Patent Description:
A quantum computer is a new concept of a computer that is capable of simultaneously processing a plurality of pieces of information using unique physical properties of quantum states, such as superposition and entanglement. As an alternative to overcome performance limitations of a classical computer due to current leakage occurring in a microcircuit of a modern semiconductor chip, a need for quantum computers is gradually increasing. A quantum computer can exponentially increase information processing and computing speeds through quantum parallel processing in quantum bits or qubits, which are quantum information units, as the basic unit of information processing, thereby quickly solving problems. Accordingly, a quantum computer is expected to bring huge innovations in various industries, such as finance, chemistry, and pharmaceuticals, due to strengths thereof in complex calculations and mass data processing, such as optimal route search, prime factorization, and mass data search.

Key element technologies forming a quantum computer include a qubit implementation technology, a quantum algorithm technology, a quantum error correction code (QECC) technology, and a quantum circuit technology. Among these element technologies, the quantum circuit technology includes a technology for implementing a quantum gate for information processing of a qubit, which is a quantum information unit, and a technology for eliminating an error existing in a quantum circuit. A representative example of the technology for eliminating the error existing in the quantum circuit is a quantum error correction (QEC) technology.

Generally, errors existing in a quantum circuit include errors according to the types of quantum gates forming the circuit and errors according to the combination order of quantum gates. That is, errors existing in a quantum circuit vary depending on not only the configuration of quantum gates but also the combination order of quantum gates. Therefore, a conventional QEC technology corrects an error existing in a quantum circuit in view of both the type of quantum gates forming the quantum circuit and the order thereof. However, this QEC technology requires a separate quantum circuit and involves a very complicate computation process for error correction, thus spending a considerable amount of time and energy in correcting an error existing in a quantum circuit. In "<NPL>ET AL present a scalable error-mitigation method that applies to gate-based quantum computers. The method generates training data and fits a linear ansatz to this data.

An aspect of the present disclosure is to address the above-mentioned problems and other problems. Another aspect of the present disclosure is to provide a quantum circuit error mitigation method and an apparatus therefor capable of effectively mitigating errors existing in a quantum circuit using a pre-trained deep learning model.

In view of the foregoing, a method according to the appended claim <NUM> and a quantum computing device according to the appended claim <NUM> are provided. Preferred embodiments are set out in the appended dependent claims.

A quantum circuit error correction method and an apparatus therefor according to exemplary embodiments of the present disclosure may have the following effects.

According to at least one of exemplary embodiments of the present disclosure, an error existing in a quantum circuit may be conveniently corrected using a pre-trained deep learning model, thereby not needing to add separate quantum gates for correcting an error in a quantum error and saving time and energy required to correct the error existing in the quantum circuit due to a simple operational process for correcting the error in the quantum circuit.

The above aspects, features and advantages of the present disclosure will be more apparent from the following detailed description taken in conjunction with the accompanying drawings, in which:.

Hereinafter, embodiments disclosed herein will be described in detail with reference to the accompanying drawings, in which like or similar elements are denoted by like reference numerals regardless of drawing numerals and redundant descriptions thereof will be omitted. As used herein, the terms "module" and "unit" for components are given or interchangeably used only for ease in writing the specification and do not themselves have distinct meanings or functions. That is, the term "unit" used herein refers to software or a hardware component, such as FPGA or ASIC, and a "unit" performs certain functions. However, a "unit" is not limited to software or hardware. A "unit" may be configured to be in an addressable storage medium or may be configured to play one or more processors. Thus, in one example, a "unit" includes components, such as software components, object-oriented software components, class components, and task components, processes, functions, properties, procedures, subroutines, segments of a program code, drivers, firmware, a microcode, circuitry, data, a database, data structures, tables, arrays, and variables. Functions provided in components and "units" may be combined into a smaller number of components and "units" or may be further divided into additional components and "units".

The present disclosure proposes a quantum circuit error correction method and an apparatus therefor, which are capable of effectively correcting (or mitigating) errors existing in a quantum circuit using a pre-trained deep learning model. The deep learning model is a deep neural network (DNN) or a hybrid convolutional neural network (H-CNN) but is not necessarily limited thereto.

Hereinafter, various embodiments of the present disclosure will be described in detail with reference to the drawings.

<FIG> illustrates the basic structure of a deep neural network (DNN) related to the present disclosure, and <FIG> illustrates a learning process of the deep neural network (DNN) illustrated in <FIG>.

Referring to <FIG> and <FIG>, a multilayer perceptron (MLP) <NUM> related to the present disclosure is the most basic structure of a deep neural network (DNN) and includes an input layer <NUM>, a hidden layer <NUM>, and an output layer <NUM>.

The multilayer perceptron <NUM> is an artificial neural network structure proposed to overcome limitations of a single perceptron. That is, the multilayer perceptron <NUM> is an artificial neural network structure proposed to enable learning of even nonlinearly separated data, such as an exclusive-OR gate. To this end, the multilayer perceptron <NUM> has a structure that further includes one or more hidden layers <NUM>, unlike a single perceptron.

The input layer <NUM> of the multilayer perceptron <NUM> refers to a layer in which an input vector corresponding to learning data is located, and the output layer <NUM> refers to a layer in which a final result value of the learning model is located. The hidden layer <NUM> refers to any layer existing between the input layer <NUM> and the output layer <NUM>. As the number of hidden layers <NUM> increases, an artificial neural network is referred to as being deeper, and a sufficiently deep artificial neural network is referred to as a deep neural network (DNN).

In this structure of the multilayer perceptron, nodes present in the input layer <NUM> do not use a parameter and an activation function, whereas nodes present in the hidden layer <NUM> and the output layer <NUM> use the parameter and the activation function. Here, the parameter is a value that is automatically changed through a learning process and may include a weight and a bias. The weight is a parameter that adjusts the influence of an input signal on a resulting output, and the bias is a parameter that adjusts how easily a node (or neuron) is activated. The activation function refers to a function of receiving, appropriately processing, and outputting a signal. The activation function may include a sigmoid function, a rectified linear unit (ReLU) function, a softmax function, an identity function, and the like but is not necessarily limited thereto.

The multilayer perceptron <NUM> has a fully-connected structure in which nodes (i.e., neurons) in the respective layers are two-dimensionally connected. The fully-connected structure is a structure in which no connection relationship exists between nodes located in the same layer and a connection relationship exists only between nodes located in immediately adjacent layers.

A learning operation of the multilayer perceptron <NUM> is briefly described as follows. First, initial values of a weight and a bias as parameters in each layer are set. Subsequently, for one piece of learning (training) data, a net input function value in each layer is calculated, and an output value (i.e., a result value) of an activation function is finally calculated. Here, the net input function value refers to a value input to an activation function of each node. Next, the weight and the bias in each layer are updated so that the difference between an output value of an activation function of the output layer and an actual value is within an allowable error. Finally, for all learning data, when the difference between an output value of an activation function of the output layer and an actual value is within the allowable error, learning is terminated.

For example, as illustrated in <FIG>, a learning process of the multilayer perceptron <NUM> may be defined as an iterative process of feedforward (FF) and backpropagation (BP). This iterative process may continue until the difference (i.e., an error) between a result value calculated in the output layer <NUM> and an actual value approaches zero.

A feedforward (FF) process refers to a series of learning processes in which each input is multiplied by a corresponding weight while moving from the input layer <NUM> to the output layer <NUM>, the sum of weights is calculated as a result and is input to an activation function of each layer, and a result value is finally output from an activation function of the output layer <NUM>.

A backpropagation (BP) process refers to a series of learning processes in which a weight and a bias of each layer are updated in order to reduce errors incurred in the feedforward process while moving from the output layer <NUM> to the input layer <NUM>. The back propagation (BP) process may employ gradient descent as a method for determining a weight but is not limited thereto.

Gradient descent is an optimization technique for finding the lowest point of a loss function, in which the slope of the loss function is obtained and is continuously and repeatedly moved toward a low slope until reaching the lowest point. Here, the loss function is a function defining the difference (i.e., an error) between a result value calculated in the output layer <NUM> and an actual value. The loss function may be a mean squared error (MSE) or a cross entropy error (CEE) but is not necessarily limited thereto.

<FIG> illustrates the basic structure of a convolutional neural network (CNN) related to the present disclosure, and <FIG> illustrates a learning process of the convolutional neural network illustrated in <FIG>.

Referring to <FIG> and <FIG>, a convolutional neural network (CNN) <NUM> related to the present disclosure includes an input layer <NUM>, at least one convolutional layer <NUM>, and at least one pooling layer <NUM>, a fully connected layer <NUM>, and an output layer <NUM>. Here, the pooling layer <NUM> may be included in the convolutional layer <NUM>.

The convolutional neural network <NUM> includes a part for extracting a feature of input data and a part for classifying input data. Here, a feature extraction part includes the input layer <NUM>, the convolutional layer <NUM>, and the polling layer <NUM>, and a classification part includes the fully connected layer <NUM> and the output layer <NUM>.

The input layer <NUM> refers to a layer to which learning data, that is, training data and test data, are input. Generally, learning data used in a convolutional neural network (CNN) may be multidimensional data, such as image data or a matrix.

The convolution layer <NUM> serves to extract a feature of input data through a convolution operation between the input data and a filter that is an aggregate of weights. The convolution layer <NUM> includes a filter for extracting a feature of input data and an activation function for converting the value of a convolutional operation between input data and a filter into a nonlinear value. The activation function may be a rectified linear unit (ReLU) function but is not necessarily limited thereto.

The convolution layer <NUM> may output a plurality of feature maps through a convolution operation between input data and various filters. Subsequently, the convolution layer <NUM> may output a plurality of activation maps by applying an activation function to the plurality of feature maps.

The pooling layer (or sub-sampling layer) <NUM> receives output data of the convolution layer <NUM> as an input and serves to reduce the size of output data (i.e., an activation map) or to emphasize specific data. As a pooling method of the pooling layer <NUM>, there are a max pooling method, an average pooling method, and a min pooling method, among which the max pooling method is most frequently used.

The fully connected layer <NUM> serves to change a data type of the convolutional neural network (CNN) <NUM> into a fully connected neural network type. That is, the fully connected layer <NUM> serves to flatten a 3D output value of the pooling layer <NUM> into a 1D vector to connect the same to all nodes of the output layer <NUM> like a general neural network connection.

The output layer <NUM> serves to output a result value of classifying input data. The output layer <NUM> may serve to normalize a value input from the fully connected layer <NUM> into a value ranging from <NUM> to <NUM> and to ensure that the sum of output values is always <NUM>. To this end, the output layer <NUM> may include an activation function, such as a softmax function.

A learning operation of the convolutional neural network <NUM> having this structure is briefly described as follows. First, initial values of a weight (W) and a bias (B) as parameters in each layer are set. Subsequently, for one piece of learning (training) data, a net input function value in each layer is calculated, and an output value (i.e., a result value) of an activation function is finally calculated. Here, the net input function value refers to a value input to an activation function of each node. Next, the weight and the bias in each layer are updated so that the difference between an output value of an activation function of the output layer and an actual value is within an allowable error. Finally, for all learning data, when the difference between an output value of an activation function of the output layer and an actual value is within the allowable error, learning is terminated.

That is, as illustrated in <FIG>, a learning process of the convolutional neural network <NUM> may be defined as an iterative process of feedforward (FF) and backpropagation (BP). This iterative process may continue until an error in the output layer <NUM> and an actual value approaches zero.

<FIG> illustrates types of quantum gates related to the present disclosure, and <FIG> illustrates an example of a quantum circuit configured using the quantum gates of <FIG>.

Referring to <FIG> and <FIG>, a quantum circuit forming a quantum computer includes a plurality of quantum gates. Although a qubit of the quantum computer can have a state of being <NUM> and <NUM> at the same time unlike a bit of a conventional computer, the quantum computer needs to be used for an operation or the like and thus needs to have a specific state during an operation. To this end, the quantum computer necessarily requires a quantum gate.

A quantum gate fundamentally implements an operation through matrix multiplication of complex vectors, because a qubit, which is the unit of quantum information of the quantum computer, is expressed as a two-dimensional vector.

Types of quantum gates include a NOT gate, a Hadamard gate, a Pauli XYZ gate, a phase shift gate (S gate and T gate), a CNOT gate, a CZ gate, and a SWAP gate.

The NOT gate is a gate that is equivalent to a NOT gate among logic gates of the conventional computer and changes the state of a qubit being <NUM> to <NUM> and the state of a qubit being <NUM> to <NUM>.

The Hadamard gate is a gate that renders a qubit in a state of <NUM> or <NUM> into an overlapping state (<NUM> and <NUM> existing at the same time). When expressed as a matrix, the Hadamard gate is represented by a determinant illustrated in the drawing.

There are three types of Pauli gates, X, Y, and Z, in total, which means that each qubit rotates about X, Y, and Z axes. When expressed as a matrix, each gate is represented by a determinant illustrated in the drawing.

The phase shift gate is a gate that changes the phase of a qubit. Types of phase shift gates include an S gate and a T gate, each of which is represented by a determinant illustrated in the drawing.

The CNOT gate and the CZ gate are gates used to observe an entanglement state in which one qubit acts on another qubit in a quantum computer. The CNOT gate is a gate that performs a NOT gate operation on a second qubit when a first qubit is <NUM>, and the CZ gate is a gate that performs a Pauli-Z gate operation on a second qubit when a first qubit is <NUM>.

The SWAP gate is a gate that swaps the states of two qubits when there are the two qubits in a quantum computer. When expressed as a matrix, the SWAP gate is represented by a determinant illustrated in the drawing.

Various quantum circuits may be configured by combining a plurality of such quantum gates. For example, as illustrated in <FIG>, a quantum circuit <NUM> may be configured by sequentially connecting a first Hadamard gate <NUM>, a CNOT gate <NUM>, and a third Hadamard gate <NUM>.

<FIG> and <FIG> schematically illustrates the structure of a quantum circuit related to the present disclosure. As illustrated in <FIG> and <FIG>, quantum circuits <NUM> and <NUM> related to the present disclosure may include a combination of unitaries U<NUM> to Uj respectively corresponding to one or more quantum gates. Here, an ideal quantum gate (i.e., a quantum gate having no error) may be represented by U, and a practical quantum gate (i.e., a quantum gate having an error) may be represented by Û.

An input state of the quantum circuits <NUM> and <NUM> may be defined as a density matrix ρi, an output state thereof may be defined as j, and a relationship between input and output of the quantum circuits <NUM> and <NUM> may be defined as the combination of uniteries corresponding to the quantum gates.

A measurement outcome probability P(j|i) without an error representing the result of measuring output of an ideal quantum circuit <NUM> may be defined by Equation <NUM>.

Here, ρi is the input state of the quantum circuit, U is an ideal unitary transformation, and Mj is a measurement operator.

A measurement outcome probability P̂(j|i) without an error representing the result of measuring output of a practical quantum circuit <NUM> may be defined by Equation <NUM>.

Here, ρi is the input state of the quantum circuit, Λ is a practical quantum process, and Mj is a measurement operator.

An error existing in the practical quantum circuit <NUM> may be quantified on the basis of the first measurement outcome probability P̂(jli) of the practical quantum circuit <NUM> and the second measurement outcome probability P(j|i) of the ideal quantum circuit <NUM>. That is, an error value E(j|i) of the quantum circuit may be calculated by Equation <NUM>.

Since a unique error exists in each quantum gate, a quantum circuit including a plurality of quantum gates includes errors accumulated in the individual quantum gates. The errors existing in the quantum circuit depend not only on a configuration of the quantum gates but also on a combination order of the quantum gates. Therefore, it is necessary to correct the errors existing in the quantum circuit in view of the configuration and combination order of the quantum gates. Hereinafter, in the present specification, a method for effectively correcting an error existing in a quantum circuit using a pre-trained deep learning model is described in detail.

<FIG> is a flowchart illustrating a quantum circuit error correction method according to an exemplary embodiment of the present disclosure.

Referring to <FIG>, a quantum circuit error correction apparatus according to an exemplary embodiment of the present disclosure may be installed in a quantum computer and may perform an operation of correcting an error in quantum circuits forming the quantum computer.

Specifically, the quantum circuit error correction apparatus may identify whether a command to request error correction of the quantum circuits forming the quantum computer is received from a user or the like (S610).

As a result of operation <NUM>, when the command to request the error correction of the quantum circuits is received from the user or the like, the quantum circuit error correction apparatus may detect a quantum circuit that is a target of error correction (hereinafter, referred to as a "quantum circuit to be corrected") (S620). Here, the quantum circuit to be corrected may be at least one of a plurality of quantum circuits forming the quantum computer. According to an embodiment, operation <NUM> may be omitted.

The quantum circuit error correction apparatus invokes a pre-trained deep learning model (S630). Here, the deep learning model is a DNN model or a hybrid CNN model.

The quantum circuit error correction apparatus may detect input data of the deep learning model corresponding to the quantum circuit to be corrected. The input data may include information about the number of <NUM>-qubit gates forming the quantum circuit, information about the number of <NUM>-qubit gates forming the quantum circuit, error information about the quantum circuit, measurement outcome probability information about the quantum circuit, and the like.

The quantum circuit error correction apparatus may infer an error correction value (or error correction matrix C(j|i) for mitigating an error existing in the quantum circuit on the basis of the pre-trained deep learning model (S640). That is, the quantum circuit error correction apparatus may input the detected input data to the pre-trained deep learning model, thereby inferring the error correction value C(j|i) for mitigating the error existing in the quantum circuit.

The quantum circuit error correction apparatus corrects the error existing in the quantum circuit using the error correction value C(j|i) inferred through the deep learning model (S650). That is, the quantum circuit error correction apparatus may subtract the error correction value C(j|i) from the result P̂(j|i) of measuring practical output of the quantum circuit, thereby correcting the error existing in the quantum circuit.

As described above, the quantum circuit error correction method according to the exemplary embodiment of the present disclosure may conveniently correct the error existing in the quantum circuit using the pre-trained deep learning model, thereby not needing to add separate quantum gates for correcting an error in a quantum error and saving time and energy required to correct the error existing in the quantum circuit due to a simple operational process for correcting the error in the quantum circuit. The deep-learning model may be a DNN model or a hybrid CNN (H-CNN) model. First, a method for correcting an error in a quantum circuit using a DNN model is described in detail.

<FIG> illustrates the structure of a DNN model according to an exemplary embodiment of the present disclosure.

Referring to <FIG>, a DNN model <NUM> according to an exemplary embodiment of the present disclosure is a learning model for correcting an error in a quantum circuit of an N-qubit system and may include one input layer <NUM>, two hidden layers <NUM> and <NUM>, and one output layer <NUM>.

Data input to a plurality of nodes present in the input layer <NUM> of the DNN model <NUM> may include information G<NUM>(a:b) about the number of <NUM>-qubit gates forming a quantum circuit, information G<NUM>(a:b) about the number of <NUM>-qubit gates forming the quantum circuit, error information Ea(. |i) about the quantum circuit, and measurement outcome probability information P̂b(. |i) about the quantum circuit. Here, a and b denote a depth of the quantum circuit. Therefore, G<NUM>(a:b) denotes the number of <NUM>-qubit gates of quantum gates disposed between a depth of the quantum circuit of a and a depth of the quantum circuit of b, and G<NUM>(a:b) denotes the number of <NUM>-qubit gates of quantum gates disposed between a depth of the quantum circuit of a and a depth of the quantum circuit of b.

For example, as illustrated in <FIG>, a quantum circuit <NUM> that is a target to be learned or corrected by the DNN model <NUM> may be expressed as a combination of a plurality of unitaries U<NUM> to UK corresponding to a plurality of quantum gates. In this structure of the quantum circuit, the information G<NUM> about the number of <NUM>-qubit gates input to the input layer <NUM> of the DNN model <NUM> may be expressed as [G<NUM>. G1N], and the information G<NUM> about the number of <NUM>-qubit gates may be expressed as [G<NUM>. The error information Ea(. |i) about the quantum circuit input to the input layer <NUM> of the DNN model <NUM> may be defined as an error of a unitary Ua positioned at a depth of the quantum circuit of a, and the measurement outcome probability information P̂b(. |i) about the quantum circuit may be defined as a measurement outcome probability of a unitary Ub positioned at a depth of the quantum circuit of b.

The input layer <NUM> of the DNN model <NUM> may include a total of 2N + <NUM>N+<NUM>(= N + N + <NUM>N + <NUM>N) nodes. Here, N nodes are nodes for inputting the number of <NUM>-qubit gates, N nodes are nodes for inputting the number of <NUM>-qubit gates, <NUM>N nodes are nodes for inputting an error Ea(. |i) of the quantum circuit, and <NUM>N nodes are nodes for inputting a measurement outcome probability P̂b(. |i)) of the quantum circuit.

Data output through a plurality of nodes present in the output layer <NUM> of the DNN model <NUM> may include an error correction value C(j|i) for reducing (or mitigating) an error existing in the quantum circuit. The output layer <NUM> may include <NUM>N nodes.

Data input through the plurality of nodes present in the output layer <NUM> of the DNN model <NUM> may include the error information Ea(. |i) about the quantum circuit. The error information Ea(. |i) may be defined as an error of a unitary Ub positioned at a depth of the quantum circuit of b. The error information Ea(. |i) may be used to calculate a loss function in a learning process of the model <NUM>.

Pieces of data input to the DNN model <NUM> may be set as independent variables of the model, and data output from the DNN model <NUM> may be set as a dependent variable of the model.

A parameter used for nodes present in the hidden layers <NUM> and <NUM> of the DNN model <NUM> may include a weight and a bias. Further, an activation function used for the nodes present in the hidden layers <NUM> and <NUM> of the DNN model <NUM> may be a sigmoid function but is not necessarily limited thereto. Therefore, instead of the sigmoid function, a ReLU function, a softmax function, or an identity function may be used depending on embodiments.

The loss function ERMS of the DNN model <NUM> may be defined by Equation <NUM>.

Here, Ef(j|i) is a value of the actual error value E(j|i) of the quantum circuit minus the error correction value (i.e., an error estimate) C(j|i), which refers to the final error value of the quantum circuit and may be defined by Equation <NUM>.

The DNN model <NUM> is subjected to a learning process of updating weights and biases of the nodes present in the hidden layers <NUM> and <NUM> using an optimization technique for finding the lowest point of the loss function. The optimization technique may be representatively a gradient descent method but is not necessarily limited thereto.

That is, the DNN model <NUM> is intended to find an error correction value that minimizes the loss function. Accordingly, a target function F of the DNN model <NUM> may be defined by Equation <NUM>.

The DNN model <NUM> is shown to include the two hidden layers <NUM> and <NUM> in this embodiment but is not necessarily limited thereto. It will be apparent to those skilled in the art that less than two or more than two hidden layers may be included.

<FIG> illustrates the structure of a DNN model according to another exemplary embodiment of the present disclosure.

Referring to <FIG>, a DNN model <NUM> according to another exemplary embodiment of the present disclosure is a learning model for correcting an error in a quantum circuit of an N-qubit system and may include one input layer <NUM>, three hidden layers <NUM>, <NUM>, and <NUM>, and one output layer <NUM>.

Unlike the DNN model <NUM> illustrated in <FIG>, the DNN model <NUM> according to the present disclosure may include one more hidden layer <NUM>. That is, the DNN model <NUM> may further include the hidden layer <NUM> that performs batch normalization (BN) only on nodes connected to specific input data. Here, the batch normalization (BN) refers to normalization performed using a mean and a variance for each batch even through data for each batch has various distributions in a learning process.

Among data input to the input layer <NUM> of the DNN model <NUM>, the number of gates of the quantum circuit has an integer value, while an error value Ea(. |i) and a measurement outcome probability P̂b(. |i) of the quantum circuit have a value ranging from <NUM> to <NUM>. Accordingly, batch normalization may be performed on nodes of a first hidden layer <NUM> connected to pieces of data G<NUM>(a:b) and G<NUM>(a:b) having an integer value, thereby uniformizing the distribution of input data of a second hidden layer <NUM> connected to the first hidden layer <NUM> to a value ranging from <NUM> to <NUM>.

Machine learning may be performed on the DNN models <NUM> and <NUM> having the above structures. Specifically, a quantum circuit to be learned belonging to a predetermined training set may be selected, and quantum gates forming the selected quantum circuit to be learned may be analyzed, thereby detecting data to be input to a DNN model. Here, the data to be input to the DNN model may include information G<NUM>(a:b) about the number of <NUM>-qubit gates of the quantum circuit to be learned, information G<NUM>(a:b) about the number of <NUM>-qubit gates (G2(a:b)), error information Ea(. |i), and measurement outcome probability information P̂b(.

When the input data is completely detected, the detected input data may be input to the DNN model to train the DNN model. Here, the DNN model may be repeatedly trained while sequentially changing variables a, b, and i of the detected input data.

When learning of the quantum circuit is completed, other quantum circuits belonging to the predetermined training set may be sequentially selected, and the same learning process may be performed thereon. This learning process may be repeatedly performed on all quantum circuits included in the training set.

<FIG> illustrates a process of selecting a quantum circuit to be learned and training a DNN model on the basis of the selected quantum circuit to be learned. As illustrated in <FIG>, quantum circuits to be learned may be selected, and a DNN model for correcting (mitigating) an error in a quantum circuit may be trained on the basis of the selected quantum circuits to be learned. Here, the quantum circuits to be learned may be quantum circuits including a predetermined first number of quantum gates or less. For example, the quantum circuits to be learned may be quantum circuits including <NUM> or less quantum gates.

<FIG> illustrates the type of a quantum circuit to be corrected and a process of correcting an error in the quantum circuit to be corrected using a pre-trained DNN model. As illustrated in <FIG>, a quantum circuit to be corrected (or a quantum circuit to be estimated) may be selected, the selected quantum circuit may be input to a pre-trained DNN model, thereby inferring an error correction value of the quantum circuit, and an error in the quantum circuit may be corrected on the basis of the inferred error correction value.

Quantum circuits to be corrected may include quantum circuits U<NUM> to Uk having the same quantum gate configuration as the quantum gate configuration of quantum circuits to be learned, quantum circuits U<NUM> to Uk+l having a configuration of a larger number of quantum gates than in the quantum gate configuration of the quantum circuits to be learned, and quantum circuits V<NUM> to Vj having a quantum gate configuration different from the quantum gate configuration of the quantum circuits to be learned. Here, the quantum circuits to be corrected may be quantum circuits including a predetermined second number of quantum gates or less. For example, the quantum circuits to be corrected may be quantum circuits including <NUM> or less quantum gates.

As described above, according to the present disclosure, a DNN model is trained on the basis of quantum circuits with a quantum gate configuration having a relatively short depth, and the pre-trained DNN model is applied to quantum circuits with a quantum gate configuration having a relatively long depth, thereby correcting an error in the quantum circuits.

The foregoing quantum circuit error correction method entails a rather complicated operation process for training a DNN model because a large number of pieces of data are input to the DNN model. This problem can be solved through a quantum circuit error correction method using a hybrid CNN model. Hereinafter, a method of correcting an error in a quantum circuit using a hybrid CNN model is described in detail.

<FIG> and <FIG> illustrate the structure of a hybrid CNN model and learning data input to an input layer and an output layer of the model according to an exemplary embodiment of the present disclosure.

Referring to <FIG> and <FIG>, a hybrid CNN model <NUM> according to an exemplary embodiment of the present disclosure is a learning model in which a deep neural network (DNN) algorithm is combined with a convolutional neural network (CNN) algorithm to improve performance of quantum circuit error correction. The H-CNN model <NUM> is a learning model for correcting an error in a quantum circuit of an N-qubit system and may include an input layer <NUM>, at least one hidden layer <NUM>, and an output layer <NUM>. Here, the input layer <NUM> may include at least one convolutional layer, a pooling layer, and a fully connected layer for preprocessing some of input data.

Data input to a plurality of nodes present in the input layer <NUM> of the H-CNN model <NUM> may include gate matrix information G'ij indicating the number of gates between qubit i and qubit j of a quantum circuit, first local error information <MAT> about the quantum circuit, second local error information <MAT> about the quantum circuit, target state information t about the quantum circuit, and target measurement outcome probability information P̂b(t|i) about the quantum circuit. Here, a and b represent a depth of the quantum circuit.

For example, as illustrated in <FIG>, the quantum circuit <NUM> that is a target to be learned or corrected by the H-CNN model <NUM> may be expressed as a combination of a plurality of unitaries U<NUM> to UK corresponding to a plurality of quantum gates. In this structure of the quantum circuit, the first local error information <MAT> about the quantum circuit input to the input layer <NUM> of the H-CNN model <NUM> may be defined as a local error of a unitary Ua positioned at an a-th depth, and the second local error information <MAT> about the quantum circuit may be defined as a local error of a unitary Ub positioned at a b-th depth. The target state information t about the quantum circuit may be defined as bit information indicating any one of <NUM>N qubit states, and the target measurement outcome probability information P̂b(t|i) about the quantum circuit may be defined as a measurement outcome probability of a target qubit state of the unitary Ub positioned at the b-th depth.

A gate matrix G'i,j input to the input layer <NUM> of the H-CNN model <NUM> is a matrix indicating the number of gates existing between qubit i and qubit j of the quantum circuit and may be defined as an N * N matrix. Here, the gate matrix G'i,j may be preprocessed through the at least one convolutional layer, the pooling layer, and the fully connected layer and may then input to the input layer <NUM>. For example, as illustrated in <FIG>, the convolution layer may generate a plurality of feature maps through a convolution operation of input data (i.e., G'i,j) and at least one filter and may generate a plurality of activation maps by applying an activation function to the feature maps are. Subsequently, the pooling layer may receive output data of the convolution layer as input and may reduce the size of the output data (i.e., the activation maps) or may emphasize specific data. The fully connected layer may change a data type of a corresponding CNN algorithm into a fully connected neural network type. Output data of the fully connected layer may be input to the input layer <NUM>. That is, the H-CNN model <NUM> may extract a feature of the gate matrix G'i,j using the CNN algorithm and may then input the feature to the input layer <NUM>.

The input layer <NUM> of the H-CNN model <NUM> may include the plurality of nodes. Here, N nodes are nodes for inputting the first local error information <MAT> about the quantum circuit, N nodes are nodes for inputting the second local error information <MAT> about the quantum circuit, and N nodes are nodes for inputting the target state information t about the quantum circuit, and one node is a node for inputting the target measurement outcome probability information P̂b(t|i) about the quantum circuit.

The H-CNN model <NUM> may input error information (e.g., <MAT>) about the quantum circuit to the input layer <NUM> in local units. That is, the H-CNN model <NUM> may input the error information about the quantum circuit in qubit units. Accordingly, unlike the foregoing DNN model <NUM>, the H-CNN model <NUM> may input only N pieces of data to the learning model, thereby simplifying the operation process of the learning model.

Data output through a node present in the output layer <NUM> of the H-CNN model <NUM> may include an error correction value C(j|i) for reducing (or mitigating) an error existing in the quantum circuit. The output layer <NUM> may include one node.

Data input to the node present in the output layer <NUM> of the H-CNN model <NUM> may include target error information Eb(t|i) about the quantum circuit. Here, the target error information Eb(t|i) may be defined as an error of a target qubit state of the unitary Ub positioned at the b-th depth of the quantum circuit. The target error information Eb(t|i) may be used to calculate a loss function in a learning process of the model.

Pieces of data input to the H-CNN model <NUM> may be set as independent variables of the model, and data output from the H-CNN model <NUM> may be set as a dependent variable of the model.

A parameter used for nodes present in the hidden layer <NUM> of the H-CNN model <NUM> may include a weight and a bias. Further, an activation function used for the nodes present in the hidden layer <NUM> of the H-CNN model <NUM> may be a sigmoid function but is not necessarily limited thereto.

The loss function ERMS of the H-CNN model <NUM> may be defined by Equation <NUM>.

Here, EC(t|i) is a value of the actual error value E(t|i) of the quantum circuit minus the error correction value C(t|i), which refers to the final error value of the quantum circuit and may be defined by Equation <NUM>.

The H-CNN model <NUM> is subjected to a learning process of updating weights and biases of the nodes present in the hidden layer <NUM> using an optimization technique for finding the lowest point of the loss function. The optimization technique may be representatively a gradient descent method but is not necessarily limited thereto.

<FIG> illustrates a process of selecting a quantum circuit to be learned and training an H-CNN model on the basis of the selected quantum circuit to be learned. As illustrated in <FIG>, quantum circuits to be learned may be selected, and an H-CNN model for correcting (mitigating) an error in a quantum circuit may be trained on the basis of the selected quantum circuits to be learned. Here, the quantum circuits to be learned may be quantum circuits including a predetermined number of quantum gates or less. For example, the quantum circuits to be learned may be quantum circuits including <NUM> or less quantum gates.

<FIG> illustrates the type of a quantum circuit to be corrected and a process of correcting an error in the quantum circuit to be corrected using a pre-trained H-CNN model. As illustrated in <FIG>, a quantum circuit to be corrected (or a quantum circuit to be inferred) may be selected, the selected quantum circuit may be input to a pre-trained H-CNN model, thereby inferring an error correction value of the quantum circuit, and an error in the quantum circuit may be corrected on the basis of the inferred error correction value.

Quantum circuits to be corrected may include quantum circuits U<NUM> to Uk having the same quantum gate configuration as the quantum gate configuration of quantum circuits to be learned, quantum circuits U<NUM> to Uk+l having a configuration of a larger number of quantum gates than in the quantum gate configuration of the quantum circuits to be learned, and quantum circuits V<NUM> to Vj having a quantum gate configuration different from the quantum gate configuration of the quantum circuits to be learned. Here, the quantum circuits to be corrected may be quantum circuits including a predetermined number of quantum gates or less. For example, the quantum circuits to be corrected may be quantum circuits including <NUM> or less quantum gates.

As described above, according to the present disclosure, an H-CNN model is trained on the basis of quantum circuits with a quantum gate configuration having a relatively short depth, and the pre-trained H-CNN model is applied to quantum circuits with a quantum gate configuration having a relatively long depth, thereby correcting an error in the quantum circuits.

<FIG> is a block diagram illustrating the configuration of a quantum computing device according to an exemplary embodiment of the present disclosure.

Referring to <FIG>, the quantum computing device <NUM> according to the exemplary embodiment of the present disclosure includes at least one processor <NUM>, a computer-readable storage medium <NUM>, and a communication bus <NUM>. The quantum computing device <NUM> may be the foregoing quantum circuit error correction apparatus or one or more components included in the quantum circuit error correction apparatus.

The processor <NUM> may cause the quantum computing device <NUM> to operate according to the foregoing illustrative embodiments. For example, the processor <NUM> may execute at least one program <NUM> stored in the computer-readable storage medium <NUM>. The at least one program may include at least one computer-executable instruction, and the computer-executable instruction may be configured to cause the quantum computing device <NUM> to perform operations according to the illustrative embodiments when executed by the processor <NUM>.

The computer-readable storage medium <NUM> is configured to store a computer-executable instruction or program code, program data, and/or other suitable types of information. The program <NUM> stored in the computer-readable storage medium <NUM> includes a set of instructions executable by the processor <NUM>. In one exemplary embodiment, the computer-readable storage medium <NUM> may be a memory (a volatile memory, such as a random access memory, a nonvolatile memory, or a suitable combination thereof), one or more magnetic disk storage devices, optical disk storage devices, flash memory devices, other types of storage media accessed by the quantum computing device <NUM> and capable of storing desired information, or a suitable combination thereof.

The communication bus <NUM> interconnects various other components of the quantum computing device <NUM> including the processor <NUM> and the computer-readable storage medium <NUM>.

The quantum computing device <NUM> may also include at least one input/output interface <NUM> and at least one network communication interface <NUM> that provide an interface for at least one input/output device <NUM>. The input/output interface <NUM> and the network communication interface <NUM> are connected to the communication bus <NUM>.

The input/output device <NUM> may be connected to other components of the quantum computing device <NUM> through the input/output interface <NUM>. The illustrative input/output device <NUM> may include a pointing device (mouse or trackpad), an input device, such as a keyboard, a touch input device (touchpad or touchscreen), a voice or sound input device, various types of sensor devices and/or an imaging device, and/or an output device, such as a display device, a printer, a speaker and/or a network card. The illustrative input/output device <NUM> may be included in the quantum computing device <NUM> as a component forming the quantum computing device <NUM> or may be connected to the quantum computing device <NUM> as a device separate from the quantum computing device <NUM>.

Claim 1:
A method for mitigating an error of a quantum circuit that is performed by a processor (<NUM>) of a quantum computing device (<NUM>), the method comprising:
detecting (S620), by the processor, a quantum circuit to be mitigated among a plurality of quantum circuits, each of the plurality of quantum circuits comprising a combination of a plurality of physical quantum gates;
invoking (S630), by the processor, a pre-trained deep learning model for mitigating an error of the detected quantum circuit;
inferring (S640), by the processor, an error correction value of the detected quantum circuit by inputting an input data corresponding to the detected quantum circuit to the invoked deep learning model; and
mitigating (S650), by the processor, an error of the detected quantum circuit based on the inferred error correction value,
wherein,
a) the deep learning model is a deep neural network (DNN) model, the input data of the deep learning model model comprises at least one of information G<NUM>(a:b) about a number of <NUM>-qubit gates of physical quantum gates positioned between depth a and depth b of the quantum circuit, information G<NUM>(a:b) about a number of <NUM>-qubit gates of the physical quantum gates positioned between the depth a and the depth b of the quantum circuit, error information Ea(.|i) about a physical quantum gate positioned at the depth a of the quantum circuit, and measurement outcome probability information P̂b(.|i) about a physical quantum gate positioned at the depth b of the quantum circuit, or
b) the deep learning model is a hybrid convolutional neural network (H-CNN) model, the input data of the deep learning model comprises at least one of gate matrix information G'ij indicating a number of gates between qubit i and qubit j of the quantum circuit, first local error information <MAT> about a physical quantum gate positioned at depth a of the quantum circuit, second local error information <MAT> about a physical quantum gate positioned at depth b of the quantum circuit, target state information t about the quantum circuit, and target measurement outcome probability information P̂b(t|i) about the physical quantum gate positioned at the depth b of the quantum circuit.