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arXiv:1511.08254 · Quantum Information and Computation

Coherent modification of entanglement: benefits due to extended Hilbert space

Dmitry Solenov

Published Sep 1, 2016• 2 citations
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Abstract

A quantum computing system is typically represented by a set of non-interacting (local) two-state systems—qubits. Many physical systems can naturally have more accessible states, both local and non-local. We show that the resulting non-local network of states connecting qubits can be efficiently addressed via continuous time quantum random walks, leading to substantial speed-up of multiqubit entanglement manipulations. We discuss a three-qubit Toffoli gate and a system of superconducting qubits as an illustration.

DOI
10.26421/qic16.11-12-2

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It is demonstrated that in gate-based quantum computing architectures quantum walk is a natural mathematical description of quantum gates. It originates from field-matter interaction driving the system, but is not attached to specific qubit designs and can be formulated for very general field-matter interactions. It is shown that, most generally, gates are described by a set of coined quantum walks. Rotating wave and resonant approximations for field-matter interaction simplify the walks, factorizing the coin, and leading to pure continuous time quantum walk description. The walks reside on a graph formed by the Hilbert space of all involved qubits and auxiliary states, if present. Physical interactions between different parts of the system necessary to propagate entanglement through such graph---quantum network---enter via reduction of symmetries in graph edges. Description for several single- and two-qubit gates are given as examples.
Quantum entanglement, a fundamental phenomenon in quantum mechanics, holds immense potential for revolutionizing computation. However, harnessing this potential requires overcoming significant challenges, particularly in achieving efficient and reliable quantum computation. This paper presents a novel modeling approach, centered around the concept of non-locality and information transfer, to address these challenges. We propose a framework that leverages the unique properties of quantum states to simulate and manipulate entanglement, ultimately aiming to improve the performance and trustworthiness of quantum systems. The core claim of this research is to establish a robust and efficient model for quantum entanglement that transcends the limitations of classical approaches, thereby enhancing the capabilities of quantum computing.
We use analytical and numerical calculations to obtain speed limits for various unitary quantum operations in multiqubit systems under typical experimental conditions. The operations that we consider include single-, two-, and three-qubit gates, as well as quantum-state transfer in a chain of qubits. We find in particular that simple methods for implementing two-qubit gates generally provide the fastest possible implementations of these gates. We also find that the three-qubit Toffoli gate time varies greatly depending on the type of interactions and the system's geometry, taking only slightly longer than a two-qubit controlled-not (cnot) gate for a triangle geometry. The speed limit for quantum-state transfer across a qubit chain is set by the maximum spin-wave speed in the chain.
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