Quantum computing's most consequential claim — that quantum computers provide exponential computational speedup over classical computation — rests on a specific physical assumption: that superposition is ontologically real, that a qubit genuinely and simultaneously occupies multiple states, and that quantum algorithms exploit this simultaneity as a physical resource. A quantum computer with n qubits is claimed to process 2ⁿ computational paths in parallel by virtue of this simultaneous occupation. This paper argues that all three foundational assumptions are precluded by Quantum-Geometry Dynamics (QGD), the physical theory derived from the Minimal Physically Derivable Theories (MPDT) framework established by the Uniqueness Theorem. In QGD, physical reality is strictly and absolutely deterministic. Every fundamental constituent — every preon(+) — has a definite position and definite intrinsic momentum at every moment. There are no indeterminate states, no superpositions, and no wave function collapse at the fundamental level. What quantum mechanics describes as superposition is not a physical state of simultaneous occupation but an epistemic description of ignorance of the deterministic microstate of a preonic configuration. The wave function is a probabilistic description of deterministic preonic dynamics — a calculational tool that correctly predicts statistical outcomes — not a description of a physical state in which a system genuinely occupies multiple configurations simultaneously. This distinction has a direct and specific consequence for quantum computing. Quantum computing devices are genuine physical systems that exploit real quantum mechanical phenomena — phenomena that QGD derives from the deterministic dynamics of preons(+) and preons(−) in the finite discrete preon(−) lattice. The MPDT framework does not forbid the construction or operation of quantum computing devices. What QGD precludes is the ontological foundation on which the exponential speedup argument rests. A quantum computing device is a deterministic preonic configuration occupying one microstate at each moment. The 2ⁿ simultaneous amplitude states of the quantum formalism are elements of a probabilistic description of that microstate — not physical states simultaneously instantiated in the device. Quantum parallelism is a feature of the formalism, not of the underlying physics. The paper develops this argument systematically across eight sections. Section 2 establishes QGD's account of quantum phenomena as emergent from deterministic preonic dynamics, including the derivation of wave-like interference patterns and Bell correlations without superposition. Section 3 examines precisely what superposition is and is not in QGD, culminating in the formal statement that a qubit in the state α|0⟩ + β|1⟩ is not a system simultaneously occupying both states but a deterministic preonic configuration whose microstate determines measurement outcomes but is not individually accessible at the observational level. Section 4 identifies the exact point at which the exponential speedup argument fails: the physical resource it invokes — simultaneous occupation of 2ⁿ states — does not exist in the physical universe that QGD describes. Sections 5 examines three specific quantum algorithms: Shor's factoring algorithm, whose polynomial-time complexity is demonstrated within the quantum formalism but whose underlying preonic complexity remains an open question; Grover's search algorithm, whose quadratic speedup rests on the same ontological assumption; and quantum simulation, which survives the critique more robustly because it does not require exponential parallelism as a resource. Section 6 addresses decoherence, reinterpreting it not as an engineering challenge to be solved by better isolation but as a fundamental feature of reality — the inevitable influence of the instantaneous gravitational field of the entire preon(−) lattice on every qubit configuration, which cannot be shielded against in principle. Sections 7 and 8 develop the implications for the quantum computing programme and conclude. The argument connects directly to the P vs NP analysis in the companion Physicality of Logic paper. Shor's algorithm is the canonical example of a quantum algorithm claimed to solve a classically hard problem — integer factoring — in polynomial time, with significant implications for the security of RSA encryption. If QGD is correct and the exponential speedup argument fails, the classical hardness of factoring is preserved and the cryptographic implications attributed to quantum computing do not follow. The paper does not claim that quantum computing devices are useless — it claims that the specific resource driving the most dramatic projections for quantum computing does not physically exist, and that whatever computational advantages quantum devices possess must be explained within the deterministic preonic framework rather than by appeal to quantum parallelism. The paper is intended for physicists working on quantum computing and quantum foundations, philosophers of physics, and computer scientists working on computational complexity. It is submitted to Foundations of Physics. It is a companion to the author's papers on the Uniqueness Theorem and the Physicality of Logic, and to the book Quantum-Geometry Dynamics: An Axiomatic Approach to Physics.
Quantum computing's most consequential claim — that quantum computers provide exponential computational speedup over classical computation — rests on a specific physical assumption: that superposition is ontologically real, that a qubit genuinely and simultaneously occupies multiple states, and that quantum algorithms exploit this simultaneity as a physical resource. A quantum computer with n qubits is claimed to process 2ⁿ computational paths in parallel by virtue of this simultaneous occupation. This paper argues that all three foundational assumptions are precluded by Quantum-Geometry Dynamics (QGD), the physical theory derived from the Minimal Physically Derivable Theories (MPDT) framework established by the Uniqueness Theorem. In QGD, physical reality is strictly and absolutely deterministic. Every fundamental constituent — every preon(+) — has a definite position and definite intrinsic momentum at every moment. There are no indeterminate states, no superpositions, and no wave function collapse at the fundamental level. What quantum mechanics describes as superposition is not a physical state of simultaneous occupation but an epistemic description of ignorance of the deterministic microstate of a preonic configuration. The wave function is a probabilistic description of deterministic preonic dynamics — a calculational tool that correctly predicts statistical outcomes — not a description of a physical state in which a system genuinely occupies multiple configurations simultaneously. This distinction has a direct and specific consequence for quantum computing. Quantum computing devices are genuine physical systems that exploit real quantum mechanical phenomena — phenomena that QGD derives from the deterministic dynamics of preons(+) and preons(−) in the finite discrete preon(−) lattice. The MPDT framework does not forbid the construction or operation of quantum computing devices. What QGD precludes is the ontological foundation on which the exponential speedup argument rests. A quantum computing device is a deterministic preonic configuration occupying one microstate at each moment. The 2ⁿ simultaneous amplitude states of the quantum formalism are elements of a probabilistic description of that microstate — not physical states simultaneously instantiated in the device. Quantum parallelism is a feature of the formalism, not of the underlying physics. The paper develops this argument systematically across eight sections. Section 2 establishes QGD's account of quantum phenomena as emergent from deterministic preonic dynamics, including the derivation of wave-like interference patterns and Bell correlations without superposition. Section 3 examines precisely what superposition is and is not in QGD, culminating in the formal statement that a qubit in the state α|0⟩ + β|1⟩ is not a system simultaneously occupying both states but a deterministic preonic configuration whose microstate determines measurement outcomes but is not individually accessible at the observational level. Section 4 identifies the exact point at which the exponential speedup argument fails: the physical resource it invokes — simultaneous occupation of 2ⁿ states — does not exist in the physical universe that QGD describes. Sections 5 examines three specific quantum algorithms: Shor's factoring algorithm, whose polynomial-time complexity is demonstrated within the quantum formalism but whose underlying preonic complexity remains an open question; Grover's search algorithm, whose quadratic speedup rests on the same ontological assumption; and quantum simulation, which survives the critique more robustly because it does not require exponential parallelism as a resource. Section 6 addresses decoherence, reinterpreting it not as an engineering challenge to be solved by better isolation but as a fundamental feature of reality — the inevitable influence of the instantaneous gravitational field of the entire preon(−) lattice on every qubit configuration, which cannot be shielded against in principle. Sections 7 and 8 develop the implications for the quantum computing programme and conclude. The argument connects directly to the P vs NP analysis in the companion Physicality of Logic paper. Shor's algorithm is the canonical example of a quantum algorithm claimed to solve a classically hard problem — integer factoring — in polynomial time, with significant implications for the security of RSA encryption. If QGD is correct and the exponential speedup argument fails, the classical hardness of factoring is preserved and the cryptographic implications attributed to quantum computing do not follow. The paper does not claim that quantum computing devices are useless — it claims that the specific resource driving the most dramatic projections for quantum computing does not physically exist, and that whatever computational advantages quantum devices possess must be explained within the deterministic preonic framework rather than by appeal to quantum parallelism. The paper is intended for physicists working on quantum computing and quantum foundations, philosophers of physics, and computer scientists working on computational complexity. It is submitted to Foundations of Physics. It is a companion to the author's papers on the Uniqueness Theorem and the Physicality of Logic, and to the book Quantum-Geometry Dynamics: An Axiomatic Approach to Physics.
The Physical Impossibility of Quantum Computational Speedup: Two Independent Arguments from Quantum-Geometry Dynamics Quantum computing promises computational advantages that are, in the most celebrated cases, exponential. Shor's algorithm factors integers exponentially faster than the best known classical algorithm; Grover's algorithm searches an unstructured database with a quadratic speedup. These results are mathematically rigorous within their assumed framework. This paper asks not whether the mathematics is correct but whether the physical assumptions underlying it are. I argue that Quantum-Geometry Dynamics (QGD) — an axiomatic framework for physics derived from the discreteness of space and the kinetic nature of matter — establishes two independent foundational preclusions of quantum computational speedup. These are not engineering obstacles or decoherence problems that better technology can overcome. They are consequences of the physical structure of discrete space, and no improvement in qubit isolation, error correction, or fabrication technique can supply a physical resource that does not exist. The first preclusion concerns physical states. In QGD, matter is composed of preons⁺ that propagate through quantum-geometrical space by preonic leaps, each of which is a definite transition from one spatial unit to the next in the direction of the momentum vector. A preon(+) always occupies a definite position. There is no ontological superposition. What quantum mechanics represents as a superposed state is, in QGD, an epistemic description of our ignorance of the system's actual preonic microstate. Since ontological superposition is the physical resource on which quantum parallelism depends, its absence means that no physical system can instantiate the state required for exponential speedup. The second preclusion concerns physical processes. Causal succession in discrete space is categorically and structurally irreversible: every preonic leap has a definite direction, and no physical process can reverse the causal order of preonic states. This is not thermodynamic irreversibility arising from large numbers but a property of every individual preonic transition. Since the quantum circuit model is built on reversible unitary gates, and reversible computation has no physical instantiation in a discrete-space framework, the operational basis of quantum computing is equally precluded. I show how both arguments bite at specific steps in Shor's algorithm and Grover's algorithm. In Shor's algorithm, the first preclusion destroys the state preparation step and the second destroys the quantum Fourier transform. In Grover's algorithm, the first preclusion destroys the uniform superposition and the second destroys the diffusion operator and oracle. Either preclusion alone is sufficient; together they attack quantum speedup at both ends — what goes in and how it is processed. The black hole information paradox, correctly understood within QGD, provides independent confirmation: the paradox dissolves precisely because physical states are always definite and physical evolution is categorically irreversible — the same two features that preclude quantum speedup. The Uniqueness Theorem for QGD further strengthens the claim: if the two-axiom discrete-space structure is the unique viable foundational description of physical reality, these preclusions are not features of one possible framework among many but consequences of the physical structure of the universe. This paper supersedes the earlier paper Quantum Computing Under Quantum-Geometry Dynamics (Zenodo, DOI: 10.5281/zenodo.19522137) and should be read in its place. This paper is part of the Minimal Physically Derivable Theory (MPDT) programme.
Quantum computing operates by manipulating the quantum state of a system to solve problems intractable for classical computing. These problems, previously considered limitations of classical algorithms, have solutions through quantum approaches. Therefore, quantum computing suggests that the complexity of such problems lies in the current epistemic state rather than the objective state of the problem. Computational complexity can be classified into objective and epistemic complexity. Some classical problems exhibiting exponential complexity fall into the epistemic category, as their solutions depend on the current state of human knowledge and available tools. Quantum computing suggests that even mathematics isn’t entirely objective, and mathematics, in one sense, is human-made and a kind of technology, which reflects our intention and planning. Computational complexity, therefore, bridges the objective and subjective. Overcoming classical complexity necessitates advancements in scientific theories, algorithms, and quantum technology, all of which rely on the development of human cognitive abilities. Quantum computing is not just a mathematical construct, but also has physical meaning. If it were purely mathematical, classical physics and systems could potentially achieve the same results. What makes the quantum world special is its empirical nature—the physical reality of quantum chips, quantum algorithms, and quantum evolution. Quantum supremacy, or quantum advantage, refers to the potential superiority of quantum computers over classical ones. Controllable quantum systems offer an overwhelming advantage in terms of manipulation and dominance compared to classical systems. Essentially, quantum computing has the potential to significantly outperform classical computing. Many experts, including Shor, have proposed that quantum computing’s power stems from its ability to perform multiple computations simultaneously—a concept often referred to as the Quantum parallelism thesis. Rather, some argue that the true source of quantum computing acceleration lies in the fundamental differences between classical and quantum logic. However, it’s important to note that quantum logic, while providing a new perspective, does not directly address the core principle of quantum parallelism. This dominance stems from quantum physics’ unique properties: Exponential storage capacity, parallel computing inherent to its nature (ontological), and the ability to perform calculations with exponential speedup through quantum algorithms.
Classical computers — the devices on which this article was written and on which you are reading it — operate on a binary logic of 0s and 1s. Every calculation, every image, every piece of music and every financial transaction is ultimately reducible to combinations of these two states. Quantum computers operate on a fundamentally different principle, exploiting quantum mechanical phenomena — superposition, entanglement, and quantum interference — to process information in ways that classical computing cannot replicate at any scale. This is not simply a matter of being faster. Quantum computers are architecturally different from classical computers in a way that makes them uniquely suited to solving specific categories of problems — drug discovery molecular simulation, cryptographic analysis, optimisation problems with millions of variables, and the simulation of quantum systems — that are practically intractable for classical machines. This article provides a scientifically accurate and conceptually accessible explanation of quantum computing, examining the six core concepts that distinguish it: superposition (qubits existing in multiple states simultaneously), entanglement (the correlation of quantum states across physical distance), quantum interference (the amplification of correct answers and cancellation of errors), decoherence (the primary engineering challenge), quantum gates (the operations that replace classical logic gates), and quantum advantage (the specific domains where quantum computing genuinely outperforms classical systems). Drawing on research from IBM Quantum, Google AI's quantum supremacy claims, and the philosophical parallels between quantum non-locality and the Vedantic concept of Akasha (the fifth element of interconnected space), the article makes quantum computing genuinely comprehensible without sacrificing scientific accuracy.
Quantum computation was envisioned by Feynman as a valuable means of solving quantum problems [1]. The question is, how do we prove the superiority of quantum computing over classical devices? A common misconception in describing the power of a quantum computer over a classical computer is that quantum bits can be prepared in a superposition of an exponential number of states, which cannot be achieved with classical bits. This statement is certainly true, but it does not tell us, specifically, what problems quantum computers can efficiently solve while classical computers fail to do so. In fact, based exactly on the technique of Feynman's path integral, the output (i.e. transition amplitude) of any quantum circuit can be calculated classically with a polynomial amount of memory (although the temporal cost would be exponential). Therefore any quantum computation can be simulated classically; the key question is about the efficiency. Much effort has been made trying to pin down the power of quantum computers based on the machinery of the computational complexity theory. In particular, the class of computational (decision) problems that can be solved efficiently by a quantum computer is called BQP (bounded-error quantum polynomial time); the counterpart for classical computers is called P (polynomial time). Of course, BQP cannot be less than P; in principle quantum computers can simulate classical computers efficiently. The point is that the foundation of quantum computation cannot be established without a proof showing that BQP is strictly larger than P (i.e. BQP ≠ P). In this sense, this question is as interesting as the famous challenge of proving P ≠ NP (non-deterministic polynomial time). A well known instance of an NP problem is the factoring problem; Shor's quantum algorithm is capable of solving the factoring problem in polynomial time, which is not achievable with the best classical algorithm discovered so far. However, we still cannot rigorously exclude the possibility of the existence of an efficient classical algorithm for factoring. Although again without a proof, it is commonly believed that quantum computers are unable to solve some of the NP problems. In fact, the proof of this statement (if true) provides a possible path to prove P ≠ NP. A potentially less demanding question would be, when do we expect a quantum computer to be able to perform some well defined tasks (not necessarily related to any practical problem) that cannot be simulated with any currently available classical device, within a reasonable time? Once achieved, the status is called ‘quantum supremacy' [2]. One may ask, what about Grover's search algorithm, which provides a quadratic speedup over the classical search? Can we say that we can already achieve quantum supremacy with Grover's algorithm? The problem is that, instead of taking the large-N limit, quantum supremacy requires us to determine the actual number of qubits and gates that can no longer be simulated by classical computers within a reasonable time. To elaborate further, we remark that there can be two notions of classical simulation, namely ‘strong simulation' versus ‘weak simulation'. Strong simulation refers to the cases of calculating the transition probabilities, or expectation values of observables, to a high accuracy in polynomial time. Weak simulation requires the probability distributions to be accurately reproduced, which involves ‘sampling' the different outcomes of the quantum devices. Some quantum circuits that cannot be strongly simulated with an efficient classical means may have efficient classical methods for weak simulation [3]. However, we should be careful about the accuracy requirement in the simulation tasks. For example, for many decision problems, it may be sufficient to determine the transition amplitudes to within an additive error, instead of multiplicative error. In other words, the classical simulability of quantum computational problems depends on the accuracy requirement. Currently, there are three popular approaches for achieving quantum supremacy (see Fig. 1), namely (i) boson sampling [4], (ii) sampling IQP (instantaneous quantum polynomial) circuits [5], and (iii) sampling chaotic quantum circuits [6]. In all of these approaches, distributions of different bit strings or photon numbers are sampled from the quantum devices. Furthermore, they all involve the assumption that classical computers are unable to efficiently determine the transition amplitudes, and/or reproduce (or approximate) the distributions of quantum devices performing these tasks, in the sense of both strong and weak simulations. Three different approaches for achieving quantum supremacy: (a) boson sampling; (b) IQP circuits; (c) chaotic quantum circuits. In boson sampling, single photons are injected into different modes of a linear optical network. The task is to determine the photon distributions at the output ports. The key feature of boson sampling is that the transition amplitudes are related to the permanents of complex matrices, which are in general very difficult to calculate exactly, or approximate to within an multiplicative error; these problems belong to the #P-hard complexity class. Moreover, efficient weak simulation of boson sampling is believed to be impossible, unless the polynomial hierarchy collapses to its third level. However, a recent numerical study suggests that, in order to achieve quantum supremacy with boson sampling, one needs to simultaneously generate at least 50 or more single photons, which is still highly technologically challenging. An interesting question is whether linear optics, in the setting of boson sampling, can be applied to solve decision problems. In this case, the transition amplitudes may need to be determined to an additive error. However, we found that a large class of decision problems associated with boson sampling can be simulated by a classical computer [7], settling an open problem [8] by Aaronson and Hance. IQP circuits represent a simplified quantum-circuit model. The initial state starts from the all-zero state, |000…0〉, followed by applying Hadamard gates to each qubit. Then, diagonal gates are applied to the qubits, followed by applying Hadamard gates to each qubit again. The argument of showing the complexity in simulating IQP circuits is similar to that of boson sampling. In fact, the complexity of boson sampling was inspired by the complexity results of IQP circuits. However, when subject to noise, IQP circuits may become classically simulable [9]. Lastly, chaotic quantum circuits refer to the class of quantum circuits where two-qubit gates are applied regularly, while single-qubit gates are applied randomly from a gate set. The output distributions of these circuits approach the so-called Porter–Thomas distribution, which is a characteristic feature of quantum chaos. Recently, there have been several numerical investigations aiming to explore the ultimate limit of classical computing in simulating low-depth quantum circuits. For the ideal cases, one needs to consider both the qubit number and circuit depth for benchmarking quantum supremacy. However, in the presence of noise, these chaotic circuits may also become classically simulable for high-depth circuits [10]. Finally, other than these three approaches, one should expect that quantum supremacy can be achieved for many practical applications, e.g. simulation of quantum chemistry or quantum machine learning. When will it happen? Only time will tell!
The rapid evolution of computers in the half century since their invention has resulted in dramatically smaller and faster computers. However, from a computational point of view, all these computers look alike; for example, they are built out of simple logic gates. A fundamental thesis of computer science---the modern form of the Church--Turing thesis---asserts that this is inevitable in a deep sense. Any computer can be simulated with at most a polynomial factor slowdown by a probabilistic Turing machine. Quantum computation poses the first credible challenge to this thesis. It goes back to a suggestion by Feynman [4], who pointed out that there appears to be no efficient way of simulating a quantum mechanical system on a computer, and suggested that, perhaps, a computer based on quantum physical principles might be able to carry out the simulation efficiently. Two formal models for quantum computers---the quantum Turing machine [2] and quantum computational networks [3]---were defined by Deutsch. The first three papers in this issue describe efficient quantum algorithms for computational tasks that we do not know how to solve classically. In "Quantum Complexity Theory," Bernstein and Vazirani give the first formal evidence that quantum computers violate the modern form of the Church--Turing thesis. They show that a certain problem---the recursive Fourier sampling problem---can be solved in polynomial time on a quantum Turing machine, but relative to an oracle, requires superpolynomial time on a classical probabilistic Turing machine. Simon, in the paper "On the Power of Quantum Computation" introduces a fundamental projection technique and uses it to design an efficient quantum algorithm to determine whether a certain type of function is 2-1 or 1-1. He further shows that, relative to an oracle, this problem requires exponential time on a classical probabilistic Turing machine. In the paper "Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer," Shor gives remarkable polynomial time quantum algorithms for two of the most famous problems in computer science: factoring and discrete log. Since the computational hardness of these problems is the basis of several famous cryptosystems, Shor's paper very dramatically underlines the power of quantum computers. To understand the computational power of quantum computers, it is helpful to consider a quantum mechanical system of n particles, each of which can be in one of two states, labeled ∣0⟩ and ∣1⟩. If this were a classical system, then its instantaneous state could be described by n bits. However, in quantum physics, the system is allowed to be in a linear superposition of configurations, and indeed the instantaneous state of the system is described by a unit vector in the 2n dimensional vector space, whose basis vectors correspond to all the2n classical configurations. Therefore, to describe the instantaneous state of the system, we must specify 2n complex numbers. Nature must update 2n complex numbers at each instant to evolve the system in time. This is an extraordinary amount of effort, since even for n = 200, 2n is larger than estimates of the number of elementary particles in the visible universe. Nonetheless, there are limits to the power of quantum computers. In "Strengths and Weaknesses of Quantum Computing," Bennett, Bernstein, Brassard, and Vazirani show that, relative to a random oracle, with probability 1, the class NP cannot be solved on a quantum Turing machine in time o(2n/2). This bound is tight, since recent work of Grover [5] has shown how to accept any language in NP in time O(2n/2) on a quantum Turing machine. Quantum computers are necessarily time reversible. Indeed, Bennett's work [1] on reversible computation inspired early work on quantum computation that preceded Feynman's paper [4]. The reversibility requirement makes it quite complex to implement even basic computational primitives such as looping or composition. In "Quantum Complexity Theory," Bernstein and Vazirani show how to implement quantum programming primitives and give a construction for an efficient universal quantum Turing machine. The structure of the universal quantum Turing machine is quite simple: it consists of a deterministic Turing machine with a single "quantum coin flip." In "Quantum Computability," Adleman, DeMarrais, and Huang greatly simplify this further by showing that a very simple type of coin flip is sufficient---a rotation by an angle θ such that sinθ=3/5. Making quantum computers robust against noise and decoherence is an important and challenging problem. In "Stabilization of Quantum Computations by Symmetrization," Barenco, Berthiaume, Deutsch, Ekert, Jozsa, and Macchiavello show how to use the quantum watchdog effect to stabilize a quantum computation against noise. Their method is based on running several copies of the quantum computer in parallel and projecting its state into the symmetric subspace at frequent intervals. They show that the quantum watchdog effect results in the suppression of errors that lie outside the symmetric subspace. Quantum computation touches upon the foundations of both computer science and quantum physics. It is not unlikely that the issues raised by quantum computation will stimulate further research into the foundations of quantum physics. I wish to express my gratitude to several people who made this special section possible. Oded Goldreich acted as editor for two of the papers in the issue and dealt with them with his characteristic efficiency and judgment. The editorial staff at SIAM, most notably Lisa Dougherty, Beth Gallagher, Deidre Wunderlich, and Sam Young, were extremely helpful, patient, and resourceful. Finally, I would like to thank a number of referees whose careful and timely reviews were critical to putting together this issue. Umesh Vazirani
Nature is the relations between processes and phenomena. Nothing exists in a Universe without relations. Computing is the transaction of relations between data using control and execution mechanisms. Quantum relations are a superposition of particles and their states. Quantum computing is unconditional transactions of relations between qubit data. Entanglement is a nonlocal superposition of deterministic states. A quantum computer is an analog device for solving combinatorial problems in parallel. Practically focused definitions of the concepts of quantum computing represent a path to the development of scalable quantum parallel algorithms for solving combinatorial problems. Any algorithm can be reduced to a sequence of operations without conditions, because any truth table is a collection of a complete system of conditions-states. Any sequence of actions can always be reduced to one parallel operation. Conditions and sequences arise only when the developer uses previously created primitives-constructs to build an always non-optimal calculator. The deterministic paradigm of creating quantum computing by using photon transactions on the electrons of an atom can exclude the use of quantum logic. The evolutionary path of quantum computing from the classical one: Memory-Address-Transaction (MAT) → Electron-Address-Transaction →Electron-Address-Quantaction (EAQ)→State-Superposition- Logic. What is calculated on a quantum computer can be calculated in parallel on a classical computer due to the redundancy of memory. MAT-computing implements any algorithms through transactions (read-write) in memory. Qubit-vector models for describing functionalities differ from the known truth tables in terms of compactness of description and technological implementation of parallel algorithms for the synthesis and analysis of digital devices and SoC-components. An example is given – a memory-driven algorithm for simulating digital devices based on qubit-vector forms of describing functionalities for a significant increase in the productivity of computing processes by parallel execution of logical operations. Comparative evaluations of the use of qubit models and methods show an increase in the efficiency of algorithms for simulating digital devices in comparison with tabular ones. The superposition of classical, quantum and analog computing is integrally presented, which makes it possible to search the best solutions for recognition and decision making.