Quantum deformed binary neural networks

1 . A method for processing data in a quantum deformed binary neural network, comprising:

determining an input state for a layer of the quantum deformed binary neural network based on input image data, wherein the quantum deformed binary neural network is configured to perform the determining of the input state based on the input image data and a quantum phase estimation;

computing statistics for one or more observables in the layer, wherein the quantum deformed binary neural network is configured to perform the computing of the statistics based on using a quantum circuit with one or more entangled qubits comprising activation bits and weight bits that are entangled with one another to process the input state;

returning, by the quantum deformed binary neural network, an output activation probability based on the statistics for the one or more observables in the layer; and

assigning a classification to the input image data based on the output activation probability.

2 . The method of claim 1 , wherein returning the output activation probability comprises performing an additional quantum phase estimation.

3 . The method of claim 1 , wherein determining the input state is performed according to

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where |ψ j is the input state for the jth layer of the quantum deformed binary neural network, where p i is an ith probability, where h i is an ith activation, where H is a Hamiltonian, and where W j is a jth row of a weight matrix for the quantum deformed binary neural network.

4 . The method of claim 1 , wherein:

the statistics for the one or more observables in the layer comprise a mean and a variance, and

computing the statistics is performed according to μ= ψ|DHD -1 |ψ , σ 2 = ψ|DH 2 D -1 |ψ −μ 2 , where μ is the mean and σ 2 is the variance, where D is the quantum circuit, and where H is a Hamiltonian.

5 . The method of claim 1 , wherein returning the output activation probability is performed according to

Φ

⁡

(

-

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μ

j

-

N

2

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σ

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,

where Φ is a cumulative distribution function of a standard normal distribution, where μ j is a mean for a jth layer of the quantum deformed binary neural network and σ j is a variance for the jth layer of the quantum deformed binary neural network, and where N is a number of input neurons.

6 . A method for training a quantum deformed binary neural network, comprising:

providing input image data to the quantum deformed binary neural network;

receiving output data from the quantum deformed binary neural network, wherein the output data comprises a plurality of class probabilities for the input image data and wherein the quantum deformed binary neural network is configured to generate the output data based on using a quantum circuit with one or more entangled qubits comprising activation bits and weight bits that are entangled with one another to process an input state determined based on the input image data and a quantum phase estimation;

calculating a loss based on the plurality of class probabilities and a known class of the input image data; and

adjusting a plurality of quantum weights of the quantum deformed binary neural network based on the loss.

7 . The method of claim 6 , wherein the quantum weights comprise quantum wave functions.

8 . The method of claim 6 , wherein the loss comprises a cross-entropy loss.

9 . A processing system, comprising:

at least one memory comprising computer-executable instructions; and

at least one processor configured to execute the computer-executable instructions and cause the processing system to:

determine an input state for a layer of a quantum deformed binary neural network based on input image data, wherein the quantum deformed binary neural network is configured to perform the determining of the input state based on the input image data and a quantum phase estimation;

compute statistics for one or more observables in the layer, wherein the quantum deformed binary neural network is configured to perform the computing of the statistics based on using a quantum circuit with one or more entangled qubits comprising activation bits and weight bits that are entangled with one another to process the input state;

return, by the quantum deformed binary neural network, an output activation probability based on the statistics for the one or more observables in the layer; and

assign a classification to the input image data based on the output activation probability.

10 . The processing system of claim 9 , wherein to return the output activation probability, the processor is further configured to perform an additional quantum phase estimation.

11 . The processing system of claim 9 , wherein the processor is further configured to determine the input state according to |ψ j =|ψ H ⊗

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W

j

,

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ψ

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=

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,

where |ψ j is the input state for the jth layer of the quantum deformed binary neural network, where p i is an ith probability, where h i is an ith activation, where H is a Hamiltonian, and where W j is a jth row of a weight matrix for the quantum deformed binary neural network.

12 . The processing system of claim 9 , wherein:

the statistics for the one or more observables in the layer comprise a mean and a variance, and

the processor is further configured to compute the statistics according to μ= ψDHD -1 |ψ , σ 2 = ψDH 2 D -1 |ψ −μ 2 , where μ is the mean and σ 2 is the variance, where D is the quantum circuit, and where H is a Hamiltonian.

13 . The processing system of claim 9 , wherein the processor is further configured to return the output activation probability according to

Φ

⁡

(

-

2

⁢

μ

j

-

N

2

⁢

σ

j

)

,

where Φ is a cumulative distribution function of a standard normal distribution, where μ j is a mean for a jth layer of the quantum deformed binary neural network and σ j is a variance for the jth layer of the quantum deformed binary neural network, and where N is a number of input neurons.

14 . A processing system, comprising:

at least one memory comprising computer-executable instructions; and

at least one processor configured to execute the computer-executable instructions and cause the processing system to:

provide input image data to a quantum deformed binary neural network;

receive output data from the quantum deformed binary neural network, wherein the output data comprises a plurality of class probabilities for the input image data and wherein the quantum deformed binary neural network is configured to generate the output data based on using a quantum circuit with one or more entangled qubits comprising activation bits and weight bits that are entangled with one another to process an input state determined based on the input image data and a quantum phase estimation;

calculate a loss based on the plurality of class probabilities and a known class of the input image data; and

adjust a plurality of quantum weights of the quantum deformed binary neural network based on the loss.

15 . The processing system of claim 14 , wherein the quantum weights comprise quantum wave functions.

16 . The processing system of claim 14 , wherein the loss comprises a cross-entropy loss.