Method and system that produces non-stabilizer quantum states that are used in various quantum circuits and systems

Patent metadata

Field	Value
Publication number	US-9269052-B2
Application number	US-201313830006-A
Country	US
Kind code	B2
Filing date	Mar 14, 2013
Priority date	Mar 14, 2013
Publication date	Feb 23, 2016
Grant date	Feb 23, 2016

Abstract

The current application is directed to methods and quantum circuits that prepare qubits in specified non-stabilizer quantum states that can, in turn, be used for a variety of different purposes, including in a quantum-circuit implementation of an arbitrary single-qubit unitary quantum gate that imparts a specified, arbitrary rotation to the state-vector representation of the state of an input qubit. In certain implementations, the methods and systems consume multiple magic-state qubits in order to carry out probabilistic rotation operators to prepare qubits with state vectors having specified rotation angles with respect to a rotation axis. These qubits are used as resources input to various quantum circuits, including the quantum-circuit implementation of an arbitrary single-qubit unitary quantum gate.

First claim

The invention claimed is:

1. A quantum-circuit subsystem that prepares a subject qubit in a non-stabilizer state represented by a state vector lying in the same plane as the state vector representing an initial, input state of the subject qubit, the quantum-circuit subsystem comprising:
one or more stages, each stage i including
a stage i control-qubit input,
a stage i subject-qubit input,
a stage i measurement output that outputs a measurement of an input control qubit following at least one internal two-qubit controlled-gate operation, and
a stage i subject-qubit output that outputs the subject qubit following the at least one internal two-qubit controlled-gate operation; and

a controller that monitors the measurements output from the measurement output of successive stages of the quantum-circuit subsystem to determine a number of stages to apply to the subject qubit in order to rotate the state vector of the subject qubit to a specified rotation angle within the plane.

2. The quantum-circuit subsystem of claim 1 wherein the subject qubit input to a first stage of the quantum-circuit subsystem has a state selected from among the states:
H 0 =cos θ 0 |0 +sin θ 0 |1 where the rotation angle

θ
0

=

π
8

;



Ψ
0
0

〉

;



Ψ
0
1

〉

;

and
⁢

⁢



Ψ
0
2

〉

.

3. The quantum-circuit subsystem of claim 1 wherein the control qubit input to each stage of the quantum-circuit subsystem has the state |H 0 .

4. The quantum-circuit subsystem of claim 1 wherein each stage further comprises:
a controlled-NOT gate; and
a measurement gate that measures the state of the control qubit following the at least one internal two-qubit controlled-gate operation and outputs an indication m of the measured state to the measurement output.

5. The quantum-circuit subsystem of claim 4 wherein, when the measurement gate returns an indication m=0 indicating that the control qubit is measured to be in a state |0 , the subject qubit is in a state |H i+1 , with the state-vector representing the state |H i+1 having a rotation angle θ i+1 .

6. The quantum-circuit subsystem of claim 5 wherein, when the measurement gate returns an indication m=1 indicating that the control qubit is measured to be in a state |1 , the subject qubit is in a state |G i−1 , with the state-vector representing the state |H i−1 having a rotation angle θ i−1 .

7. The quantum-circuit subsystem of claim 6 wherein the measurement gate returns an indication m=0 with a probability p greater than or equal to 0.75 and returns an indication m=1 with a probability p less than or equal to 0.25 at each stage.

8. The quantum-circuit subsystem of claim 1 wherein the subject qubit output from a stage i subject-qubit output is input to a stage i+1 subject-qubit input.

9. The quantum-circuit subsystem of claim 8 wherein, after application of a next stage i of the quantum-circuit subsystem to a subject qubit input to the stage i in state |H i , when the measurement gate of the stage returns an indication m=0 indicating that the control qubit is measured to be in a state |0 , the subject qubit is in state |H i+1 and has a rotation angle θ i+1 k characteristic of the subject qubit input to the first stage of the quantum-circuit subsystem, k, and of the stage i.

10. The quantum-circuit subsystem of claim 9 wherein the controller:
initially determines a number of stages j to apply to the subject qubit in order to rotate the state vector of the subject qubit to a specified rotation angle; and
while j is greater than 0,
applies a next stage to the subject qubit,
when the measurement value m output after applying the next stage is 0, decrements j, and
when the measurement value m output after applying the next stage is 1, increments j.

11. A method that prepares a subject qubit in a non-stabilizer state represented by a state vector lying in the same plane as the state vector representing an initial input state of the subject qubit, the method comprising:
by a controller for a quantum circuit in which the subject qubit is located, initially determining a number of stages i to apply to the subject qubit in order to rotate the state vector of the subject qubit to a specified rotation angle, each stage i including a stage i control-qubit input, a stage i subject-qubit input, a stage i measurement output that outputs a measurement of an input control qubit following at least one internal two-qubit controlled-gate operation, and a stage i subject-qubit output that outputs the subject qubit following the at least one internal two-qubit controlled-gate operation; and
while i is greater than 0,
with the quantum circuit, applying a next stage to the subject qubit and a control qubit,
when a measurement value m output by the next stage is 0, indicating that the control qubit is measured by the stage to be in state |0 , decrementing i, and
when the measurement value m output by the next stage is 1, indicating that the control qubit is measured by the stage to be in state |1 , incrementing i.

12. The method of claim 11 wherein each stage includes:
application of a controlled-NOT gate to the subject qubit and a control qubit; and
application of a measurement gate that measures the state of the control qubit following application of the controlled-NOT gate to the subject qubit and the control qubit.

13. The method of claim 12 wherein a first stage is applied to the subject qubit in a state selected from among the states: |H 0 ; |Ψ 0 0 ; |Ψ 0 1 ; and |Ψ 0 2 .

14. The method of claim 12 , wherein the control qubit input to each stage of the quantum-circuit subsystem has the state



H
0

〉

=

cos
⁢

⁢

θ
0

⁢


0
〉

+

sin
⁢

⁢

θ
0

Assignees

• Microsoft Corp
• Microsoft Technology Licensing Llc

Inventors

• Svore Krysta
• Duclos-Cianci Guillaume

Classifications

• G06N10/20 Primary

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

• G06N99/002 Primary

  Physics · mapped topic