Topological Qubits as Carriers of Quantum Information in Optics (original) (raw)
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Engineering and manipulating topological qubits in 1D quantum wires
Journal of the Korean Physical Society, 2013
We investigate the Josephson effect in TNT and NTN junctions, consisting of topological (T) and normal (N) phases of semiconductor-superconductor 1D heterostructures in the presence of a Zeeman field. A key feature of our setup is that, in addition to the variation of the phase of the superconducting order parameter, we allow the orientation of the magnetic field to change along the junction. We find a novel magnetic contribution to the Majorana Josephson coupling that permits the Josephson current to be tuned by changing the orientation of the magnetic field along the junction. We also predict that a spin current can be generated by a finite superconducting phase difference, rendering these materials potential candidates for spintronic applications. Finally, this new type of coupling not only constitutes a unique fingerprint for the existence of Majorana bound states but also provides an alternative pathway for manipulating and braiding topological qubits in networks of wires.
by David S. Simon, Casey A. Fitzpatrick, Shuto Osawa, and Alexander V. Sergienko. It is shown that quantum walks on one-dimensional arrays of special linear optical units allow the simulation of discrete-time Hamiltonian systems with distinct topological phases. In particular, a slightly modified version of the Su-Schrieffer-Heeger (SSH) system can be simulated, which exhibits states of nonzero winding number and has topologically-protected boundary states. In the large-system limit this approach uses quadratically fewer resources to carry out quantum simulations than previous linear-optical approaches and can be readily generalized to higher-dimensional systems. The basic optical units that implement this simulation consist of combinations of novel optical multiports that allow photons to reverse direction.
Joint entanglement of topology and polarization enables error-protected quantum registers
New Journal of Physics, 2018
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.
Topological Phase for Spin-Orbit Transformations on a Laser Beam
Physical Review Letters, 2007
We investigate the topological phase associated with the double connectedness of the SO(3) representation in terms of maximally entangled states. An experimental demonstration is provided in the context of polarization and spatial mode transformations of a laser beam carrying orbital angular momentum. The topological phase is evidenced through interferometric measurements and a quantitative relationship between the concurrence and the fringes visibility is derived. Both the quantum and the classical regimes were investigated.
Manipulating Topological Edge Spins in a One-Dimensional Optical Lattice
Physical Review Letters, 2013
We propose to observe and manipulate topological edge spins in 1D optical lattice based on currently available experimental platforms. Coupling the atomic spin states to a laser-induced periodic Zeeman field, the lattice system can be driven into a symmetry protected topological (SPT) phase, which belongs to the chiral unitary (AIII) class protected by particle number conservation and chiral symmetries. In free-fermion case the SPT phase is classified by a Z invariant which reduces to Z4 with interactions. The zero edge modes of the SPT phase are spin-polarized, with left and right edge spins polarized to opposite directions and forming a topological spin-qubit (TSQ). We demonstrate a novel scheme to manipulate the zero modes and realize single spin control in optical lattice. The manipulation of TSQs has potential applications to quantum computation.
arXiv: Mesoscale and Nanoscale Physics, 2018
Novel classical wave phenomenon analogs of the quantum spin Hall effect are mostly based on the construction of pseudo-spins. Here we show that the non-trivial topology of a system can also be realized using orbital angular momentum through angular-momentum-orbital coupling. The idea is illustrated with a tight-binding model and experimentally demonstrated with a transmission line network. We show experimentally that even a very small network cluster exhibits one-way topological edge states, and their properties can be described in terms of local Chern numbers. Our work provides a new mechanism to realize counterparts of the quantum spin Hall effect in classical waves and may offer insights for other systems.
Nature Communications, 2019
Novel classical wave phenomenon analogs of the quantum spin Hall effect are mostly based on the construction of pseudo-spins. Here we show that the non-trivial topology of a system can also be realized using orbital angular momentum through a coupling between the angular momentum and the wave vector. The idea is illustrated with a tight-binding model and experimentally demonstrated with a transmission line network. We show experimentally that even a very small network cluster exhibits angular momentum-dependent one-way topological edge states, and their properties can be described in terms of local Chern numbers. Our work provides a new mechanism to realize counterparts of the quantum spin Hall effect in classical waves and may offer insights for other systems.
MDPI Quantum Reports Journal , 2022
We recently proposed that topological quantum computing might be based on SL(2,C) representations of the fundamental group π1(S3\K) for the complement of a link K in the three-sphere. The restriction to links whose associated SL(2,C) character variety V contains a Fricke surface κd=xyz−x2−y2−z2+d is desirable due to the connection of Fricke spaces to elementary topology. Taking K as the Hopf link L2a1, one of the three arithmetic two-bridge links (the Whitehead link 521, the Berge link 622 or the double-eight link 623) or the link 723, the V for those links contains the reducible component κ4, the so-called Cayley cubic. In addition, the V for the latter two links contains the irreducible component κ3, or κ2, respectively. Taking ρ to be a representation with character κd (d<4), with |x|,|y|,|z|≤2, then ρ(π1) fixes a unique point in the hyperbolic space H3 and is a conjugate to a SU(2) representation (a qubit). Even though details on the physical implementation remain open, more generally, we show that topological quantum computing may be developed from the point of view of three-bridge links, the topology of the four-punctured sphere and Painlevé VI equation.
Quantum computations on a topologically encoded qubit
The construction of a quantum computer remains a fundamental scientific and technological challenge, in particular due to unavoidable noise. Quantum states and operations can be protected from errors using protocols for fault-tolerant quantum computing (FTQC). Here we present a step towards this by implementing a quantum error correcting code, encoding one qubit in entangled states distributed over 7 trapped-ion qubits. We demonstrate the capability of the code to detect one bit flip, phase flip or a combined error of both, regardless on which of the qubits they occur. Furthermore, we apply combinations of the entire set of logical single-qubit Clifford gates on the encoded qubit to explore its computational capabilities. The implemented 7-qubit code is the first realization of a complete Calderbank-Shor-Steane (CSS) code and constitutes a central building block for FTQC schemes based on concatenated elementary quantum codes. It also represents the smallest fully functional instance of the color code, opening a route towards topological FTQC.