Reducing unitary error in a quantum computation system

1. A method, executed on a quantum processor of a quantum computing system, for reducing error in a result of a quantum algorithm by modifying the quantum algorithm to a modified quantum algorithm to determine the result, the method comprising:

accessing, at random from a datastore of a classical computing system, a primary error reduction operation pair of a plurality of primary error reduction operation pairs associated with a primary quantum operation included in the quantum algorithm, the primary quantum operation producing a primary operation result, and each primary error reduction operation pair producing an equivalent operation result to the primary operation result when quantum operations of the primary error reduction operation pair are executed before and after the primary quantum operation;

generating, using the classical computing system, the modified quantum algorithm, the modified quantum algorithm comprising:

a first quantum operation of the primary error reduction operation pair executed before the primary quantum operation,

a second quantum operation of the primary error reduction operation pair executed after the primary quantum operation, wherein:

the first quantum operation, the primary quantum operation, and the second quantum operation executed in series produce the primary operation result; and

executing, using the quantum processor of the quantum computing system, the modified quantum algorithm to determine the result.

2. The method of claim 1 , wherein the quantum algorithm includes a secondary quantum operation, the secondary quantum operation producing a secondary operation result, wherein the primary quantum operation and the secondary quantum operation are executed in series to produce a tertiary operation result, and further comprising:

accessing, at random, a secondary error reduction operation pair of a plurality of secondary error reduction operation pairs associated with the secondary quantum operation, each secondary error reduction operation pair for producing an equivalent operation result to the secondary operation result when executed about the secondary quantum operation; and

wherein the generated generating the modified quantum algorithm comprises includes:

a third quantum operation of the secondary error reduction operation pair executed before the secondary quantum operation;

a fourth quantum operation of the secondary error reduction operation pair executed after the secondary quantum operation, and wherein:

the third quantum operation, the secondary quantum operation, and the fourth quantum operation are executed in series produce the secondary operation result.

3. The method of claim 2 , wherein the modified quantum algorithm includes the first quantum operation, the primary quantum operation, the second quantum operation, the third quantum operation, the secondary quantum operation, and the fourth quantum operation that when executed in series produce the tertiary operation result.

4. The method of claim 2 , further comprising:

determining a replacement quantum operation based on the second quantum operation and the third quantum operation; and

generating a reduced quantum algorithm by further modifying the modified quantum algorithm, the modification comprising replacing the second quantum operation and the third quantum operation in the modified quantum algorithm with the replacement quantum operation.

5. The method of claim 4 , further comprising:

executing the reduced quantum algorithm on the quantum processor to determine the result of the quantum algorithm.

6. The method of claim 4 , wherein the reduced quantum algorithm includes the first quantum operation, the primary quantum operation, the replacement quantum operation, the secondary quantum operation, and the fourth quantum operation that when executed in series produce the tertiary operation result.

7. The method of claim 4 , wherein the reduced quantum algorithm generates fewer unitary errors than the quantum algorithm and is executed more quickly than the modified quantum algorithm.

8. The method of claim 1 , wherein executing the primary quantum operation and the second quantum operation of the primary error reduction operation pair is equivalent to executing a representative quantum operation and the primary quantum operation, and wherein the first quantum operation of the primary error reduction operation pair is an inverse of the representative quantum operation.

9. The method of claim 8 , wherein the first quantum operation of the primary error reduction operation pair executed in series with the representative quantum operation produces an identity matrix.

10. The method of claim 8 , wherein the second quantum operation of the primary error reduction operation pair is a unitary operation, and wherein the first quantum operation of the primary error reduction operation pair is a conjugate transpose of the representative quantum operation.

11. The method of claim 1 wherein the modified quantum algorithm generates fewer unitary errors than the quantum algorithm.

12. The method of claim 1 , wherein reducing error in the quantum algorithm occurs for any of a superconducting circuit based quantum processor, an ion trapped based quantum processor, or a spin system based quantum processor.

13. The method of claim 1 , where a type of the quantum processor is any of a superconducting circuit, an ion trap, or a spin system.

14. A system for reducing error when executing a quantum algorithm by modifying the quantum algorithm to a modified quantum algorithm to determine a result, the system comprising:

a classical processing system including one or more processors;

a non-transitory, computer-readable storage medium storing a computer program executable by the classical processing system to perform steps comprising:

accessing, at random from a datastore of a classical computing system, a primary error reduction operation pair of a plurality of primary error reduction operation pairs associated with a primary quantum operation included in the quantum algorithm, the primary quantum operation producing a primary operation result, and each primary error reduction operation pair producing an equivalent operation result to the primary operation result when quantum operations of the primary error reduction operation pair are executed before and after the primary quantum operation;

generating, using the classical computing system, the modified quantum algorithm, the modified quantum algorithm comprising:

a first quantum operation of the primary error reduction operation pair executed before the primary quantum operation,

a second quantum operation of the primary error reduction operation pair executed after the primary quantum operation, wherein:

the first quantum operation, the primary quantum operation, and the second quantum operation executed in series produce the primary operation result; and

a quantum processing system configured to execute the modified quantum algorithm on a quantum processor, wherein the modified quantum algorithm, when executed, determines the result of the quantum algorithm with less error than when the quantum algorithm is executed on the quantum processor.

15. A non-transitory computer-readable storage medium storing computer instructions for reducing error in a result of a quantum algorithm by modifying the quantum algorithm to a modified quantum algorithm to determine the result, the computer instructions, when executed by one or more processors, causing the one or more processors to:

accessing, at random from a datastore of a classical computing system, a primary error reduction operation pair of a plurality of primary error reduction operation pairs associated with a primary quantum operation included in the quantum algorithm, the primary quantum operation producing a primary operation result, and each primary error reduction operation pair producing an equivalent operation result to the primary operation result when quantum operations of the primary error reduction operation pair are executed before and after the primary quantum operation;

generating, using the classical computing system, the modified quantum algorithm, the modified quantum algorithm comprising:

a first quantum operation of the primary error reduction operation pair executed before the primary quantum operation,

a second quantum operation of the primary error reduction operation pair executed after the primary quantum operation, wherein:

the first quantum operation, the primary quantum operation, and the second quantum operation executed in series produce the primary operation result; and

executing, using the quantum processor of the quantum computing system, the modified quantum algorithm to determine the result.