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Entropy

A Quantum Cellular Automata Type Architecture with Quantum Teleportation for Quantum Computing

Dimitris Ntalaperas, Konstantinos Giannakis, Nikos Konofaos

Published Dec 17, 2019• 1 citation
Publisher

Abstract

We propose an architecture based on Quantum Cellular Automata which allows the use of only one type of quantum gate per computational step, using nearest neighbor interactions. The model is built in partial steps, each one of them analyzed using nearest neighbor interactions, starting with single-qubit operations and continuing with two-qubit ones. A demonstration of the model is given, by analyzing how the techniques can be used to design a circuit implementing the Quantum Fourier Transform. Since the model uses only one type of quantum gate at each phase of the computation, physical implementation can be easier since at each step only one kind of input pulse needs to be applied to the apparatus.

DOI
10.3390/e21121235

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We propose an architecture based on Quantum Cellular Automata which allows the use of only one type of quantum gate per computational step, using nearest neighbor interactions. The model is built in partial steps, each one of them analyzed using nearest neighbor interactions, starting with single-qubit operations and continuing with two-qubit ones. A demonstration of the model is given, by analyzing how the techniques can be used to design a circuit implementing the Quantum Fourier Transform. Since the model uses only one type of quantum gate at each phase of the computation, physical implementation can be easier since at each step only one kind of input pulse needs to be applied to the apparatus.
We propose an architecture based on Quantum cellular Automata which allows the use of only one type of quantum gates per computational step in order to perform nearest neighbor interactions. The model is built in partial steps, each one of them analyzed using nearest neighbor interactions, starting with single qubit operations and continuing with two qubit ones. The effectiveness of the model is tested and valuated by developing a quantum circuit implementing the Quantum Fourier Transform. The important outcome of this validation was that the operations are performed in a local and controlled manner thus reducing the error rate of each computational step.
Several proposed schemes for the physical realization of a quantum computer consist of qubits arranged in a cellular array. In the quantum circuit model of quantum computation, an often complex series of two-qubit gate operations is required between arbitrarily distant pairs of lattice qubits. An alternative model of quantum computation based on quantum cellular automata (QCA) requires only homogeneous local interactions that can be implemented in parallel. This would be a huge simplification in an actual experiment. We find some minimal physical requirements for the construction of unitary QCA in a one-dimensional Ising spin chain and demonstrate optimal pulse sequences for information transport and entanglement distribution. We also introduce the theory of nonunitary QCA and show by example that nonunitary rules can generate environment assisted entanglement.
We define quantum cellular automata as infinite quantum lattice systems with discrete time dynamics, such that the time step commutes with lattice translations and has strictly finite propagation speed. In contrast to earlier definitions this allows us to give an explicit characterization of all local rules generating such automata. The same local rules also generate the global time step for automata with periodic boundary conditions. Our main structure theorem asserts that any quantum cellular automaton is structurally reversible, i.e., that it can be obtained by applying two blockwise unitary operations in a generalized Margolus partitioning scheme. This implies that, in contrast to the classical case, the inverse of a nearest neighbor quantum cellular automaton is again a nearest neighbor automaton. We present several construction methods for quantum cellular automata, based on unitaries commuting with their translates, on the quantization of (arbitrary) reversible classical cellular automata, on quantum circuits, and on Clifford transformations with respect to a description of the single cells by finite Weyl systems. Moreover, we indicate how quantum random walks can be considered as special cases of cellular automata, namely by restricting a quantum lattice gas automaton with local particle number conservation to the single particle sector.
Quantum cellular automata are alternative quantum-computing paradigms to quantum Turing machines and quantum circuits. Their working mechanisms are inherently automated, therefore measurement free, and they act in a translation invariant manner on all cells or qudits of a register, generating a global rule that updates cell states locally, i.e., based solely on the states of their neighbors. Although desirable features in many applications, it is generally not clear to which extent these fully automated discrete-time local updates can generate and sustain long-range order in the (noisy) systems they act upon. In particular, whether and how quantum cellular automata can perform quantum error correction remain open questions. We close this conceptual gap by proposing quantum cellular automata with quantum-error-correction capabilities. We design and investigate two (quasi)one dimensional quantum cellular automata based on known classical cellular-automata rules with density-classification capabilities, namely the local majority voting and the two-line voting. We investigate the performances of those quantum cellular automata as quantum-memory components by simulating the number of update steps required for the logical information they act upon to be afflicted by a logical bit flip. The proposed designs pave a way to further explore the potential of new types of quantum cellular automata with built-in quantum-error-correction capabilities.
Studies of quantum computer implementations suggest cellular quantum computer architectures. These architectures can simulate the evolution of quantum cellular automata, which can possibly simulate both quantum and classical physical systems and processes. It is however known that except for the trivial case, unitary evolution of one-dimensional homogeneous quantum cellular automata with one qubit per cell is not possible. Quantum cellular automata that comprise two qubits per cell are defined and their evolution is studied using a quantum computer simulator. The evolution is unitary and its linearity manifests itself as a periodic structure in the probability distribution patterns.
Quantum cellular automata are alternative quantum-computing paradigms to quantum Turing machines and quantum circuits. Their working mechanisms are inherently automated, therefore measurement free, and they act in a translation invariant manner on all cells/qudits of a register, generating a global rule that updates cell states locally, i.e., based solely on the states of their neighbors. Although desirable features in many applications, it is generally not clear to which extent these fully automated discrete-time local updates can generate and sustain long-range order in the (noisy) systems they act upon. In special, whether and how quantum cellular automata can perform quantum error correction remain open questions. We close this conceptual gap by proposing quantum cellular automata with quantum-error-correction capabilities. We design and investigate two (quasi-)one dimensional quantum cellular automata based on known classical cellular-automata rules with density-classification capabilities, namely the local majority voting and the two-line voting. We investigate the performances of those quantum cellular automata as quantum-memory components by simulating the number of update steps required for the logical information they act upon to be afflicted by a logical bit flip. The proposed designs pave a way to further explore the potential of new types of quantum cellular automata with built-in quantum error correction capabilities.