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Theoretical and Applied Informatics

Searching for quantum circuits preparing maximally multipartite

Przemysław Sadowski

Published Dec 30, 2013• 0 citations
OpenAlex

Abstract

In this work genetic programming is applied to the problem of generating maximum entanglement in multi-qubit systems of different structures. We provide quantum circuits that prepares multipartite entangled states in systems consisting of up to 8 qubits. We present results pertaining to the minimum size of a quantum circuit preparing a maximally entangled multi-qubit state in cases of reduced sets of quantum gates that correspond to spin chain quantum systems.

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In this work genetic programming is applied to the problem of generating maximum entanglement in multi-qubit systems of different structures. We provide quantum circuits that prepares multipartite entangled states in systems consisting of up to 8 qubits. We present results pertaining to the minimum size of a quantum circuit preparing a maximally entangled multi-qubit state in cases of reduced sets of quantum gates that correspond to spin chain quantum systems.
In this paper, we provide a genetic programming (GP) based method for generating quantum circuits preparing maximally multipartite entangled states (MMES). The presented method is faster that known realizations thanks to the applied fitness function and several modifications to the GP schema. Moreover, we enrich the described method by the unique possibility to define an arbitrary structure of a system. We use the developed method to find new quantum circuits, which are simpler from known results. We also analyze the efficiency of generating entanglement in the spin chain system and in the system of complete connections.
Numerical optimization methods such as hillclimbing and simulated annealing have been applied to search for highly entangled multi-qubit states. Here the genetic algorithm is applied to this optimization problem -- to search not only for highly entangled states, but also for the corresponding quantum circuits creating these states. Simple quantum circuits for maximally (highly) entangled states are discovered for 3, 4, 5, and 6-qubit systems; and extension of the method to systems with more qubits is discussed. Among other results we have found explicit quantum circuits for maximally entangled 5 and 6-qubit circuits, with only 8 and 13 quantum gates respectively. One significant advantage of our method over previous ones is that it allows very simple construction of quantum circuits based on the quantum states found.
The paper presents a new representation and corresponding set of genetic operators for a scheme to evolve quantum circuits with various properties. The scheme is a variant on the techniques of genetic programming and genetic algorithms, having components borrowed from each. By recognising the foundation of a quantum circuit as being a collection of gates, each operating on various categories of qubits and each taking parameters, the scheme can successfully search for most circuits. The algorithm is applied to the problem of entanglement production.
We study the approximate state preparation problem on noisy intermediate-scale quantum (NISQ) computers by applying a genetic algorithm to generate quantum circuits for state preparation. The algorithm can account for the specific characteristics of the physical machine in the evaluation of circuits, such as the native gate set and qubit connectivity. We use our genetic algorithm to optimize the circuits provided by the low-rank state preparation algorithm introduced by Araujo et al., and find substantial improvements to the fidelity in preparing Haar random states with a limited number of CNOT gates. Moreover, we observe that already for a 5-qubit quantum processor with limited qubit connectivity and significant noise levels (IBM Falcon 5T), the maximal fidelity for Haar random states is achieved by a short approximate state preparation circuit instead of the exact preparation circuit. We also present a theoretical analysis of approximate state preparation circuit complexity to motivate our findings. Our genetic algorithm for quantum circuit discovery is freely available at https://github.com/beratyenilen/qc-ga.
We use a random search technique to find quantum gate sequences that implement perfect quantum state preparation or unitary operator synthesis with arbitrary targets. This approach is based on the recent discovery that there is a large multiplicity of quantum circuits that achieve unit fidelity in performing a given target operation, even at the minimum number of single-qubit and two-qubit gates needed to achieve unit fidelity. We show that the fraction of perfect-fidelity quantum circuits increases rapidly as soon as the circuit size exceeds the minimum circuit size required for achieving unit fidelity. This result implies that near-optimal quantum circuits for a variety of quantum information processing tasks can be identified relatively easily by trying only a few randomly chosen quantum circuits and optimizing their parameters. In addition to analyzing the case where the cnot gate is the elementary two-qubit gate, we consider the possibility of using alternative two-qubit gates. In particular, we analyze the case where the two-qubit gate is the BBB gate, which is known to reduce the minimum quantum circuit size for two-qubit operations. We apply the random search method to the problem of decomposing the four-qubit Toffoli gate and find a 15-cnot-gate decomposition.
We study the approximate state preparation problem on noisy intermediate-scale quantum (NISQ) computers by applying a genetic algorithm to generate quantum circuits for state preparation. The algorithm can account for the specific characteristics of the physical machine in the evaluation of circuits, such as the native gate set and qubit connectivity. We use our genetic algorithm to optimize the circuits provided by the low-rank state preparation algorithm introduced by Araujo et al., and find substantial improvements to the fidelity in preparing Haar random states with a limited number of CNOT gates. Moreover, we observe that already for a 5-qubit quantum processor with limited qubit connectivity and significant noise levels (IBM Falcon 5T), the maximal fidelity for Haar random states is achieved by a short approximate state preparation circuit instead of the exact preparation circuit. We also present a theoretical analysis of approximate state preparation circuit complexity to motivate our findings. Our genetic algorithm for quantum circuit discovery is freely available at https://github.com/beratyenilen/qc-ga .