0) of the second quantum register and the first register, where R is the right regular representation of Sn; and performing a quantum Fourier Transform (QFT(Sn)) on the first and second quantum registers. 9. The quantum method of claim 6, wherein the quantum method performs the Schur transform using a representation theory of symmetric groups. 10. The quantum method of claim 1, wherein the quantum method performs the Schur transform using a Schur-Weyl duality.