Abstract
Linear-optical systems can implement photonic quantum walks that simulate systems with nontrivial topological properties. Here, such photonic walks are used to jointly entangle polarization and winding number. This joint entanglement allows information processing tasks to be performed with interactive access to a wide variety of topological features. Topological considerations are used to suppress errors, with polarization allowing easy measurement and manipulation of qubits. We provide three examples of this approach: production of two-photon systems with entangled winding number (including topological analogs of Bell states), a topologically error-protected optical memory register, and production of entangled topologically-protected boundary states. In particular it is shown that a pair of quantum memory registers, entangled in polarization and winding number, with topologically-assisted error suppression can be made with qubits stored in superpositions of winding numbers; as a result, information processing with winding number-based qubits is a viable possibility.
Highlights
States with integer-valued topological invariants, such as winding and Chern numbers, exhibit a variety of physically interesting effects in solid-state systems [1, 2, 3, 4, 5], including integer and fractional quantum Hall effects [6, 7, 8, 9, 10]
When systems with different values of topological invariants are brought into contact, states arise that are highly localized at the boundaries
Because of the inability to continuously interpolate between discrete values of the topological invariant, these surface states are protected from scattering and are highly robust against degradation, making them prime candidates for use in error-protected quantum information processing
Summary
States with integer-valued topological invariants, such as winding and Chern numbers, exhibit a variety of physically interesting effects in solid-state systems [1, 2, 3, 4, 5], including integer and fractional quantum Hall effects [6, 7, 8, 9, 10]. When systems with different values of topological invariants are brought into contact, states arise that are highly localized at the boundaries. In the quest to carry out practical quantum information processing tasks, it is of great interest to examine more closely the types of topologically-protected states that can be optically engineered. Topological protection of boundary states is well-known, but less widely recognized is the fact that bulk wavefunctions have a degree of resistance to changes in winding numbers [26]. This effect is discussed in the appendix and will be used to reduce polarization-flip errors of qubits stored in the optical register, greatly reducing the need for additional error correction
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