A quantum processing unit for a quantum classifier neuron

Abstract

The invention relates to a quantum processing unit configured to set the total angular momentum quantum number of neurons to be greater than 1 / 2 in a quantum neural network model with nonlinear activation or in artificial reservoir models, a neuromorphic quantum computer operating dissipatively and comprising said quantum processing unit, and a hybrid system composed of at least one classical computer and a quantum computer.

Description

[0001] A QUANTUM PROCESSING UNIT FOR A QUANTUM CLASSIFIER NEURON

[0002] Technical Field of the Invention

[0003] The invention relates to a quantum processing unit for adjusting the total angular momentum quantum number of neurons in a quantum neural network model with nonlinear activation or artificial reservoir models, and to a dissipatively operating neuromorphic quantum computer comprising said quantum processing unit, and to a hybrid system consisting of at least one classical computer and a quantum computer.

[0004] State of the Art of the Invention

[0005] The learning theory of artificial neural networks is based on mathematical models that mimic the functioning of the human brain, as first proposed by McCulloch, Pitts and Rosenblatt [1], [2]. Artificial neural networks (ANNs) play a crucial role in machine learning. In the last two decades, especially with the increase in the capacity of computer processors, complex tasks have been achieved with artificial neural network models [3]-[6]. However, the increasing volume of data to be processed and the approaching end of Moore's law pose significant challenges to the rate of performance improvement of artificial neural networks [7].

[0006] The promising performance boost offered by quantum computing has led to the idea of applying this to neural networks. The studies on this subject can be divided into two main categories: Simulation of quantum neural networks with standard quantum circuit model and hardware based implementation. However, the ability to capture nonlinear behavior in neural networks using a computational process that often incorporates principles of linear quantum mechanics remains a major challenge in both categories.

[0007] Quantum computing is a computational paradigm that utilizes resources that have no classical counterpart [8]. With just a few algorithms offered by this paradigm, it has been shown that it is possible to solve some problems believed to be impossible with classical computational methods [9]-[l l]. For the reasons mentioned above, in parallel with the growing interest in quantum computing, proposals for machine learning and neural network models based on the existing advantages of quantum computing have started to emerge

[0012] -

[0015] . Despite various proposals regarding quantum neural networks

[0016] ,

[0017] , the lack of agreement on a widely accepted model has made the topic an open research area. Especially at a very fundamental level, the problem of simulating the nonlinearity of a quantum neuron with the broadly linear properties of quantum computing is an important problem to solve.

[0008] Implementation proposals for artificial neural networks

[0018] ,

[0019] and nonlinear quantum neurons

[0020] ,

[0021] in standard quantum circuit models often require high resource costs. Furthermore, when the algorithm tailored to the problem to be solved needs multi-control gates for the neuron gate, the need for time-dependent optimization to create these gates has the potential to limit the effectiveness of the algorithm. Furthermore, current quantum computers being built are largely affected by quantum noise, which severely limits the efficiency of quantum algorithms that require high resources. This period of noisy performance of quantum computers is referred to as Noisy Intermediate Scale Quantum computing

[0022] (NISQ). The dissipative quantum computing model is depicted as the equivalent of the standard circuit quantum computing model

[0023] . Therefore, the dissipative model offers robustness against quantum noise and is also an independent analog quantum computing model.

[0009] In document with publication number WO2023034594A1, a method and system for quantum- assisted Hamiltonian learning is described. Here, experimental data points according to a Hamiltonian containing parameters with unknown values is obtained with a classical processor. The estimated values of the parameters are iteratively optimized by a non-unitary processor until predetermined completion criteria are met to minimize the cost function of the obtained parameters. Here also the cost function depends on multiple experimental data points and at each iteration the derivatives of the cost function with respect to the corresponding estimated values of the parameters for the previous iteration are again calculated on a quantum computer. Said quantum circuit model is only a closed (isolated and noise-free) circuit model, and the working principle thereof is based on unitary evolution and it will not operate in an open quantum system.

[0010] As a result all the above-mentioned problems have made it imperative to make an innovation in the relevant field. Object and Summary of the Invention

[0011] The main object of the invention is to create classifier neurons with strong activation behavior for artificial neural networks and artificial reservoir models to be executed in multilayer neuromorphic quantum computers or hybrid quantum computing systems in dissipative quantum computing models providing robustness against quantum noise, to establish the structure of a processing unit for running artificial neural networks and artificial reservoir models composed of said neurons, and of a hybrid quantum computing system within layered neuromorphic quantum computers, particularly neuromorphic hardware-based quantum computers running on the NISQ (Noisy Intermediate Scale Quantum) regime equipped with this processing unit.

[0012] The object of the invention is to create a quantum neuron that operates according to an explicit quantum dissipative model, with analogous, strongly non-linear behavior that can be successfully derived in possible learning processes.

[0013] The object of the invention is to create a quantum neuron that is highly resistant to dissipative quantum neuron noise effects and will contribute to a quantum accelerator model that can perform classical-like calculations in quantum hardware without transfer to a classical computer.

[0014] A quantum processing unit has been developed to achieve these objects. Said quantum processing unit is specifically configured to tune / manipulate / control the total angular momentum quantum number. The configuration of said processing unit sets the angular momentum quantum number to be greater than ’A. Surprisingly, it was found that when the angular momentum quantum number is greater than ’A, the neuron exhibits activation behavior similar to hyperbolic tangent activation, which can be easily used in dissipative quantum computing models providing robustness especially against quantum noise.

[0015] The neuron obtained with said quantum processing unit can be used to create a quantum neuron model with nonlinear activation, such as a quantum artificial neural network and an artificial reservoir, which operates within the framework of an open quantum system, can perform binary classification, and is differentiable. The quantum artificial neural network model exhibits a response behavior similar to the hyperbolic tangent function well known in the classical artificial neural network literature. Based on the results obtained in the model, it appears that the nonlinear behavior is amplified by the total angular momentum value J of the system.

[0016] Said neural network model allows for easy parameterization of the input quantum information and introduces differentiable, nonlinear activation functions of this dissipative model based on repeated interactions.

[0017] The present invention also discloses a nonlinear response diffusion assisted quantum neuron model operating as a binary classifier quantum detector, where the binary decision is read by a probe quantum system (PQS) with spin angular momentum of J > 1 / 2. In the model, the PQS is in contact with multiple, different quantum environments in pure quantum states with random connection rates as input quantum data. In the scenario, the PQS goes through an dissipative equilibration process and reaches a steady state where the binary decision is encoded. Steady-state magnetization is the success quantifier in this model. The propagation process is characterized by a collision model based on repeated interactions, which effectively characterizes open quantum systems and allows easy parameterization of the input quantum information contained by reservoirs

[0024] —

[0027] . Environments carrying quantum information are called information reservoirs

[0028] ,

[0029] .

[0018] It is shown that the quantum neuron responds as a tangent hyperbolic-like activation that can be controlled by the value of J. Steady state solutions are also obtained analytically with the master equation derived. Finally, the stationary response of the neuron driven by nonequilibrium environments involves quantum coherence that does not vanish. This opens up the possibility for future work to use non-classical quantum sources in a steady state.

[0019] Descriptions of the Figures Describing the Invention

[0020] The figures and the related descriptions used in order to better describe the device designed with this invention are as follows.

[0021] Fig. la. Graph showing the temporal evolution of PQS (for J = 1 / 2) for a single reservoir as a function of the number of collisions (NC) in the presence of varying 0 parameters. Fig. lb. Graph showing the temporal evolution of PQS (for J = 5 / 2) for a single reservoir as a function of the number of collisions (NC) in the presence of varying 0 parameters.

[0022] Fig. 2a. Graph showing the steady state values according to 0. (for J = 1 / 2)

[0023] Fig. 2b. Graph showing the steady state values according to 0. (for J = 5 / 2)

[0024] Fig. 2c. Graph showing the steady state values according to 0. (for J = 9 / 2)

[0025] Fig. 3. Graph showing the steady-state magnetization of the target qubit depending on the variation of the couplings to the reservoirs.

[0026] Fig. 4. Graph showing the variation of the steady-state magnetization of the target qubit with respect to the hyperbolic tangent depending on parameter J.

[0027] Detailed Description of the Invention

[0028] The present invention relates to a quantum processing unit for adjusting the total angular momentum quantum number of neurons in a quantum neural network model with nonlinear activation or artificial reservoir models, and to a dissipatively operating neuromorphic quantum computer comprising said quantum processing unit, and to a hybrid system consisting of at least one classical computer and a quantum computer.

[0029] Said quantum processing unit sets the total angular momentum quantum number of neurons (nodes) used in artificial neural networks or artificial reservoirs to be greater than Yi. The total angular momentum quantum number is determined by the combination of the total angular momentum quantum number, the intrinsic spin, and the orbital angular momentum.

[0030] The quantum processing unit can be configured in a variety of ways to fulfill said task. By using certain parameters of a quantum system, such as the strength and orientation of magnetic fields, one can adjust the total angular momentum quantum number or the parameters affecting the total angular momentum quantum number. Furthermore, the total angular momentum quantum number or the parameters affecting the total angular momentum quantum number can be adjusted on the arrangement of the parameters of the qubit frequencies, the coupling strengths or the design of the gates performing the gate operations.

[0031] In addition, physical properties such as the type of qubits used and the materials, they are made of can adjust the total angular momentum quantum number or the parameters affecting the total angular momentum quantum number depending on the effect of certain quantum properties.

[0032] The proposed processing unit is not defined for a specific hardware platform. It is suitable for any quantum processing platform where the collision model and the J>l / 2 state can be successfully implemented. For example, the NV-center platform where J>l / 2 values are observed or the superconducting circuits platform where J>l / 2 nuclear spin states are simulated can be shown as possible hardware candidates

[0030] .

[0033] Said quantum processing unit is organized such that it is able to execute the models obtained both for the generation of neurons and for the training of artificial neural network systems and artificial reservoirs created based on these neuron or neurons (only the reading layer is trained in artificial reservoirs) and for the realization of predictions.

[0034] In the following, the mathematical basis and explanations are given for the creation of a model with a strong activation behavior similar to the desired hyperbolic tangent by setting the total angular momentum quantum number to be greater than Yi.

[0035] In classical neural networks, the perceptron is a fundamental component of the neural network that performs binary classification tasks. Essentially, it gives binary label of 0 or 1 depending on the input represented as wherein is the set of input features and is the corresponding weight vectors. This binary output is generated via a non-linear function , wherein and the decision rule is set to otherwise Specific binary labels may change as needed. While the use of non-linear activation functions is useful for multilayer ANN applications, it is important to note that a neuron with an identity activation function can still produce linear classification.

[0036] The model of the present invention, based on quantum mechanics, as mentioned earlier, operates based on a protocol that dissipates energy. Input data presented in a classical way is represented as a weighted sum of input characteristics. The energy-dissipative quantum equivalent of the above expression is defined as follows: wherein 0^, is a completely positive trace-preserving (CPTP) quantum dynamics map acting on the research system characterized by the density matrix p0, and Pt represents the probability that the i. reservoir of the map will interact. The subscript t in equation (2) represents the time dependence of the maps generated by a physical process with a unitary emitter Ut acting on both the PQS and the reservoir. The i. reservoir quantum state is represented by pj?. and the partial trace on the i. reservoir is represented by

[0037] Quantum reservoirs provide initial quantum data consisting of uncorrelated, non-interacting two-level quantum systems (subunits), each described by its tensor product.

[0038] Here is the k. subunit of the i. information reservoir. These subunits are initially prepared in pure quantum states with the same Bloch parameters, which ensures the energy- dissipative equivalence of the model with parameterized quantum circuits.

[0039] The model described is based on a standard quantum collision model for their dynamics. The probe system experiences an energy-dissipative process due to multiple independent chambers with arbitrary connections. The steady state of the probe is read out through the spin observable Sz, which provides a binary classification output. Dynamics are given by: wherein nr is the elapsed time of the map after the collision n and is the unitary emitter that applies the fcth collision to the ith reservoir. According to these definitions, the initial quantum state of the whole system is read as p(0) = po(O) 0 Sig- Only the probe system lives in a time-dependent manner and the reservoir states are reset after each collision.

[0040] Taking the Hamiltonian of the system and the i. information reservoir as here the terms free refer to: while the term interaction refers to:

[0041] Here h is the reduced Planck constant, is the Pauli-z operator, and are the Pauli raising and lowering operators, respectively. is the number of atoms in the system. For simplicity, the probe qubit frequency and the reservoir qubit frequencies are defined as equal . The coupling rate assumed to be an adjustable parameter is denoted by g. It also determines the gt oc Ptprobability of the binding of the probe qubit to each reservoir, experienced from the corresponding reservoir as shown in equation (2), provided that it is in the weak coupling regime.

[0042] As mentioned above, the output results are read from a quantum system, PQS, that behaves in the spin state J > 1 / 2. In quantum mechanics, systems that behave like spin with J > 1 / 2 have a 2 / + 1 orientation with respect to the quantization axis. This result shows that high spin states can be adapted to a multi-class classification problem with observables in these methods.

[0043] Regardless of the total J of the PQS system, it always outputs a binary classification result associated with Szobservables that are nonlinearly related to the input quantum data weighted by the coefficients g^. The methods of our previous work

[0031] are used, where the derivation of the master equation and the analytical results are limited to J > 1 / 2 and give only linear activation results. In this study, how PQS behaves as a nonlinear activation function for the J > 1 / 2 cases and its effects on minimizing the cost function are presented. It is also discussed in a separate section how PQS for J > 1 / 2 can be physically implemented.

[0044] For any spin value J, the corresponding generalized density matrix expression can be defined in terms of polarization operators. Therefore, the density operator expression for PQS can be expressed as follows.

[0045] Here 1 is the d-dimensional unitary operator, r is the generalized Bloch vector with elements and is the corresponding spin polarization vector. Alternative generalized density matrix representations are also possible via the generalized Gell-Mann matrix basis or the Weyl operator basis

[0032] .

[0046] In the following, analytical results are presented in a polarization operator-based representation.

[0047] Micromaser theory

[0033] ,

[0034] has in the past opened up an enlightening research area in the experimental understanding of light-matter interactions. Today, this theory is being revisited in the context of the study of open quantum dynamics based on repeated interactions

[0037] . A micromaser-like master equations based on repeated interactions is developed to propose an explicit quantum classifier model

[0035] ,

[0036] . The derivation of the classifier's analytical operation principle based on the standard collision model with a micromaser-like master equation allows the model to make a convenient connection with realistic physical systems. Firstly, the unitary propagator of the collision model is evaluated in the interaction picture (h = 1) with respect to Ho. The unitary time-evolution operator is expressed as Wherein: and according to the second order approximation with respect to T the unitary emitter is obtained. Here, na= 2. Therefore, the second order approximation

[0048] ••• is used. In this case, unitary emitter is obtained. When the expressions are written in equation (11), the unitary emitter is expressed as:

[0049] Here is the spin step operators acting on the PQS and is the collective operators weighted by gt.

[0050] The expression of the emitter can be written in matrix form for any value of the spin angular momentum J of the PQS using expression (10). Here, only the expression for J = 1 is presented for simplicity, with analytical calculations given in the following sections for higher values of The spin operators for J = 1 read as follows:

[0051] In this way, U and U2operators can be written in matrix form as follows:

[0052]

[0053] Upon writing equations (13. a) and ( 14.b) in equation (10), the matrix form of the time-evolution operator expressed in equation (11) is obtained. When similar calculations are performed for J = 3 / 2 for only one reservoir state, the matrix form of the time-evolution operator is given below.

[0054] Since the reservoir states are reset to their initial state after each interaction, it is assumed that the entire system is factored as Unitary interactions defined by the Poisson process are examined in the context of micromaser theory. Dynamics of the system is expressed in δt time interval. Here r8t gives the probability of an interaction event at Poisson rate r and 1 — r6t gives the probability of a non-interaction state. The master equation defining the dynamics of the probe qubit is obtained in the limit 8t -> 0.

[0055] Equation (17) takes master equation form of:

[0056] Equation (10) is rearranged as Here, it is and When this expression is written in equation (18)

[0057] Here terms larger than second order, such as are eliminated. After some analytical adjustments following the methods in reference

[0037] , the final form of the master equation is obtained

[0038] . is the effective Hamiltonian representing a coherent drive on the probe qubit. Wherein describes averages computed over the ith repository, describes the standard Lindblad super operator, and describes a squeezing effect by the reservoir, coefficients contain diagonal inputs and coefficients contain off-diagonal inputs. The Lindblad coefficients indicate the information transferred from information reservoirs with a total number of terms N’ = N (N — l) / 2. Explicit form of the master equation for the probe qubit is obtained as follows by tracing the information environment through the degrees of freedom and using the linearity and cyclic properties of the tracing process:

[0058] The above expression provides mathematical proof of information transfer from reservoirs to PQS through the calculation of average values obtained with Pauli operators. The relation between these average values and the density matrix elements of the information reservoirs representing the input quantum information is related to the respective parametrizations as:

[0059] Herein p^. is the i-th reservoir density matrix. The density matrix representation of the initial state of PQS can be expressed as follows.

[0060] Here while for J = 1 the fundamental bases of Szare ,and It is expressed as and Writing the explicit forms of and expressions in equation (25); the stable quantum state of the probe qubit for the condition and is obtained

[0031] .

[0061] Here Please note that the coefficients in equation (10) are directly related to the elements of the density matrix of reservoir units and the coefficients y^n (21) are the weighted sum of these elements. These results analytically prove that PQS gives the weighted sum of the input quantum data at steady state.

[0062] As mentioned earlier, the presented model makes the binary classification decision in a steady state. Therefore, steady-state solutions of the master equation and the Bloch equations are obtained. The steady state of the PQS density matrix is expressed as the solution of p0= 0 in equation (24). Steady-state solutions of Bloch equations are found as:

[0063] Here are diagonal elements of the density matrix of reservoir units. When similar calculations are performed for , it is noted that naatomic number term is achieved in

[0064]

[0065] The numerical analysis starts with the study of the simplest scenario, where the PQS depends on a single (only information reservoir within the quantum state = The progression of events is tracked by the number of collisions with quantum data parameters represented by 0. Throughout the analysis, 0 is set to 0 without loss of generalization. The initial state of the PQS is a spin-compatible state with empty magnetization, wherein \j, m) is the standard angular momentum ground states, and with Here m is the spin projection number with Simulations are performed using the QUTIP package in Python

[0039] and the parameters are based on superconducting circuits

[0040] —

[0042] , which serve as a reliable platform for quantum information processing.

[0066] In this architecture, transmon qubits are connected via a resonator transmission line, allowing interaction through virtual photon exchange

[0043] . The coupling strength between the qubits can be adjusted by a dispersion coupling to the transmission line resonator.

[0067] In the most general definition, the weak coupling limit in open quantum systems is when the coupling frequencies are much smaller than the system frequency. The following are realistic parameters for superconducting platforms that meet these limit conditions.

[0068] A superconducting circuit with weakly coupled transmon qubits typically has a resonator frequency and a qubit-resonator pairing and an effective qubit-qubit pairing g~l — 100 MHz and a qubit energy relaxation time T1~40 — 150 ps

[0041] ,

[0043] ,

[0069] Fig. la and lb show the temporal evolution of PQS (for and J for a single reservoir as a function of the number of collisions (NC) in the presence of varying 0 parameters. Here the probe qubit magnetization is balanced against the number of collisions as a function of the reservoir qubit amplitude parameter 0. The spin-coherent state |n) was used as the initial state of the probe qubit. For 0 = 0°, 60°, 80°, 90°, 100°, 120°, 180° and (p = 0, the reservoir qubit was initialized as The target qubit reservoir interaction time r = 3 and the coupling coefficient g = 0.02 are dimensionless and scale with wr= 109Hz.

[0070] The quantity monitored is the normalized magnetization, defined as It is noted that after n~2 x 103collisions the PQS reaches a steady state, i = 3 ns interaction time is obtained, the time required to reach steady state is nr « 6gs, which is much smaller than value.

[0071] It has been reported that the time required to reach steady state is reduced when PQS interacts with media containing multiple qubits

[0044] . By keeping all parameters constant except parameter J and setting J = 5 / 2 as shown in Fig. lb, the values corresponding to the 0 parameters of the entire information reservoir, exhibits a nonlinear behavior and approach the steady state values and — 1. In principle, single-input quantum data can still be classified. As the model with a single reservoir is continued to be examined, a study of the behavior of the model in the presence of multiple information environments will be conducted.

[0072] In order to comprehensively understand the behavior of the proposed model, besides a transient evaluation, the focus is on studying the steady-state values with respect to 0, as shown in Figs. 2a-2c (for J Here the activation function is in the form of the equilibrium dynamics of the probe qubit magnetization versus the reservoir qubit amplitude parameter 0. The spin-coherent state |n) was used as the initial state of the probe qubit. For 0 = 0°, 60°, 80°, 90°, 100°, 120°, 180° and 0 = 0 , the reservoir qubit was initialized as The target qubit reservoir interaction time r = 3 and the connection coefficient g = 0.02 are dimensionless and scale with wr= 109Hz.

[0073] The steady- state magnetization values of the PQS marked as dots in the figure correspond to different values of the parameter J, which is analogous to the tanh(x) activation function. For a better comparison, the tanh(x) function represented by a continuous line in the figure is also included. As is well known, 0 is a geometric parameter of the Bloch sphere that characterizes the input quantum data and can take values between 0 and TT. The tanh(x) function takes any real value of x and returns the values 1 and — 1. Therefore, these two functions cannot be compared directly, but a relative comparison can be made with appropriately constructed scales. For this purpose, Fig. 2 is constructed for two different scales, such as x and The initial value of is a conscious choice to make a proper comparison between (Sz) and tan(x).

[0074] In Fig. 2a, where PQS is expressed as J = 1 / 2, the linear behavior of magnetization is observed over a wide range of values. While this behavior is sufficient for the model to perform linear classification tasks on its own, it may be insufficient for modeling complex, nonlinear relationships in multilayer networks built with this parameter. On the other hand, Fig. 2b shows that the steady-state response of the model for J = 5 / 2 PQS value coincides with the hyperbolic tangent function tanh(x) at the given scales. As shown Fig. 2c, for higher values of J, the system response converges more strongly towards values of 1 and — 1.

[0075] The hyperbolic tangent is often used as a differentiable activation function in neural networks where the gradient can be easily calculated

[0045] ,

[0046] . However, tanh(x) saturates at large positive and negative values, making it difficult to train deep neural networks. This problem is known as the vanishing gradient problem, where the gradients become very small, making it difficult for the optimization algorithm to update the weights. The behavior of the proposed model is similar to the function mentioned above, suggesting that it may have similar advantages and disadvantages. Nevertheless, note that the proposed model has the capacity to control its stable behavior by adjusting the parameter J. Moreover, the analytical results show that, regardless of the number of quantum input data, the summability of quantum dynamics maps can be achieved by considering the convex structure of the density matrix formalism. As a result, the model will always behave as if it is receiving input information from a single reservoir with an effective 0 between 0 and 0.

[0076] After observing the nonlinear behavior of a single input quantum reservoir, study the simplest case of multiple reservoirs is studied. Fig. 3 shows the normalized permanent magnetization of PQS with varying 6g. The spin angular quantum number is shown by two separate lines / and PQS is bound to two separate quantum reservoirs, and The connection strengths of PQS to each reservoir are gt= and with g = 0.01 and Here 6g represents a fraction of g. The probe qubit is initially prepared in the spin-coherent state |n). With 01= 0, and , it interacted collisional with reservoir units The target qubit reservoir interaction time T = 3 and the connection coefficient g = 0.02 are dimensionless and scale with wr. In the limit case where = 0 and g2= g i.e. the PQS is only bound to the reservoir |1). In this case, as shown in Fig. 3, the magnetization is as expected. For intermediate values of delta in the given range, the observed magnetization changes to and for 6g = 0.5 the other limit value (Sz) = 1 is reached. Henceforth, for the sake of simplicity, the tilde symbol used to denote magnetization is omitted.

[0077] Fig. 4 shows the hyperbolic tangent variation with respect to the values of the magnetization of the probe qubit depending on the spin angular momentum number. In this way, the activation function control is achieved by the parameter fy. The spin angular quantum numbers are shown for and in the graph. The variations of the pairing ratios are and Here 6g represents a fraction of g. The probe qubit is initially prepared in the spin-coherent state |n). With 01= O,0X= 0 and 02= TI, 02 = 0, it interacted collisional with reservoir units |0(0j, 0Q). The target qubit reservoir interaction time T = 3 and the connection coefficient g = 0.02 are dimensionless and scale with wr. REFERENCES

[0078] [1] W. S. McCulloch and W. Pitts, ‘A logical calculus of the ideas immanent in nervous activity’, Bulletin of Mathematical Biophysics, vol. 5, no. 4, pp. 115-133, Dec. 1943, doi: 10.1007 / BF02478259.

[0079] [2] F. Rosenblatt, ‘The perceptron: A probabilistic model for information storage and organization in the brain.’, Psychological Review, vol. 65, no. 6, pp. 386^408, 1958, doi: 10.1037 / h0042519.

[0080] [3] K. Arulkumaran, M. P. Deisenroth, M. Brundage, and A. A. Bharath, ‘Deep Reinforcement Learning: A Brief Survey’, IEEE Signal Processing Magazine, vol. 34, no. 6, pp. 26-38, 2017, doi: 10.1109 / MSP.2017.2743240.

[0081] [4] Z. Md. Fadlullah et al., ‘ State-of-the-Art Deep Learning: Evolving Machine Intelligence Toward Tomorrow’s Intelligent Network Traffic Control Systems’, IEEE Communications Surveys & Tutorials, vol. 19, no. 4, pp. 2432-2455, 2017, doi: 10.1109 / COMST.2017.2707140.

[0082] [5] M. Mahmud, M. S. Kaiser, A. Hussain, and S. Vassanelli, ‘Applications of Deep Learning and Reinforcement Learning to Biological Data’, IEEE Transactions on Neural Networks and Learning Systems, vol. 29, no. 6, pp. 2063-2079, 2018, doi:

[0083] 10.1109 / TNNLS.2018.2790388.

[0084] [6] D. Silver et al., ‘Mastering the game of Go with deep neural networks and tree search’, Nature, vol. 529, no. 7587, pp. 484-489, 2016, doi: 10.1038 / naturel6961.

[0085] [7] I. L. Markov, ‘Limits on fundamental limits to computation’, Nature, vol. 512, no. 7513, pp. 147-154, 2014, doi: 10.1038 / naturel3570.

[0086] [8] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition, Anniversary edition. Cambridge ; New York: Cambridge University Press, 2011.

[0087] [9] S. Hallgren, ‘Polynomial-time quantum algorithms for Pell’s equation and the principal ideal problem’, Journal of the ACM, vol. 54, no. 1, p. 4: 1-4:19, 2007, doi: 10.1145 / 1206035.1206039.

[0088]

[0010] P. W. Shor, ‘Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer’, SIAM Journal on Computing, vol. 26, no. 5, pp. 1484-1509, 1997, doi: 10.1137 / S0097539795293172.

[0011] W. van Dam, S. Hallgren, and L. Ip, ‘Quantum Algorithms for Some Hidden Shift Problems’, SIAM Journal on Computing, vol. 36, no. 3, pp. 763-778, 2006, doi: 10.1137 / S009753970343141X.

[0089]

[0012] J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, and S. Lloyd, ‘Quantum machine learning’, Nature, vol. 549, no. 7671, pp. 195-202, 2017.

[0090]

[0013] I. Cong, S. Choi, and M. D. Lukin, ‘Quantum convolutional neural networks’, Nature Physics, vol. 15, no. 12, 2019.

[0091]

[0014] A. W. Harrow, A. Hassidim, and S. Lloyd, ‘Quantum Algorithm for Linear Systems of Equations’, Physical Review Letters, vol. 103, no. 15, p. 150502, 2009, doi: 10.1103 / PhysRevLett.103.150502.

[0092]

[0015] S. Lloyd, M. Mohseni, and P. Rebentrost, ‘Quantum principal component analysis’, Nature Physics, vol. 10, no. 9, pp. 631-633, 2014, doi: 10.1038 / nphys3029.

[0093]

[0016] M. Schuld, I. Sinayskiy, and F. Petruccione, ‘The quest for a Quantum Neural Network’, Quantum Inf Process, vol. 13, no. 11, pp. 2567-2586, Nov. 2014, doi: 10.1007 / sl 1128-014-0809-8.

[0094]

[0017] F. V. Massoli, L. Vadicamo, G. Amato, and F. Falchi, ‘A Leap among Quantum Computing and Quantum Neural Networks: A Survey’, ACM Computing Surveys, vol. 55, no. 5, p. 98: 1-98:37, 2022, doi: 10.1145 / 3529756.

[0095]

[0018] J. Zhao, Y.-H. Zhang, C.-P. Shao, Y.-C. Wu, G.-C. Guo, and G.-P. Guo, ‘Building quantum neural networks based on a swap test’, Physical Review A, vol. 100, no. 1, p. 012334, 2019, doi: 10.1103 / PhysRevA.100.012334.

[0096]

[0019] C. A. Monteiro, G. I. S. Filho, M. H. J. Costa, F. M. de Paula Neto, and W. R. de Oliveira, ‘Quantum neuron with real weights’, Neural Networks, vol. 143, pp. 698-708, 2021, doi: 10.1016 / j.neunet.2021.07.034.

[0097]

[0020] F. M. de Paula Neto, T. B. Ludermir, W. R. de Oliveira, and A. J. da Silva,

[0098] ‘Implementing Any Nonlinear Quantum Neuron’, IEEE Transactions on Neural Networks and Learning Systems, vol. 31, no. 9, pp. 3741-3746, 2020, doi:

[0099] 10.1109 / TNNLS.2019.2938899.

[0100]

[0021] S. Yan, H. Qi, and W. Cui, ‘Nonlinear quantum neuron: A fundamental building block for quantum neural networks’, Physical Review A, vol. 102, no. 5, p. 052421, 2020, doi: 10.1103 / PhysRevA.102.052421.

[0101]

[0022] J. Preskill, ‘Quantum Computing in the NISQ era and beyond’, Quantum, vol. 2, p. 79, Aug. 2018, doi: 10.2233 l / q-2018-08-06-79.

[0023] F. Verstraete, M. M. Wolf, and J. Ignacio Cirac, ‘Quantum computation and quantumstate engineering driven by dissipation’, Nature Phys, vol. 5, no. 9, pp. 633-636, Sep. 2009, doi: 10.1038 / nphysl342.

[0102]

[0024] V. Scarani, M. Ziman, P. Stelmachovic, N. Gisin, and V. Buzek, ‘Thermalizing Quantum Machines: Dissipation and Entanglement’, Phys. Rev. Lett., vol. 88, no. 9, p. 097905, Feb. 2002, doi: 10.1103 / PhysRevLett.88.097905.

[0103]

[0025] M. Ziman, P. Stelmachovic, V. Buzek, M. Hillery, V. Scarani, and N. Gisin, ‘Diluting quantum information: An analysis of information transfer in system-reservoir interactions’, Phys. Rev. A, vol. 65, no. 4, p. 042105, Mar. 2002, doi: 10.1103 / PhysRevA.65.042105.

[0104]

[0026] M. Cattaneo, G. De Chiara, S. Maniscalco, R. Zambrini, and G. L. Giorgi, ‘Collision Models Can Efficiently Simulate Any Multipartite Markovian Quantum Dynamics’, Phys. Rev. Lett., vol. 126, no. 13, p. 130403, Apr. 2021, doi: 10.1103 / PhysRevLett.126.130403.

[0105]

[0027] F. Ciccarello, S. Lorenzo, V. Giovannetti, and G. M. Palma, ‘Quantum collision models: Open system dynamics from repeated interactions’, Physics Reports, vol. 954, pp. 1-70, 2022.

[0106]

[0028] S. Deffner, ‘Information-driven current in a quantum Maxwell demon’, Phys. Rev. E, vol. 88, no. 6, p. 062128, Dec. 2013, doi: 10.1103 / PhysRevE.88.062128.

[0107]

[0029] S. Deffner and C. Jarzynski, ‘Information Processing and the Second Law of Thermodynamics: An Inclusive, Hamiltonian Approach’, Phys. Rev. X, vol. 3, no. 4, p. 041003, Oct. 2013, doi: 10.1103 / PhysRevX.3.041003.

[0108]

[0030] Rollano, V., de Ory, M.C., Buch, C.D. et al. High cooperativity coupling to nuclear spins on a circuit quantum electrodynamics architecture. Commun Phys 5, 246 (2022). https: / / doi.org / 10.1038 / s42005-022-01017-8

[0109]

[0031] U. Korkmaz and D. Tiirkpenge, ‘Quantum collisional classifier driven by information reservoirs’, Phys. Rev. A, vol. 107, no. 1, p. 012432, Jan. 2023, doi: 10.1103 / PhysRevA.107.012432.

[0110]

[0032] R. A. Bertlmann and P. Krammer, ‘Bloch vectors for qudits’, Journal of Physics A: Mathematical and Theoretical, vol. 41, no. 23, p. 235303, 2008, doi: 10.1088 / 1751- 8113 / 41 / 23 / 235303.

[0111]

[0033] P. Filipowicz, J. Javanainen, and P. Meystre, ‘Theory of a microscopic maser’, Phys. Rev. A, vol. 34, no. 4, pp. 3077-3087, Oct. 1986, doi: 10.1103 / PhysRevA.34.3077.

[0112]

[0034] J. D. Cresser, ‘Quantum-field model of the injected atomic beam in the micromaser’, Phys. Rev. A, vol. 46, no. 9, pp. 5913-5931, Nov. 1992, doi: 10.1103 / PhysRevA.46.5913.

[0035] P. Strasberg, G. Schaller, T. Brandes, and M. Esposito, ‘Quantum and Information Thermodynamics: A Unifying Framework Based on Repeated Interactions’, Phys. Rev. X, vol. 7, no. 2, p. 021003, Apr. 2017, doi: 10.1103 / PhysRevX.7.021003.

[0113]

[0036] J.-Q. Liao, H. Dong, and C. P. Sun, ‘Single-particle machine for quantum thermalization’, Phys. Rev. A, vol. 81, no. 5, p. 052121, May 2010, doi: 10.1103 / PhysRevA.81.052121.

[0114]

[0037] R. Roman- Ancheyta, B. Qakmak, and O. E. Mustecaphoglu, ‘Spectral signatures of non-thermal baths in quantum thermalization’, Quantum Sci. Technol., vol. 5, no. 1, p. 015003, Dec. 2019, doi: 10.1088 / 2058-9565 / ab5e4f.

[0115]

[0038] U. Korkmaz and D. Tiirkpenge, ‘Transfer of quantum information via a dissipative protocol for data classification’, Physics Leters A, vol. 426, p. 127887, Feb. 2022, doi: 10.1016 / j.physleta.2021.127887.

[0116]

[0039] J. R. Johansson, P. D. Nation, and F. Nori, ‘QuTiP 2: A Python framework for the dynamics of open quantum systems’, Computer Physics Communications, vol. 184, no. 4, pp. 1234-1240, Apr. 2013, doi: 10.1016 / j.cpc.2012.11.019.

[0117]

[0040] A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, ‘Circuit quantum electrodynamics’, Rev. Mod. Phys., vol. 93, no. 2, p. 025005, May 2021, doi: 10.1103 / RevModPhys.93.025005.

[0118]

[0041] X.-H. Deng, E. Barnes, and S. E. Economou, ‘Robustness of error- suppressing entangling gates in cavity-coupled transmon qubits’, Phys. Rev. B, vol. 96, no. 3, p. 035441, Jul. 2017, doi: 10.1103 / PhysRevB .96.035441.

[0119]

[0042] P. Krantz, M. Kjaergaard, F. Yan, T. P. Orlando, S. Gustavsson, and W. D. Oliver, ‘A quantum engineer’s guide to superconducting qubits’, Applied Physics Reviews, vol. 6, no. 2, p. 021318, Jun. 2019, doi: 10.1063 / 1.5089550.

[0120]

[0043] J. Majer et al., ‘Coupling superconducting qubits via a cavity bus’, Nature, vol. 449, no. 7161, pp. 443-447, Sep. 2007, doi: 10.1038 / nature06184.

[0121]

[0044] D. Tiirkpenge and R. Roman- Ancheyta, ‘Tailoring the thermalization time of a cavity field using distinct atomic reservoirs’, JOSA B, vol. 36, no. 5, pp. 1252-1259, 2019.

[0122]

[0045] A. Apicella, F. Donnarumma, F. Isgro, and R. Prevete, ‘A survey on modem trainable activation functions’, Neural Networks, vol. 138, pp. 14-32, 2021, doi: 10.1016 / j.neunet.2021.01.026.

[0123]

[0046] M. Bianchini and F. Scarselli, ‘On the Complexity of Neural Network Classifiers: A Comparison Between Shallow and Deep Architectures’, IEEE Transactions on Neural Networks and Learning Systems, vol. 25, no. 8, pp. 1553-1565, 2014, doi: 10.1109 / TNNLS.2013.2293637.

Claims

CLAIMS1. A quantum processing unit configured to form a quantum classifier neuron for use in a quantum neural network model with nonlinear activation or an artificial reservoir model, characterized in that: it is configured to adjust the classifier neurons of said quantum neural network model such that the total angular momentum quantum number is greater thanx / i in order to provide hyperbolic tangent activation behavior.

2. The quantum processing unit according to claim 1, characterized in that: it is configured to execute a quantum neural network model with a classifier consisting of neurons with a total angular momentum quantum number greater thanx / i in order to provide hyperbolic tangent activation behavior.

3. The quantum processing unit according to claim 1, characterized in that: it is configured to execute an artificial reservoir model with a classifier consisting of neurons with a total angular momentum quantum number greater thanx / i in order to provide hyperbolic tangent activation behavior.

4. The quantum processing unit according to claim 2 or 3, characterized in that it is configured to transfer the quantum information to the decision-making system by a repeated collision model in order for the model to perform a linear summation of the input quantum information before the decision.

5. The quantum processing unit according to claim 4, characterized in that said decisionmaking system is a probe qubit PQS.

6. The quantum processing unit according to any one of the preceding claims, characterized in that it is configured to operate in the weak coupling limit of open quantum system dynamics.

7. A dissipatively operating neuromorphic quantum computer comprising the quantum processing unit according to any one of claims 1-6.

8. A neuromorphic quantum computer configured to operate dissipatively in a noisy medium scale quantum regime, comprising the quantum processing unit according to any one of claims 1-6.

9. A hybrid quantum computing system comprising a quantum computer comprising the quantum processing unit according to any one of claims 1-6 and a classical computer.