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Advanced Quantum Technologies

Implementation of General Qubit‐quNit Quantum Computation

Gui‐Long Jiang, Bing‐Wen Yin, Xiao‐Xuan Yin, Zi‐Xin Xiang, Zhu‐Lei Liu, Jun‐Yi Long, Wen‐Qiang Liu, Hai‐Rui Wei

Published Jun 11, 2025• 2 citations
Publisher

Abstract

Abstract A high‐dimensional system, so‐called quNit (‐level quantum system with ), provides several unique advantages, and high‐precision manipulation of arbitrary single‐quNit is demonstrated. In this study, a program to construct arbitrary qubit‐quNit quantum computation up to a global phase, and an efficient construction that requires single‐particle and generalized controlled (GCX) gates in the worst case are proposed. Moreover, by encoding the computing basis in polarization and spatial degrees of freedom of a single‐photon state, the optical architectures to implement the elementary‐gate library GCX, single‐partite rotation in a high‐dimension system are designed using linear optics. The necessary single‐photon polarization state and flexibility of linear optical elements make the quantum circuit feasible with current experimental technologies.

DOI
10.1002/qute.202500143

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Abstract Implementation of high-dimensional (HD) quantum gates shows very promising perspectives for HD quantum computation. A bipartite quantum system with arbitrary dimensions n and m is termed a quNit–quMit. Here we propose a synthesis scheme to construct the quantum circuit for general quNit–quMit gates with controlled increment (CINC) gates and local gates. This shows that CINC gates combined with local gates form a universal gate set for HD quantum computation. An upper bound of O ( n 2 ) CINC gates is achieved for arbitrary quNit–quMit gate implementation in the proposed scheme, which is the best known result. Especially for the controlled quNit–quMit gates, our scheme requires only 2 CINC gates, whereas the previous scheme required 2 n .
Implementation of high-dimensional (HD) quantum gates shows very promising perspectives for HD quantum computation. A bipartite quantum system with arbitrary dimensions nnn and mmm is termed a quNit-quMit. Here we propose a synthesis scheme to construct the quantum circuit for general quNit-quMit gates with controlled increment (CINC) gates and local gates. This shows that CINC gates combined with local gates form a universal gate set for HD quantum computation. An upper bound of O(n2)O(n^2)O(n2) CINC gates is achieved for arbitrary quNit-quMit gate implementation in the proposed scheme, which is the best known result. Especially for the controlled quNit-quMit gates, our scheme requires only 2 CINC gates, whereas the previous scheme required 2n2n2n.
Abstract Quantum gates are the essential block for quantum computers. High‐dimensional quantum gates exhibit remarkable advantages over their 2D counterparts for some quantum information processing tasks. Here, a family of entanglement‐based optical controlled‐SWAP gates on is presented. With the hybrid encoding, the control qubits and target qudits are encoded in photonic polarization and spatial degrees of freedom, respectively. The circuit is constructed using only () linear optics, beating an earlier result of 14 linear optics with . The circuit depth five is much lower than an earlier result of 11 with . Besides, the fidelity of the presented circuit can reach 99.4%, and it is higher than the previous counterpart with . The scheme is constructed in a deterministic way without any borrowed ancillary photons or measurement‐induced nonlinearities. Moreover, the approach allows .
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.
Abstract Quantum circuits of a general quantum gate acting on multiple ‐level quantum systems play a prominent role in multi‐valued quantum computation. A recursive Cartan decomposition of semi‐simple unitary Lie group (arbitrary ‐qutrit gate) is first proposed with a rigorous proof, which completely decomposes an ‐qutrit gate into local and non‐local operations. On this basis, an explicit quantum circuit is designed for implementing arbitrary two‐qutrit gates, and the cost of the construction is 21 generalized controlled (GCX) and controlled increment (CINC) gates less than the earlier best result of 26 GGXs. Furthermore, the program is extended to the ‐qutrit system, and the quantum circuit of generic ‐qutrit gates contained GGXs and CINCs is presented. Such asymptotically optimal structure is the best known result so far and its strength becomes more remarkable as increases, for example, when , the program saves 7146 GCXs compared to the previous best result. In addition, concrete recursive decomposition expressions is given for each non‐local operation instead of only quantum circuit diagrams.
Abstract Quantum circuit model is the most popular paradigm for implementing complex quantum computation. Based on Cartan decomposition, it is shown generalized controlled‐X (GCX) gates, 6 single‐qubit rotations about the y‐ and z‐axes, and single‐partite y‐ and z‐rotation‐types which are defined in this paper are sufficient to simulate a controlled‐unitary gate with controlling on . In the scenario of the unitary gate with that is locally equivalent to a diagonal unitary on , GCX gates and single‐partite y‐ and z‐rotation‐types are required to simulate it. The quantum circuit for implementing and are presented. Furthermore, it is found that with controlling has Schmidt rank two, and in other cases the diagonalized form of the target unitaries can be expanded in terms of specific simple types of product unitary operators.