Quantum neural network
A quantum neural network architecture. In one aspect, a quantum neural network trained to perform a machine learning task includes: an input quantum neural network layer comprising (i) multiple qubits prepared in an initial quantum state encoding a machine learning task data input, and (ii) a target qubit; a sequence of intermediate quantum neural network layers, each intermediate quantum neural network layer comprising multiple quantum logic gates that operate on the multiple qubits and target qubit; and an output quantum neural network layer comprising a measurement quantum gate that operates on the target qubit and provides as output data representing a solution to the machine learning task.
1 . A quantum neural network system implemented by one or more quantum processors, the quantum neural network comprising:
an input quantum neural network layer comprising a plurality of qubits prepared in an initial quantum state and encoding a machine learning task data input;
a sequence of intermediate quantum neural network layers, each intermediate quantum neural network layer comprising multiple parameterized quantum logic gates that operate on the plurality of qubits, wherein values of parameters of the multiple parameterized quantum logic gates are determined during training using a loss function; and
an output quantum neural network layer comprising multiple measurement quantum gates, wherein the output quantum neural network layer provides as output a measurement result that represents a solution to the machine learning task;
wherein the machine learning task comprises a binary classification task; and
wherein the machine learning task data input comprises a Boolean function input {0, 1} n and the solution to the machine learning task comprises a Boolean function output {0, 1}.
2 . The quantum neural network system of claim 1 , wherein the multiple parameterized quantum logic gates comprise Y gates.
3 . The quantum neural network system of claim 1 , wherein the multiple parameterized quantum logic gates comprise single qubit gates of the form exp(−iθ j X j ), wherein j indexes the single qubit, θ i represents parameters of the single qubit gate, and X i represents a Pauli X operator on qubit j.
4 . The quantum neural network system of claim 1 , wherein the multiple parameterized quantum logic gates comprise two qubit gates of the form exp(−iθZ i Z k ), wherein θ represents parameters of the two qubit gate, Z i represents a Pauli Z operator on qubit j, and Z k represents a Pauli Z operator on qubit k.
5 . The quantum neural network system of claim 1 , wherein the loss function is given by
Loss
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where θ represents the parameters of the multiple quantum logic gates, ψ(θ, z s ) represents an evolved quantum state of the plurality of qubits, σ v out represents the measurement quantum gates, and y s represents a known binary classification for a corresponding Boolean function input.
6 . The quantum neural network system of claim 1 , wherein the sequence of intermediate quantum neural network layers evolve the initial quantum state under a sequence of unitary operators that is parameterized by the parameters of the multiple parameterized quantum logic gates.
7 . A method for processing a data input using a quantum neural network that has been trained to perform a machine learning task, the method comprising:
preparing multiple qubits of an input quantum neural network layer in an initial quantum state to encode machine learning task data input;
processing the initial quantum state using one or more intermediate quantum neural network layers to generate an evolved quantum state, each intermediate quantum neural network layer comprising multiple parameterized quantum logic gates that operate on the multiple qubits, wherein values of parameters of the multiple parameterized quantum logic gates are determined during training using a loss function; and
measuring the multiple qubits in the evolved quantum state using multiple measurement quantum gates in an output quantum neural network layer to generate an output that represents a solution to the machine learning task;
wherein the machine learning task comprises a binary classification task; and
wherein the machine learning task data input comprises a Boolean function input {0, 1} n and the solution to the machine learning task comprises a Boolean function output {0, 1}.
8 . The method of claim 7 , wherein the multiple parameterized quantum logic gates comprise Y gates.
9 . The method of claim 7 , wherein processing the initial quantum state using the one or more intermediate quantum neural network layers comprises, for each intermediate quantum neural network layer and in a sequence, applying quantum logic gates in the intermediate quantum neural network layer to a current quantum state of the multiple qubits.
10 . The method of claim 7 , wherein the multiple parameterized quantum logic gates comprise single qubit gates of the form exp(−θ i X i ), wherein j indexes the single qubit, θ i represents parameters of the single qubit gate, and X i represents a Pauli X operator on qubit j.
11 . The method of claim 7 , wherein the multiple parameterized quantum logic gates comprise two qubit gates of the form exp(−iθZ j Z k ), wherein θ represents parameters of the two qubit gate, Z j represents a Pauli Z operator on qubit j, and Z k represents a Pauli Z operator on qubit k.
12 . The method of claim 7 , wherein the loss function is given by
Loss
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σ
y
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ψ
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where θ represents the parameters of the multiple quantum logic gates, ψ(θ, z s ) represents an evolved quantum state of the multiple qubits, σ y out represents the measurement quantum gates, and y s represents a known binary classification for a corresponding Boolean function input.
13 . The method of claim 7 , wherein the intermediate quantum neural network layers evolve the initial quantum state under a sequence of unitary operators that is parameterized by the parameters of the multiple parameterized quantum logic gates.
14 . A method for training a quantum neural network, the method comprising:
obtaining multiple training examples, each training example comprising a machine learning task input paired with a known classification for the machine learning task input; and
training the quantum neural network on the training examples, comprising, for each training example:
preparing multiple qubits of an input quantum neural network layer in an initial quantum state to encode a machine learning task input included in the training example;
processing the initial quantum state using one or more intermediate quantum neural network layers, to generate an evolved quantum state, each intermediate quantum neural network layer comprising multiple parameterized quantum logic gates that operate on the multiple qubits;
measuring the multiple qubits in the evolved quantum state using multiple measurement quantum gates in an output quantum neural network layer to generate an output that represents a solution to the machine learning task;
using a loss function to compare the output to a known classification included in the training example and determine one or more adjustments to parameters of the multiple parameterized quantum logic gates; and
adjusting values of the gate parameters from initial values to trained values.
15 . The method of claim 14 , wherein the multiple parameterized quantum logic gates comprise Y gates.
16 . The method of claim 14 , wherein the multiple parameterized quantum logic gates comprise single qubit gates of the form exp(−iθ j X i ), wherein j indexes the single qubit, θ j represents parameters of the single qubit gate, and X j represents a Pauli X operator on qubit j.
17 . The method of claim 14 , wherein the multiple parameterized quantum logic gates comprise two qubit gates of the form exp(−iθZ j Z k ), wherein θ represents parameters of the two qubit gate, Z j represents a Pauli Z operator on qubit j, and Z k represents a Pauli Z operator on qubit k.
18 . The method of claim 14 , wherein the loss function is given by
Loss
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s
,
θ
)
=
(
〈
ψ
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θ
,
z
s
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❘
"\[LeftBracketingBar]"
σ
y
out
❘
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ψ
(
θ
,
z
s
)
〉
-
y
s
)
2
where θ represents the parameters of the multiple quantum logic gates, ψ(θ, z s ) represents an evolved quantum state of the multiple qubits, σ y out our represents the measurement quantum gates, and y z represents a known binary classification for a corresponding Boolean function input.
19 . The method of claim 14 , wherein the intermediate quantum neural network layers evolve the initial quantum state under a sequence of unitary operators that is parameterized by the parameters of the multiple parameterized quantum logic gates.
20 . The method of claim 14 , wherein processing the initial quantum state using the one or more intermediate quantum neural network layers comprises, for each intermediate quantum neural network layer and in a sequence, applying quantum logic gates in the intermediate quantum neural network layer to a current quantum state of the multiple qubits.