	US 12,353,952 B2
	Systems and methods for preparation of normal distributions on quantum computers
Yue Sun, Short Hills, NJ (US); Marco Pistoia, Amawalk, NY (US); Pierre Minssen, New York, NY (US); and Arthur G. Rattew, Sag Harbor, NY (US)
Assigned to JPMORGAN CHASE BANK, N.A., New York, NY (US)
Filed by JPMORGAN CHASE BANK, N.A., New York, NY (US)
Filed on Jun. 3, 2021, as Appl. No. 17/337,831.
Prior Publication US 2022/0391468 A1, Dec. 8, 2022
Int. Cl. G06N 10/60 (2022.01); G06N 10/00 (2022.01)

CPC G06N 10/00 (2019.01) [G06N 10/60 (2022.01)]

12 Claims

1. A method for preparation of normal distributions on a quantum computer, comprising:

receiving, at a quantum computer program, a mean, a standard deviation, and a discretization;

determining, by the quantum computer program, a number of iterations based on the mean and the standard deviation;

identifying, by the quantum computer program, a first value from the discretization;

setting, by the quantum computer program, a plurality of qubits in a register equal to the first value;

identifying, by the quantum computer program, a value X₀from the mean;

initializing, by the quantum computer program, a state of the plurality of qubits in the register and a state of an ancilla qubit to |0>;

applying, by the quantum computer program, a first Hadamard gate to the plurality of qubits in the register;

applying, by the quantum computer program, a quantum Fourier transform to the register;

applying, by the quantum computer program, a +X₀gate to the register;

applying, by the quantum computer program, a Y-Rotation operation with an angle π/2 to the ancilla qubit;

applying, by the quantum computer program, a controlled +1 gate to the register controlled by the ancilla qubit;

applying, by the quantum computer program, a second Hadamard gate to the ancilla qubit;

measuring, by the quantum computer program, a value of the ancilla qubit;

applying, by the quantum computer program, an inverse quantum Fourier transform to the register; and

outputting, by the quantum computer program, a normal distribution, wherein the normal distribution comprises amplitudes of basis states of the plurality of qubits in the register.