A method and associated systems for using wreath products and invariance groups to test a partially symmetric quantum-logic circuits. A test system receives information that describes the architecture of a quantum-logic circuit to be tested. The system uses this information to hierarchically organize the circuit's inputs into non-overlapping blocks. The system creates set of groups associated with the blocks, and then generates an invariance group that contains one or more invariant permutations of the inputs by computing a wreath product of the set of groups. These invariant permutations identify a minimal number of tests required to verify the circuit for all possible input vectors. The system then directs a test apparatus to perform the resulting optimized test sequence upon the circuit.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A quantum-logic test-development system comprising a processor, a memory coupled to the processor, and a computer-readable hardware storage device coupled to the processor, the storage device containing program code configured to be run by the processor via the memory to implement a method for optimizing testing of a partially symmetric quantum-logic circuit by using wreath products and invariance groups, the method comprising: the system receiving architectural information about a quantum-logic circuit capable of being represented by a function f( ); the system evenly dividing a set of inputs of the circuit into a set of non-intersecting first-level blocks, where every first-level block contains a same number of inputs; the system evenly partitioning the set of first-level blocks into a set of non-intersecting second-level blocks, where every second-level block contains a same number of first-level blocks; the system creating a first-level group G1 that comprises a set of first-level indices and a set of one or more first-level permutation operations capable of being performed upon the set of first-level indices; the system defining a second-level group G2 that comprises a set of second-level indices and a set of one or more second-level permutation operations capable of being performed upon the set of second-level indices, where a number of the set of second-level indices equals the number of first-level blocks in each second-level block; and the system generating a first wreath product G1 G2 as a function of the evenly dividing and the evenly partitioning, where is an unrestricted wreath-product operator, and where the first wreath product represents a first invariance group of the function f( ). 2. The system of claim 1, where the first invariance group comprises a set of invariant permutations that each identify a permutation of at least two inputs of the set of inputs, and where no output of the quantum-logic circuit changes state when the quantum-logic circuit receives a permuted input vector generated by performing a permutation of the set of invariant permutations upon the circuit's most recent input vector. 3. The system of claim 2, further comprising: the system optimizing a procedure for testing the quantum-logic circuit, where the procedure comprises a series of tests that each verify correct operation of the quantum-logic circuit in response to receiving a distinct input vector of a set of input vectors, and where the optimizing comprises deleting from the series of tests any test that would attempt to verify correct operation of the quantum-logic circuit in response to receiving a permuted input vector generated by performing a permutation of the set of invariant permutations upon an input vector already verified by another test of the series of tests. 4. The system of claim 1, where the quantum-circuit has at least sixteen inputs divided into at least eight non-intersecting first-level blocks and at least four non-intersecting second-level blocks, the method further comprising: the system evenly apportioning, as a function of the architectural information, the at least four second-level blocks into at least two non-intersecting third-level blocks, where every third-level block contains a same number of second-level blocks; the system identifying a third-level group G3 that comprises a set of third-level indices and a set of one or more third-level permutation operations capable of being performed upon the set of third-level indices, where a number of the set of third-level indices equals the number of second-level blocks in each third-level block; and the system generating a second wreath product (G1 G2) G3, where the second wreath product represents a second invariance group of the function f( ), where the second invariance group comprises a second set of invariant permutations that each identify a permutation of at least inputs of the at least sixteen inputs, and where no output of the quantum-logic circuit changes state when the quantum-logic circuit receives a permuted input vector generated by performing a permutation of the second set of invariant pemutations upon the circuit's most recent input vector. 5. The system of claim 1, where the first wreath product equals the group ((G1 x . . . Gm)x H, X x Y), where x is a Cartesian product operator, where m=the number of first-level blocks contained in each second-level block, where each group G1 . . . Gm is an identical copy of the set of first-level indices, where H=the set of second-level indices, where X=the set of first-level permutation operations, and where Y=the set of second-level permutation operations. 6. The system of claim 4, where the first wreath product equals the group ((G1 x . . . x Gm) x H, X x Y), where x is a Cartesian product operator, where m=the number of first-level blocks contained in each second-level block, where each group G1 . . . Gm is an identical copy of the set of first-level indices, where H=the set of second-level indices, where X=the set of first-level permutation operations, where Y=the set of second-level permutation operations, where the second wreath product equals the group ((H1 x . . . x Hp) x L, X x Y x Z)=(((G1 x G2 . . . x Gm) x H1) x ((Gm+1 x Gm+2 . . . x G2m) x H2 . . . x ((G(p−1)m+1 x Gp−1)m+2 . . . x Gpm) x Hp)) x L, X x Y x Z), where p=the number of second-level blocks contained in each third-level block, where each group H1 . . . Hp is an identical copy of the set of second-level indices, where L=the set of third-level indices, and where Z=the set of third-level permutation operations. 7. The system of claim 1, where the received architectural information identifies a number of inputs of the circuit, a number of outputs of the circuit, a number of states that may be assumed by each input of the circuit, and a number of states that may be assumed by each output of the circuit. 8. The system of claim 3, further comprising: the system directing a test apparatus to perform the series of tests upon the quantum-logic circuit, where the series of tests are selected as a function of the optimized procedure for testing the circuit. 9. A method for optimizing testing of a partially symmetric quantum-logic circuit by using wreath products and invariance groups, the method comprising: receiving architectural information about a quantum-logic circuit capable of being represented by a function f( ); evenly dividing a set of inputs of the circuit into a set of non-intersecting first-level blocks, where every first-level block contains a same number of inputs; evenly partitioning the set of first-level blocks into a set of non-intersecting second-level blocks, where every second-level block contains a same number of first-level blocks; creating a first-level group G1 that comprises a set of first-level indices and a set of one or more first-level permutation operations capable of being performed upon the set of first-level indices; defining a second-level group G2 that comprises a set of second-level indices and a set of one or more second-level permutation operations capable of being performed upon the set of second-level indices, where a number of the set of second-level indices equals the number of first-level blocks in each second-level block; and generating a first wreath product G1 G2 as a function of the evenly dividing and the evenly partitioning, where is an unrestricted wreath-product operator, and where the first wreath product represents a first invariance group of the function f( ). 10. The method of claim 9, where the first invariance group comprises a set of invariant permutations that each identify a permutation of at least two inputs of the set of inputs, and where no output of the quantum-logic circuit changes state when the quantum-logic circuit receives a permuted input vector generated by performing a permutation of the set of invariant permutations upon the circuit's most recent input vector. 11. The method of claim 10, further comprising: the system optimizing a procedure for testing the quantum-logic circuit, where the procedure comprises a series of tests that each verify correct operation of the quantum-logic circuit in response to receiving a distinct input vector of a set of input vectors, and where the optimizing comprises deleting from the series of tests any test that would attempt to verify correct operation of the quantum-logic circuit in response to receiving a permuted input vector generated by performing a permutation of the set of invariant permutations upon an input vector already verified by another test of the series of tests. 12. The method of claim 9, where the quantum-circuit has at least sixteen inputs divided into at least eight non-intersecting first-level blocks and at least four non-intersecting second-level blocks, the method further comprising evenly apportioning, as a function of the architectural information, all the at least four second-level blocks into at least two non-intersecting third-level blocks, where every third-level block contains a same number of second-level blocks; identifying a third-level group G3 that comprises a set of third-level indices and a set of one or more third-level permutation operations capable of being performed upon the set of third-level indices, where a number of the set of third-level indices equals the number of second-level blocks in each third-level block; and generating a second wreath product (G1 G2) G3, where the second wreath product represents a second invariance group of the function f( ), where the second invariance group comprises a second set of invariant permutations that each identify a permutation of at least inputs of the at least sixteen inputs, and where no output of the quantum-logic circuit changes state when the quantum-logic circuit receives a permuted input vector generated by performing a permutation of the second set of invariant permutations upon the circuit's most recent input vector. 13. The method of claim 9, where the first wreath product equals the group ((G1 x . . . Gm) x H, X x Y), where x is a Cartesian product operator, where m=the number of first-level blocks contained in each second-level block, where each group G1 . . . Gm is an identical copy of the set of first-level indices, where H=the set of second-level indices, where X=the set of first-level pe ion operations, and where Y=the set of second-level permutation operations. 14. The method of claim 12, where the first wreath product equals the group ((G1 x . . . Gm) x H, X x Y), where x is a Cartesian product operator, where m=the number of first-level blocks contained in each second-level block, where each group G1 . . . Gm is an identical copy of the set of first-level indices, where H=the set of second-level indices, where X=the set of first-level permutation operations, where Y=the set of second-level permutation operations, where the second wreath product equals the group ((H1 x . . . x Hp) x L, X x Y x Z)=(((G1 x G2 . . . x Gm) x H1) x ((Gm+1 x Gm+2 . . . x G2m) x H2 . . . x ((G(p−1)m+1 x G(p−1)m+2 . . . x Gpm) x Hp)) x L, X x Y x Z), where p=the number of second-level blocks contained in each third-level block, where each group H1 . . . Hp is an identical copy of the set of second-level indices, where L=the set of third-level indices, and where Z=the set of third-level permutation operations. 15. The method of claim 9, further comprising providing at least one support service for at least one of creating, integrating, hosting, maintaining, and deploying computer-readable program code in the computer system, wherein the computer-readable program code in combination with the computer system is configured to implement the receiving, the evenly dividing, the evenly partitioning, the creating, the defining, and the generating. 16. A computer program product, comprising a computer-readable hardware storage device having a computer-readable program code stored therein, the program code configured to be executed by a quantum-logic test-development system comprising a processor, a memory coupled to the processor, and a computer-readable hardware storage device coupled to the processor, the storage device containing program code configured to be run by the processor via the memory to implement a method for optimizing testing of a partially symmetric quantum-logic circuit by using wreath products and invariance groups, the method comprising: the system receiving architectural information about a quantum-logic circuit capable of being represented by a function f( ); the system evenly dividing a set of inputs of the circuit into a set of non-intersecting first-level blocks, where every first-level block contains a same number of inputs; the system evenly partitioning the set of first-level blocks into a set of non-intersecting second-level blocks, where every second-level block contains a same number of first-level blocks; the system creating a first-level group G1 that comprises a set of first-level indices and a set of one or more first-level permutation operations capable of being performed upon the set of first-level indices; the system defining a second-level group G2 that comprises a set of second-level indices and a set of one or more second-level permutation operations capable of being performed upon the set of second-level indices, where a number of the set of second-level indices equals the number of first-level blocks in each second-level block; and the system generating a first wreath product G1 G2 as a function of the evenly dividing and the evenly partitioning, where is an unrestricted wreath-product operator, and where the first wreath product is a first invariance group of the function f( ), where the first wreath product equals the group ((G1 x . . . Gm) x H, X x Y), where x is a Cartesian product operator, where m=the number of first-level blocks contained in each second-level block, where each group G1 . . . Gm is an identical copy of the set of first-level indices, where H=the set of second-level indices, where X=the set of first-level permutation operations, and where Y=the set of second-level permutation operations. 17. The computer program product of claim 16, where the first invariance group comprises a set of invariant permutations that each identify a permutation of at least two inputs of the set of inputs, and where no output of the quantum-logic circuit changes state when the quantum-logic circuit receives a permuted input vector generated by performing a permutation of the set of invariant permutations upon the circuit's most recent input vector. 18. The computer program product of claim 16, further comprising: the system optimizing a procedure for testing the quantum-logic circuit, where the procedure comprises a series of tests that each verify correct operation of the quantum-logic circuit in response to receiving a distinct input vector of a set of input vectors, and where the optimizing comprises deleting from the series of tests any test that would attempt to verify correct operation of the quantum-logic circuit in response to receiving a permuted input vector generated by performing a permutation of the set of invariant permutations upon an input vector already verified by another test of the series of tests. 19. The computer program product of claim 16, where the quantum-circuit has at least sixteen inputs divided into at least eight non-intersecting first-level blocks and at least four non-intersecting second-level blocks, the method further comprising: the system evenly apportioning, as a function of the architectural information, all the at least four second-level blocks into at least two non-intersecting third-level blocks, where every third-level block contains a same number of second-level blocks; the system identifying a third-level group G3 that comprises a set of third-level indices and a set of one or more third-level permutation operations capable of being performed upon the set of third-level indices, where a number of the set of third-level indices equals the number of second-level blocks in each third-level block; and the system generating a second wreath product (G1 G2) G3, where the second wreath product represents a second invariance group of the function f( ); where the second invariance group comprises a second set of invariant permutations that each identify a permutation of at least two inputs of the at least sixteen inputs, and where no output of the quantum-logic circuit changes state when the quantum-logic circuit receives a permuted input vector generated by performing a permutation of the second set of invariant permutations upon the circuit's most recent input vector. 20. The computer program product of claim 19, where the second wreath product equals the group ((H1 x . . . x Hp) x L, X x Y x Z)=(((G1 x G2 . . . x Gm) x H1) x ((Gm+1 x Gm+2 . . . G2m) x H2 . . . x ((G(p−1)m+1 x G(p−1)m+2 . . . x Gpm) x Hp)) x L, X x Y x Z), where p=the number of second-level blocks contained in each third-level block, where each group H1 . . . Hp is an identical copy of the set of second-level indices, where L=the set of third-level indices, and where Z=the set of third-level permutation operations.