Granted Patent B2

US 12,198,003 · App. 17/360,792 · Granted Jan 14, 2025

Inventor: Prasanth Shyamsundar (Chicago, IL)

Assignee: Fermi Research Alliance, LLC

G06N10/00G06N10/60H03K19/195G06N10/20

Abstract

Claims (76)

1. A method of performing quantum calculation on an oracle U φ for a non-boolean function φ, comprising:

initializing an ancilla qubit in a |+ state and an input qubit in a |ψ 0 state of a plurality of eigenstates |x to define a two-register state |Ψ 0 ≡|+,ψ 0 ;

for each of a plurality K of iterations

receiving, using the input qubit, a respective one of the plurality of eigenstates |x defining an input basis state,

for odd iterations, acting on the input basis state using a selective phase-flip unitary operator circuit S Ψ 0 and a controlled unitary operator circuit U φ , and

for even iterations, acting on the input basis state using the selective phase-flip unitary operator circuit S Ψ 0 and a controlled inverse unitary operator circuit U φ † .

2. The method according to claim 1 , further comprising measuring, after the plurality K of iterations, the ancilla qubit in a 0/1 basis.

3. The method according to claim 1 , wherein the selective phase-flip unitary operator circuit S Ψ 0 further comprises:

a Hadamard transform H,

a unitary operator A 0 ,

a unitary operator I, and

an inverse unitary operator A 0 † ;

wherein the selective phase-flip unitary operator S Ψ 0 =[H⊗A 0 ][2|0,0 0,0|−I][H⊗A 0 † ].

4. The method according to claim 1 , wherein the acting on the input basis state using the selective phase-flip unitary operator circuit S Ψ 0 and the controlled unitary operator circuit U φ further comprises, for the ancilla qubit in a state |0 , acting on the input qubit as U φ |0,x =e +iφ(x) |0,x , U φ |1,x =e −iφ(x) |1,x .

5. The method according to claim 1 , wherein the acting on the input basis state using the selective phase-flip unitary operator circuit S Ψ 0 and the controlled inverse unitary operator circuit U φ † further comprises, for the ancilla qubit in a state |1 , acting on the input qubit as U φ † |0,x =e +iφ(x) |0,x , U φ † |1,x =e −iφ(x) |1,x .

6. The method according to claim 1 , further comprising:

receiving, using the input qubit, the |ψ 0 state defining an input random state;

acting on the input random state using a controlled estimation unitary operator circuit U φ−π/2 .

7. The method according to claim 6 , wherein the controlled estimation unitary operator circuit U φ−π/2 further comprises:

the controlled unitary operator circuit U φ ,

at least one bit-flip operator X, and

at least one phase-shift operator R ϕ ;

wherein the controlled estimation unitary operator circuit U φ−π/2 =e −iπ/2 |0 0|⊗U φ +e iπ/2 |1 1|⊗U φ † .

8. A quantum computing device for performing quantum calculation on an oracle U φ for a non-boolean function φ, comprising:

a two-register quantum system comprising

an ancilla qubit, and

an input qubit; and

a non-boolean quantum oracle comprising

a selective phase-flip unitary operator circuit S Ψ 0 ,

a controlled unitary operator circuit U φ , and

a controlled inverse unitary operator circuit U φ † ;

wherein the quantum computing device is configured to

initialize the ancilla qubit in a |+ state and the input qubit in a |ψ 0 state of a plurality of eigenstates |x to define a two-register state |Ψ 0 ≡|+,ψ 0 ;

for each of a plurality K of iterations

receive, using the input qubit, a respective one of the plurality of eigenstates |x defining an input basis state,

for odd iterations of the plurality K of iterations, act on the input basis state using the selective phase-flip unitary operator circuit S Ψ 0 and the controlled unitary operator circuit U φ , and

for even iterations of the plurality K of iterations, act on the input basis state using the selective phase-flip unitary operator circuit S Ψ 0 and the controlled inverse unitary operator circuit U φ † .

9. The quantum computing device according to claim 8 , further configured to measure, after the plurality K of iterations, the ancilla qubit in a 0/1 basis.

10. The quantum computing device according to claim 8 , wherein the selective phase-flip unitary operator circuit S Ψ 0 further comprises:

a Hadamard transform H,

a unitary operator A 0 ,

a unitary operator I, and

an inverse unitary operator A 0 † ;

wherein the selective phase-flip unitary operator S Ψ 0 =[H⊗A 0 ][2|0,0 0,0|−I][H⊗A 0 † ].

11. The quantum computing device according to claim 8 , further configured, for the ancilla qubit in a state |0 , to act on the input qubit as U φ |0,x =e +iφ(x) |0,x , U φ |1,x =e −iφ(x) |1,x .

12. The quantum computing device according to claim 8 , further configured, for the ancilla qubit in a state |1 , to act on the input qubit as U φ † |0,x =e +iφ(x) |0,x , U φ † |1,x =e −iφ(x) |1,x .

13. The quantum computing device according to claim 8 , further comprising a controlled estimation unitary operator circuit U φ−π/2 , and configured to:

receive, using the input qubit, the |ψ 0 state defining an input random state; and

act on the input random state using the controlled estimation unitary operator circuit U φ−π/2 .

14. The quantum computing device according to claim 13 , wherein the controlled estimation unitary operator circuit U φ−π/2 further comprises:

the controlled unitary operator circuit U φ ,

at least one bit-flip operator X, and

at least one phase-shift operator R ϕ ;

wherein the controlled estimation unitary operator circuit U φ−π/2 =e −iπ/2 |0 0|⊗U φ +e iπ/2 |1 1|⊗U φ † .

15. A system of quantum circuits for implementing an oracle U q for a non-boolean function φ, the system configured to:

initialize an ancilla qubit in a |+ state and an input qubit in a |ψ 0 state of a plurality of eigenstates |x to define a two-register state |Ψ 0 ≡|+,ψ 0 ;

for each of a plurality K of iterations

receive, using the input qubit, a respective one of the plurality of eigenstates |x defining an input basis state,

for odd iterations of the plurality K of iterations, act on the input basis state using a selective phase-flip unitary operator circuit S Ψ 0 and a controlled unitary operator circuit U φ , and

for even iterations of the plurality K of iterations, act on the input basis state using the selective phase-flip unitary operator circuit S Ψ 0 and a controlled inverse unitary operator circuit U φ † .

16. The system according to claim 15 , further configured to measure, after the plurality K of iterations, the ancilla qubit in a 0/1 basis.

17. The system according to claim 15 , wherein the selective phase-flip unitary operator circuit S Ψ 0 further comprises:

a Hadamard transform H,

a unitary operator A 0 ,

a unitary operator I, and

an inverse unitary operator A 0 † ;

wherein the selective phase-flip unitary operator S Ψ 0 =[H⊗A 0 ][2|0,0 0,0|−I][H⊗A 0 † ].

18. The system according to claim 15 , further configured, for the ancilla qubit in a state |0 , to act on the input qubit as U φ |0,x =e +iφ(x) |0,x , U φ |1,x =e −iφ(x) |1,x .

19. The system according to claim 15 , further configured, for the ancilla qubit in a state |1 , to act on the input qubit as U φ † |0,x =e +iφ(x) |0,x , U φ † |1,x =e −iφ(x) |1,x .

20. The system according to claim 15 , further configured to:

receive, using the input qubit, the |ψ 0 state defining an input random state; and

act on the input random state using a controlled estimation unitary operator circuit U φ−π/2 comprising:

the controlled unitary operator circuit U φ ,

at least one bit-flip operator X, and

at least one phase-shift operator R ϕ ;

wherein the controlled estimation unitary operator circuit U φ−π/2 =e −iπ/2 |0 0|⊗U φ +e iπ/2 |1 1|⊗U φ † .

Assignments (3)

Continuity (1)

References Cited (64)