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arXiv:2105.02748 · Physical Review Letters

Scheme for Universal High-Dimensional Quantum Computation with Linear Optics

Stefano Paesani, Jacob F. F. Bulmer, Alex E. Jones, Raffaele Santagati, Anthony Laing

Published Jun 11, 2021• 62 citations
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Abstract

Photons are natural carriers of high-dimensional quantum information, and, in principle, can benefit from higher quantum information capacity and noise resilience. However, schemes to generate the resources required for high-dimensional quantum computing have so far been lacking in linear optics. Here, we show how to generate GHZ states in arbitrary dimensions and numbers of photons using linear optical circuits described by Fourier transform matrices. Combining our results with recent schemes for qudit Bell measurements, we show that universal linear optical quantum computing can be performed in arbitrary dimensions.

DOI
10.1103/physrevlett.126.230504

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Quantum gates are the essential block for quantum computer. High-dimensional quantum gates exhibit remarkable advantages over their two-dimensional counterparts for some quantum information processing tasks. Here we present a family of entanglement-based optical controlled-SWAP gates on C2⊗Cd⊗Cd\mathbb{C}^{2}\otimes \mathbb{C}^{d}\otimes \mathbb{C}^{d}C2⊗Cd⊗Cd. With the hybrid encoding, we encode the control qubits and target qudits in photonic polarization and spatial degrees of freedom, respectively. The circuit is constructed using only (2+3d)(2+3d)(2+3d) (d≥2d\geq 2d≥2) linear optics, beating an earlier result of 14 linear optics with d=2d=2d=2. The circuit depth 5 is much lower than an earlier result of 11 with d=2d=2d=2. Besides, the fidelity of the presented circuit can reach 99.4\%, and it is higher than the previous counterpart with d=2d=2d=2. Our scheme are constructed in a deterministic way without any borrowed ancillary photons or measurement-induced nonlinearities. Moreover, our approach allows d>2d>2d>2.