Application US20190378208

QUANTUM CIRCUIT RISK ANALYSIS
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US20190378208

1. A system comprising, (4) (3)

an uncertainty modeling component that models uncertainty of one or more random variables to provide a first quantum sub-circuit by mapping the one or more variables to quantum states represented by a selected number of qubits using quantum gates;

a risk metric encoding component that encodes a risk metric into a second quantum sub-circuit, the second quantum sub-circuit comprising a first ancilla qubit and Y-rotations controlled by one or more other qubits; and

an amplitude estimation component that performs amplitude estimation based on the first sub-circuit and the second sub-circuit to extract a probability value corresponding to the risk metric, wherein the probability value represents a probability of measuring a one state in the ancilla qubit.

2. The system of claim 1, wherein the risk metric encoding component approximates the second sub-circuit using multi-controlled qubit rotations with rotation angles corresponding to polynomials to determine the risk metric as an expected value. (0)

3. The system of claim 1, wherein the risk metric encoding component approximates the second sub-circuit using multi-controlled qubit rotations with rotation angles corresponding to polynomials to determine the risk metric as a variance value. (1) (0)

4. The system of claim 1, wherein the risk metric encoding component encodes the risk metric to determine a value at risk quantity. (1) (0)

6. The system of claim 1, wherein the risk metric encoding component encodes the risk metric to determine a conditional value at risk quantity. (1) (0)

9. A computer-implemented method comprising, (3) (3)

modeling, by a device operatively coupled to a processor, uncertainty of one or more random variables to provide a first quantum sub-circuit by mapping the one or more variables to quantum states represented by a selected number of qubits using quantum gates;

encoding, by the device, a risk metric into a second quantum sub-circuit, the second quantum sub-circuit comprising a first ancilla qubit and Y-rotations controlled by one or more other qubits; and

performing, by the device, amplitude estimation based on the first sub-circuit and the second sub-circuit to extract a probability value corresponding to the risk metric, wherein the probability value represents a probability of measuring a one state in the ancilla qubit.

10. The computer-implemented method of claim 9, further comprising, computing an expected value or a variance value based on the probability value. (0)

11. The computer-implemented method of claim 9, wherein the risk metric comprises a value at risk quantity at a probability level, and further comprising, performing a bisection search to obtain a smallest level at which the probability value obtained via amplitude estimation is above a given threshold, wherein the value at risk quantity corresponds to the smallest level. (1) (0)

13. The computer-implemented method of claim 9, further comprising, determining a polynomial function, with multi-controlled qubit rotations with rotation angles corresponding to the polynomial function, and mapping the polynomial function to the second quantum sub-circuit. (2) (0)

16. A computer program product facilitating estimating a risk analysis result for a risk analysis metric, the computer program product comprising a computer readable storage medium having program instructions embodied therewith, the program instructions executable by a processor to cause the processor to: (3) (3)

model uncertainty of one or more random variables to provide a first quantum sub-circuit by mapping the one or more variables to quantum states represented by a selected number of qubits using quantum gates;

encode a risk metric into a second quantum sub-circuit, the second quantum sub-circuit comprising a first ancilla qubit and Y-rotations controlled by one or more other qubits; and

perform amplitude estimation based on the first sub-circuit and the second sub-circuit to extract a probability value corresponding to the risk metric, wherein the probability value represents a probability of measuring a one state in the ancilla qubit.

17. The computer program product of claim 16, wherein the risk metric comprises a value at risk quantity at a probability level, and wherein the program instructions are further executable by the processor to cause the processor to determine the risk metric based on the probability value by performing a bisection search to obtain a smallest level at which the probability value obtained via amplitude estimation is above a given threshold, wherein the value at risk quantity corresponds to the smallest level. (0)

18. The computer program product of claim 16, wherein the ancilla qubit comprises a first ancilla qubit, wherein the risk metric comprises a conditional value at risk quantity at a probability level, and wherein the program instructions are further executable by the processor to cause the processor to estimate the conditional value at risk quantity by adding a second ancilla qubit to the second sub-circuit, and controlling an operator that acts on the other qubits and the second ancilla qubit. (0)

19. The computer program product of claim 16, wherein the program instructions are further executable by the processor to cause the processor to construct the second quantum sub-circuit by determining a polynomial function, with multi-controlled qubit rotations with rotation angles corresponding to the polynomial function, and mapping the polynomial function to the second quantum sub-circuit. (0)

20. A computer-implemented method, comprising: (1) (3)

providing, by a device operatively coupled to a processor, a first quantum sub-circuit that models uncertainty of one or more random variables by mapping the one or more variables to quantum states represented by a selected number of qubits using quantum gates;

constructing, by the device, a second quantum sub-circuit comprising quantum gates and a first ancilla qubit, the constructing comprising, determining a polynomial function with multi-controlled qubit rotations with rotation angles corresponding to the polynomial function, and mapping the polynomial function to Y-rotation components of the second quantum sub-circuit; and

estimating, by the device, a risk metric quantity, comprising applying Y-rotations to the gates of the second quantum sub-circuit, determining an estimated probability value of measuring a one state in the first ancilla qubit, and determining the risk metric based on the estimated probability value.

21. The computer-implemented method of claim 20, wherein the estimating the risk metric quantity based on the estimated probability value further comprises performing a bisection search to obtain a smallest level at which the probability value obtained via amplitude estimation is above a given threshold, wherein a value at risk quantity corresponds to the smallest level. (1) (0)

23. A computer program product facilitating estimating a risk analysis quantity for a risk analysis metric, the computer program product comprising a computer readable storage medium having program instructions embodied therewith, the program instructions executable by a processor to cause the processor to: (1) (3)

provide a first quantum sub-circuit that models uncertainty of one or more random variables by mapping the one or more variables to quantum states represented by a selected number of qubits using quantum gates;

construct a second quantum sub-circuit comprising quantum gates and a first ancilla qubit, comprising determining a polynomial function with multi-controlled qubit rotations with rotation angles corresponding to the polynomial function, and mapping the polynomial function to Y-rotation components of the second quantum sub-circuit; and

estimate a risk metric quantity, comprising applying Y-rotations to the quantum gates of the second quantum sub-circuit, determining an estimated probability value of measuring a one state in the first ancilla qubit, and determining the risk metric based on the estimated probability value.

24. A computer program product of claim 23, wherein the program instructions are further executable by the processor to estimate the risk metric quantity based on the estimated probability value by performing a bisection search to obtain a smallest level at which the probability value obtained via amplitude estimation is above a given threshold, wherein a value at risk quantity corresponds to the smallest level. (1) (0)

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Application US20190378208

QUANTUM CIRCUIT RISK ANALYSIS

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