Method and system for performing quantum calculations in a quantum neural network and for implementing quantum neural networks

Patent metadata

Field	Value
Publication number	US-2025103932-A1
Application number	US-202218725835-A
Country	US
Kind code	A1
Filing date	Dec 29, 2022
Priority date	Dec 30, 2021
Publication date	Mar 27, 2025
Grant date	—

Abstract

A computer implemented method for performing quantum calculations in a quantum neural network is described.The neural network considered in this method comprises at least one input layer comprising a first number Nin of input layer neurons adapted to receive respective input values xi belonging to an input vector x. Each input layer neuron is configured to multiply the respective input value xi by a respective weight value wi belonging to a weight vector w. The aforesaid neural network further comprises at least one calculation neuron, operatively connected to the aforesaid input layer, and configured to provide a computation result y=f(z) calculated by applying an activation function ƒ to an argument z. Such an argument z is a scalar number calculated by the calculation neuron as the sum of the products of the input values xi by the respective weights wi plus a bias value b.The method comprises the following steps:encoding, by a first quantum process, the input values xi of the input vector x into probability amplitudes of a n-qubits initial first quantum state, stored in an input register q, through a n-to-2n input encoding model, wherein the number of qubits n of the initial first quantum state is such that 2n is greater or equal to a second number equal to Nin+3, where Nin corresponds to the input vector dimension;applying a quantum operator, depending on the weight values wi of the weight vector w and the bias b, to said input register q to calculate said argument z as the addition of the bias b and the inner product of the input vector x and the weight vector w;by the application of said quantum operator, producing as result a second quantum state, of the input register q, which has the value 1 and the value of the argument (z) encoded;processing, by a second quantum process, said second quantum state of the input register (q), to calculate a value of each of a number of powers (d−1) of said argument (z), from the second order power (z2) up to the d-th order power (zd), using an additional quantum buffer register (a);by the application of said second quantum process, producing as result a third (n+d)-qubits quantum state, of the input register (q) and the additional quantum buffer register (a), which has said values (1, z, z2, . . . ,zd) encoded;processing, by a third quantum process, said third quantum state to calculate said computation result y as a polynomial series expansion of the activation function ƒ, through quantum states rotations, with the rotation angles depending on coefficients of said activation function polynomial series expansion;encoding said calculated computation result y into a fourth quantum state, which is suitable either to be measured and detected or to be provided, as a not yet measured quantum state, to a further neuron of the neural network.A computer implemented method for implementing a quantum neural network is also described.A quantum computation system for performing quantum calculations in a quantum neural network and a quantum computation system for implementing a quantum neural network are also described.

First claim

1 . A computer implemented method for performing quantum calculations in a quantum neural network,
wherein said neural network comprises at least one input layer comprising a first number (N in ) of input layer neurons adapted to receive respective input values (x i ) belonging to an input vector (x), each input layer neuron being configured to multiply the respective input value (x i ) by a respective weight value (w i ) belonging to a weight vector (w), and wherein said neural network further comprises at least one calculation neuron, operatively connected to said input layer, and configured to provide a computation result (y=f(z)) calculated by applying an activation function (ƒ) to an argument (z), said argument (z) being a scalar number calculated by the calculation neuron as the sum of the products of the input values (x i ) by the respective weights (w i ) plus a bias value (b), wherein the method comprises the steps of:
encoding, by a first quantum process, the input values (x i ) of the input vector (x) into probability amplitudes of a n-qubits initial first quantum state, stored in an input register (q), through a n-to-2 n input encoding model, wherein the number of qubits (n) of the initial first quantum state is such that 2 n is greater or equal to a second number equal to N in +3, where N in corresponds to the input vector dimension;
applying a quantum operator, depending on the weight values (w i ) of the weight vector (w) and the bias (b), to said input register (q) to calculate said argument (z) as the addition of the bias (b) and the inner product of the input vector (x) and the weight vector (w);
by the application of said quantum operator, producing as result a second quantum state, of the input register q, which has the value 1 and the value of the argument (z) encoded;
processing, by a second quantum process, said second quantum state of the input register (q), to calculate a value of each of a number of powers (d- 1 ) of said argument (z), from the second order power (z 2 ) up to the d-th order power (z d ), using an additional quantum buffer register (a);
by the application of said second quantum process, producing as result a third (n+d)-qubits quantum state, of the input register (q) and the additional quantum buffer register (a), which has said values (1, z, z 2 , . . . ,z d ) encoded;
processing, by a third quantum process, said third quantum state to calculate said computation result (y) as a polynomial series expansion of the activation function (ƒ), through quantum states rotations, with the rotation angles depending on coefficients of said activation function polynomial series expansion;
encoding said calculated computation result (y) into a fourth quantum state, which is suitable either to be measured and detected or to be provided, as a not yet measured quantum state, to a further neuron of the neural network.

2 . Method according to claim 1 , wherein said step of applying a quantum operator to the input register (q) provides the following quantum operations:
2 n -1 quantum states rotations, with the rotation angles depending on the weight values (w i ) of the weight vector (w) and the bias (b) such that 2 n is greater or equal to said second number (N in +3); processing said n-qubits initial first quantum state and the quantum operator depending on the weight and bias to calculate said argument (z) as the addition of the bias (b) and the inner product of the input vector (x) and the weight vector (w).

3 . Method according to claim 1 , wherein said number of powers (d) is less than 10 so that the activation function is approximated by a Taylor series expansion having 10 addends or less.

4 . Method according to claim 3 , wherein said number of powers (d) is 3 so that the activation function is approximated by a Taylor series expansion having 3 addends.

5 . Method according to any claim 1 , wherein said weights (w i ) and bias (b) are comprised in the closed range of real numbers comprised between −1 and 1.

6 . Method according to claim 1 , wherein said step of processing, by a second quantum process, the second quantum state to calculate a value of each of a number of powers (d- 1 ) of the argument (z) comprises:
applying by the second quantum process a unitary transformation U z (x, w, b) which satisfies the following equation:

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7 . Method according to claim 1 , wherein said step of producing a third (n+d)-qubits quantum state comprises:
transforming the input register (q) and the additional quantum buffer register (a) from an initial state |0> a | 0> q to a (n+d)-qubit entangled state |ψ z d > according to the relationship:

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Assignees

• Consiglio Nazionale Ricerche

Inventors

• Prati Enrico
• Maronese Marco

Classifications

• G06N10/20 Primary

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

• G06N3/048 Primary

  Activation functions · CPC title