Systems and methods for preparation of normal distributions on quantum computers

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 X0 from 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 +X0 gate 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.