US-12626171-B2 - Hadamard-free clifford circuits over linear nearest neighbor architecture

Abstract

According to an embodiment of the present invention, a method, system, and computer program product for reducing and performing quantum circuits. The Embodiment may include receiving, by a classical computer, a quantum circuit comprising a CZ layer and a CNOT layer. The Embodiment may include creating, by a classical computer, a modified quantum circuit based on the CZ layer and the CNOT layer, wherein the modified quantum circuit includes phase gates with CNOT gates that perform similar functions of the CZ gates in the CZ layer. The embodiment may include performing, on a quantum computer, the modified quantum circuit. The embodiment may reduce the depth of a quantum circuit, thereby enabling faster and more accurate computation of the quantum circuit.

Inventors

• Dmitri MASLOV
• Muye Yang

Assignees

• INTERNATIONAL BUSINESS MACHINES CORPORATION

Dates

Publication Date

20260512

Application Date

20221026

Claims (17)

1. 1 . A method comprising: receiving, by a classical computer, a quantum circuit comprising a CZ layer and a CNOT layer; creating, by the classical computer, a modified quantum circuit based on the CZ layer and the CNOT layer, wherein the modified quantum circuit includes phase gates with CNOT gates that perform functions of CZ gates in the CZ layer; and performing, on a quantum computer, the modified quantum circuit.
2. 2 . The method of claim 1 , wherein the quantum circuit further comprises a phase layer including one or more phase gates, and wherein creating the modified quantum circuit includes modifying phase gates of the phase layer based on the CZ gates in the CZ layer.
3. 3 . The method of claim 1 , wherein creating the modified quantum circuit comprises: determining a CNOT gate of the CNOT layer corresponding to a CZ gate of the CZ layer, wherein an operation performed by the CZ gate is included in an operation of the CNOT gate; determining one or more phase gates to apply to one or more CNOT gates such that the operation of the one or more phase gates and the one or more CNOT gates provides the same result as the CZ layer and the CNOT layer.
4. 4 . The method of claim 1 , wherein the CNOT layer comprises swap gates and swap+ gates, and wherein creating the modified quantum circuit comprises: determining an initial phase gate for each CNOT gate, wherein the phase gate is applied as a swap gate containing an equivalent calculation to a CZ gate from the CZ layer; for each swap+ gate: replace the swap gate used to determine the initial phase gate with a swap+ gate; and determine an updated phase gate based on the replaced swap+ gate; and repeat until all swap+ gates in original CNOT layer are introduced and an updated phase gate layer is created.
5. 5 . The method of claim 4 , wherein determining the initial phase gate comprises applying a phase gate to each swap gate containing an equivalent calculation to a CZ gate from the CZ layer.
6. 6 . The method of claim 4 , wherein determining the updated phase gates comprises updating six phase gates.
7. 7 . A system comprising one or more processors, one or more computer readable memories, one or more computer readable storage devices, one or more computer-readable storage devices, and program instructions stored on the one or more computer readable storage devices for execution by one or more processors via the one or more memories, the program instructions comprising instructions for: receiving, by a classical computer, a quantum circuit comprising a CZ layer and a CNOT layer; creating, by a classical computer, a modified quantum circuit based on the CZ layer and the CNOT layer, wherein the modified quantum circuit includes phase gates with CNOT gates that perform functions of CZ gates in the CZ layer; and performing, on a quantum computer, the modified quantum circuit.
8. 8 . The system of claim 7 , wherein the quantum circuit further comprises a phase layer including one or more phase gates, and wherein creating the modified quantum circuit includes modifying phase gates of the phase layer based on the CZ gates in the CZ layer.
9. 9 . The system of claim 7 , wherein creating the modified quantum circuit comprises: determining a CNOT gate of the CNOT layer corresponding to a CZ gate of the CZ layer, wherein an operation performed by the CZ gate is included in an operation of the CNOT gate; determining one or more phase gates to apply to one or more CNOT gates such that the operation of the one or more phase gates and the one or more CNOT gates provides the same result as the CZ layer and the CNOT layer.
10. 10 . The system of claim 7 , wherein the CNOT layer comprises swap gates and swap+ gates, and wherein creating the modified quantum circuit comprises: determining an initial phase gate for each CNOT gate, wherein the phase gate is applied as a swap gate containing an equivalent calculation to a CZ gate from the CZ layer; for each swap+ gate: replace the swap gate used to determine the initial phase gate with a swap+ gate; and determine an updated phase gate based on the replaced swap+ gate; and repeat until all swap+ gates in original CNOT layer are introduced and an updated phase gate layer is created.
11. 11 . The system of claim 10 , wherein determining the initial phase gate comprises applying a phase gate to each swap gate containing an equivalent calculation to a CZ gate from the CZ layer.
12. 12 . The system of claim 10 , wherein determining the updated phase gates comprises updating six phase gates.
13. 13 . A computer program product comprising one or more processors, one or more computer readable memories, one or more non-transitory computer readable storage devices, and program instructions stored on the one or more computer readable storage devices for execution by one or more processors via the one or more memories, the program instructions comprising instructions for: receiving, by a classical computer, a quantum circuit comprising a CZ layer and a CNOT layer; creating, by a classical computer, a modified quantum circuit based on the CZ layer and the CNOT layer, wherein the modified quantum circuit includes phase gates with CNOT gates that perform functions of CZ gates in the CZ layer; and performing, on a quantum computer, the modified quantum circuit.
14. 14 . The computer program product of claim 13 , wherein the quantum circuit further comprises a phase layer including one or more phase gates, and wherein creating the modified quantum circuit includes modifying phase gates of the phase layer based on the CZ gates in the CZ layer.
15. 15 . The computer program product of claim 13 , wherein creating the modified quantum circuit comprises: determining a CNOT gate of the CNOT layer corresponding to a CZ gate of the CZ layer, wherein an operation performed by the CZ gate is included in an operation of the CNOT gate; and determining one or more phase gates to apply to one or more CNOT gates such that the operation of the one or more phase gates and the one or more CNOT gates provides the same result as the CZ layer and the CNOT layer.
16. 16 . The computer program product of claim 13 , wherein the CNOT layer comprises swap gates and swap+ gates, and wherein creating the modified quantum circuit comprises: determining an initial phase gate for each CNOT gate, wherein the phase gate is applied as if it were a swap gate containing an equivalent calculation to a CZ gate from the CZ layer; for each swap+ gate: replace the swap gate used to determine the initial phase gate with a swap+ gate; and determine an updated phase gate based on the replaced swap+ gate; and repeat until all swap+ gates in original CNOT layer are introduced and an updated phase gate layer is created.
17. 17 . The computer program product of claim 16 , wherein the determining the initial phase gate comprises applying a phase gate to each swap gate containing an equivalent calculation to a CZ gate from the CZ layer.

Description

BACKGROUND The present invention relates to Quantum Computing, and more specifically, to circuit transformations to improve the performance of quantum computers. SUMMARY According to an embodiment of the present invention, a method, system, and computer program product for reducing and performing quantum circuits. The Embodiment may include receiving, by a classical computer, a quantum circuit comprising a CZ layer and a CNOT layer. The Embodiment may include creating, by a classical computer, a modified quantum circuit based on the CZ layer and the CNOT layer, wherein the modified quantum circuit includes phase gates with CNOT gates that perform similar functions of the CZ gates in the CZ layer. The embodiment may include performing, on a quantum computer, the modified quantum circuit. The embodiment may reduce the depth of a quantum circuit, thereby enabling faster and more accurate computation of the quantum circuit. The embodiment above may further include an embodiment where the quantum circuit further comprises a phase layer including one or more phase gates, and wherein creating the modified quantum circuit includes modifying phase gates of the phase layer based on the CZ gates in the CZ layer. The embodiment may reduce the depth of a quantum circuit, thereby enabling faster and more accurate computation of the quantum circuit. The embodiment(s) above may further include an embodiment of creating the modified quantum circuit by determining a CNOT gate of the CNOT layer corresponding to a CZ gate of the CZ layer, wherein an operation performed by the CZ gate is included in an operation of the CNOT gate. Creating the modified quantum circuit may further include determining one or more phase gates to apply to one or more CNOT gates such that the operation of the one or more phase gates and the one or more CNOT gates provides the same result as the CZ layer and the CNOT layer. The embodiment may reduce the depth of a quantum circuit, thereby enabling faster and more accurate computation of the quantum circuit. The embodiment(s) above may further include an embodiment where the CNOT layer having swap gates and swap+ gates. The embodiment may also determine an initial phase gate for each CNOT gate, wherein the phase gate is applied as if it were a swap gate containing an equivalent calculation to a CZ gate from the CZ layer. The embodiment may for each swap+ gate replace the swap gate used to determine the initial phase gate with a swap+ gate; determine an updated phase gate based on the replaced swap+ gate; and repeat until all swap+ gates in original CNOT layer are introduced and an updated phase gate layer is created. The embodiment may reduce the depth of a quantum circuit to 5n by eliminating the CZ layer, thereby enabling faster and more accurate computation of the quantum circuit. The embodiment(s) above may further include an embodiment where determining the initial phase gate comprises applying a phase gate to each swap gate containing an equivalent calculation to a CZ gate from the CZ layer. The embodiment may reduce the depth of a quantum circuit to 5n by eliminating the CZ layer, thereby enabling faster and more accurate computation of the quantum circuit. The embodiment(s) above may further include an embodiment where determining the updated phase gates comprises updating six phase gates. The embodiment may reduce the depth of a quantum circuit to 5n by eliminating the CZ layer, thereby enabling faster and more accurate computation of the quantum circuit. The embodiment(s) above may further include an embodiment where determining the updated phase gates is based on: a⊕b⊕c+a⊕b+a⊕c+b⊕c+a+b+c≡0(mod 4). The embodiment may reduce the depth of a quantum circuit to 5n by eliminating the CZ layer, thereby enabling faster and more accurate computation of the quantum circuit. BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 depicts an classical computing system, according to an exemplary embodiment; FIG. 2A depicts an environment containing classical and quantum computers for performing quantum and hybrid computations, according to an exemplary embodiment; FIG. 2B depicts an example process flow for performing quantum and hybrid computations using the classical and quantum computers of FIG. 2A, according to an exemplary embodiment; FIG. 3 depicts a process flow of reducing and executing a quantum circuit, according to an exemplary embodiment; FIG. 4 depicts a process flow of reducing a quantum circuit of LNN architecture, according to an exemplary embodiment; FIGS. 5A and 5B depict pseudo-code for implement portions of the process flow of FIG. 4, according to an exemplary embodiment. FIG. 6 is a circuit diagram in accordance with one or more embodiments. FIG. 7 is an illustration of a matrix that a diagonalization of a circuit in accordance with one or more embodiments. DETAILED DESCRIPTION Various aspects of the present disclosure are described by narrative text, flowcharts, block diagrams of computer systems