Patent US10366339

Method for efficient implementation of diagonal operators over clifford+T basis
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US10366339

1. A method of defining a quantum circuit for implementing a diagonal unitary in a quantum computer, comprising: (3) (5)

receiving a definition of the diagonal unitary with respect to a set of n qubits, wherein n is a positive integer;

receiving an approximation precision;

based on a phase context, processing the diagonal unitary so as to select a plurality of single-qubit rotation operators having rotation angles in the phase context;

defining the quantum circuit based on the plurality of rotation operators applied to an ancillary qubit; and

implementing the quantum circuit based on the definition.

2. The method of claim 1, wherein the phase context is sparse. (0)

3. The method of claim 1, further comprising assessing a cost associated with the quantum circuit as defined based on the phase context. (2) (0)

4. The method of claim 3, wherein the quantum circuit defined based on the phase context includes a plurality of cascaded entanglement gate sequence pairs, and the cost of the quantum circuit is estimated based on the plurality of cascaded entanglement gate sequence pairs. (1) (0)

6. The method of claim 3, wherein the cost is associated with a number of single qubit rotations or a number of T-gates in the quantum circuit. (0)

7. The method of claim 1, wherein the quantum circuit is defined in a Clifford+T basis. (1) (0)

11. A system for designing a quantum computer, comprising: (5) (2)

a communication connection that receives a definition of a diagonal unitary over n qubits; and

a processor that: factors the diagonal unitary so that the diagonal unitary is representable as a product of the factors of the form V(ϕ_m,1_m)=diag(1, . . . , 1, ϕ_m, . . . , ϕ_m), wherein m is a positive integer, ϕ_mis a phase in a phase context, and 1_mis a number of occurrences of the phase ϕ_min V(ϕ_m,1_m); and

produces a quantum circuit design corresponding to the diagonal unitary based on the factors V(ϕ_m,1_m).

12. The system of claim 11, wherein the processor further establishes a single single-qubit rotation gate and at least one cascaded entanglement circuit with each of the factors V(ϕ_m,1_m), and the quantum circuit design is based on gate sequences associated with the single-qubit rotation gates and the cascaded entanglement circuits. (1) (0)

14. The system of claim 11, wherein processor defines gates for the at least one cascaded entanglement circuit associated with each of the factors V(ϕ_m,1_m) based on 1_mand a number of qubits n. (1) (0)

16. The system of claim 11, wherein the processor further establishes the phase context as a set of random phases. (0)

17. The system of claim 11, wherein the phase context is sparse. (1) (0)

19. The system of claim 11, wherein the processor produces the quantum circuit design based on quantum gates of the Clifford+T basis. (0)

20. A computer-assisted quantum circuit design method, comprising: (1) (3)

classifying a diagonal unitary as phase sparse or phase dense;

producing a quantum circuit design based on a factorization of the diagonal unitary over a phase context for any diagonal unitary classified as phase sparse; and

implementing the quantum circuit based on the quantum circuit design.

21. The computer-assisted quantum circuit design method of claim 20, wherein the quantum circuit design includes rotation circuits and entanglement circuits, and further comprising defining at least one entangling circuit based on a number of occurrences of a corresponding phase in the diagonal unitary. (0)

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Patent US10366339

Method for efficient implementation of diagonal operators over clifford+T basis

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