Quantum hyper-CPHASE gates with polarisation and orbital angular momentum degrees of freedom and generalisation to arbit
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Quantum hyper-CPHASE gates with polarisation and orbital angular momentum degrees of freedom and generalisation to arbitrary hyper-conditional gates Mrittunjoy Guha Majumdar1 Received: 16 May 2020 / Accepted: 7 September 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this paper, a controlled-phase (CPHASE) gate using the polarisation and orbital angular momentum degrees of freedom for single-photon two-qubit quantum logic is proposed. This is critical to the realisation of quantum cluster states and graph networks using transverse degrees of freedom. A generalisation of the proposed scheme to arbitrary number and kinds of degrees of freedom, for optical systems, as well as arbitrary operations to be conditionally performed is proposed. Keywords Entanglement · Quantum operation · Cluster states
1 Introduction Universal quantum information processing can be performed with single-qubit rotations and the two-qubit controlled-NOT operations, among other possible sets of universal generators of quantum gates [1,2]. Quantum information processing in optical systems, using photonic qubits and qumodes, has been realised for gate-based as well as measurement-based quantum computation and communication [3–7]. In optical systems, single-qubit operations as well as controlled logic operations over two or more qubits can be realised using linear optical elements such as beam-splitters and waveplates [8–11]. Quantum information processing can be done over multiple transverse degrees of freedom in optical systems, using hyper-entanglement and hybrid-entanglement [12,13]. This allows efficient computation and communication using multiple qubits over a lesser number of photons. Measurement-based quantum computation has been realised in optical systems [14,15], with Yokoyama et al. [16] multiplexing generating and characterised a continuous-variable cluster state containing more than 10,000 entangled modes, and Larsen et al. [17] recently proposed a
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Mrittunjoy Guha Majumdar [email protected] Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India 0123456789().: V,-vol
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scheme to generate more than 30,000 entangled modes in a two-dimensional cluster state. In cluster-state quantum computing, the role of the controlled-PHASE (CPHASE), as an entangler, is primary [18,19]. It can be used as a stand-alone two-qubit operation as well as an entangling gate, as is the case in the generation of entanglement in cluster states. The CPHASE operation has the form ⎛
UCPHASE
1 ⎜0 =⎜ ⎝0 0
0 1 0 0
0 0 1 0
⎞ 0 0⎟ ⎟ 0⎠ −1
(1)
In optical systems with multiple degrees of freedom, the realisation of a CPHASE gate has previously been undertaken, between polarisation and momentum degrees of freedom, thereby helping create a high-fidelity four-qubit linear cluster state [20]. Cluster states have been created using the simultaneous entanglement of photons in three degrees of freedom, in a hybrid approach to one-way quantum
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