Method and system for quantum circuit synthesis using quaternion algebra

Patent metadata

Field	Value
Publication number	US-10740689-B2
Application number	US-201615565413-A
Country	US
Kind code	B2
Filing date	Apr 5, 2016
Priority date	Apr 10, 2015
Publication date	Aug 11, 2020
Grant date	Aug 11, 2020

Abstract

Quantum circuits are synthesized based on a projective gate set derived from a set of single-qubit gates, typically a basis set such as the Clifford+T gates or the V-gates. An initial projective gate set is used to determine at least one characteristic of a quaternion algebra, and the quaternion algebra is used to define a new projective gate set. Exactly synthesizable unitaries are identified, and a circuit approximating a target unitary is defined in the single-qubit gate set by mapping from the new projective gate set.

First claim

The invention claimed is:

1. A quantum circuit synthesis method implemented on a classical processor, comprising:
with the classical processor, selecting a single-qubit gate set; and
with the classical processor, processing the single-qubit gate set and determining a projective gate set corresponding to the single-qubit gate set, wherein the projective gate includes gates representable in a form

(

x

-

y
*

⁢

b

y
⁢

b

x
*

)

,

wherein x and y are complex numbers and b is a real number and x, y, and b specify the gates of the projective gate set.

2. The quantum circuit synthesis method of claim 1 , further comprising determining a mapping of the projective gate set to a quaternion algebra.

3. The quantum circuit synthesis method of claim 2 , wherein determining the mapping comprises establishing elements of the quaternion algebra.

4. The quantum circuit synthesis method of claim 2 , wherein the mapping is associated with a selected nth root of unity.

5. The quantum circuit synthesis method of claim 4 , wherein the mapping is associated with an 8 th or 10 th root of unity.

6. The quantum circuit synthesis method of claim 2 , wherein the elements of the quaternion algebra are established based on at least one Pauli matrix.

7. The quantum circuit synthesis method of claim 2 , wherein the elements of the quaternion algebra are established so that a first element corresponds to an identity matrix and a second element is associated with at least one of a Pauli X, Y, or Z matrix.

8. The quantum circuit synthesis method of claim 2 , further comprising determining a maximal order associated with the quaternion algebra that includes elements corresponding to the single-qubit gate set.

9. The quantum circuit synthesis method of claim 8 , further comprising determining a set of ideals corresponding to the single-qubit gate set.

10. The quantum circuit synthesis method of claim 2 , wherein the single-qubit gate set is associated with the Clifford+T basis or the V-basis.

11. A quantum circuit synthesizer, comprising:
a processor; and
at least one memory coupled to the processor and having stored thereon processor-executable instructions for a method that includes:
with the processor, selecting a single-qubit gate set, and
with the processor, processing the single-qubit gate set and determining a projective gate set corresponding to the single-qubit gate set, wherein the projective gate set includes gates representable in a form

(

x

-

y
*

⁢

b

y
⁢

b

x
*

)

,

wherein x and y are complex numbers and b is a real number and x, y, and b specify the gates of the projective gate set.

12. The quantum circuit synthesizer of claim 11 , wherein the method further comprises determining a mapping of the projective gate set to a quaternion algebra.

13. The quantum circuit synthesizer of claim 11 , wherein determining the mapping comprises establishing elements of the quaternion algebra.

14. The quantum circuit synthesizer of claim 11 , wherein the mapping is associated with a selected nth root of unity.

15. The quantum circuit synthesizer of claim 11 , wherein the mapping is associated with an 8 th or 10 th root of unity.

16. The quantum circuit synthesizer of claim 11 , wherein the elements of the quaternion algebra are established based on at least one Pauli matrix or wherein the elements of the quaternion algebra are established so that a first element corresponds to an identity matrix and a second element is associated with at least one of a Pauli X, Y, or Z matrix.

17. The quantum circuit synthesizer of claim 11 , wherein the method further comprises determining a maximal order associated with the quaternion algebra that includes elements corresponding to the single-qubit gate set.

18. The quantum circuit synthesizer of claim 11 , wherein the method further comprises determining a set of ideals corresponding to the single-qubit gate set.

19. The quantum circuit synthesizer of claim 11 , wherein the single-qubit gate set is associated with the Clifford+T basis or the V-basis.

Assignees

• Microsoft Technology Licensing Llc

Inventors

• Kliuchnikov Vadym
• Yard Jon

Classifications

• G06N10/20 Primary

  Models of quantum computing, e.g. quantum circuits or universal quantum computers · CPC title

• G06F17/16

  Matrix or vector computation {, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization (matrix transposition G06F7/78)} · CPC title

• G06N10/00 Primary

  Quantum computing, i.e. information processing based on quantum-mechanical phenomena · CPC title