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1. Spin‐s$$s$$ Dicke States and Their Preparation

   https://doi.org/10.1002/qute.202400057  

   Nepomechie, Rafael_I; Ravanini, Francesco; Raveh, David (September 2024, Advanced Quantum Technologies)

   Abstract The notion of spin‐ Dicke states is introduced, which are higher‐spin generalizations of usual (spin‐1/2) Dicke states. These multi‐qudit states can be expressed as superpositions of qudit Dicke states. They satisfy a recursion formula, which is used to formulate an efficient quantum circuit for their preparation, whose size scales as , where is the number of qudits and is the number of times the total spin‐lowering operator is applied to the highest‐weight state. The algorithm is deterministic and does not require ancillary qudits. 

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2. q-analog qudit Dicke states

   https://doi.org/10.1088/1751-8121/ad1ea4  

   Raveh, David; Nepomechie, Rafael_I (February 2024, Journal of Physics A: Mathematical and Theoretical)

   Abstract Dicke states are completely symmetric states of multiple qubits (2-level systems), and qudit Dicke states are theird-level generalization. We define hereq-deformed qudit Dicke states using the quantum algebra $s{u}_q\left(d\right)$. We show that these states can be compactly expressed as a weighted sum over permutations withq-factors involving the so-called inversion number, an important permutation statistic in Combinatorics. We use this result to compute the bipartite entanglement entropy of these states. We also discuss the preparation of these states on a quantum computer, and show that introducing aq-dependence does not change the circuit gate count. 

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3. Deterministic Generation of Qudit Photonic Graph States from Quantum Emitters

   https://doi.org/10.1103/PRXQuantum.5.020346  

   Raissi, Zahra; Barnes, Edwin; Economou, Sophia E (May 2024, PRX Quantum)

   We propose and analyze deterministic protocols to generate qudit photonic graph states from quantum emitters. We show that our approach can be applied to generate any qudit graph state and we exemplify it by constructing protocols to generate one- and two-dimensional qudit cluster states, absolutely maximally entangled states, and logical states of quantum error-correcting codes. Some of these protocols make use of time-delayed feedback, while others do not. The only additional resource requirement compared to the qubit case is the ability to control multilevel emitters. These results significantly broaden the range of multiphoton entangled states that can be produced deterministically from quantum emitters. Published by the American Physical Society2024 

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4. Asymptotic improvements to quantum circuits via qutrits

   https://doi.org/10.1145/3307650.3322253  

   Gokhale, Pranav; Baker, Jonathan M.; Duckering, Casey; Brown, Natalie C.; Brown, Kenneth R.; Chong, Frederic T. (June 2019, ISCA '19 Proceedings of the 46th International Symposium on Computer Architecture)

   Quantum computation is traditionally expressed in terms of quantum bits, or qubits. In this work, we instead consider three-level qutrits. Past work with qutrits has demonstrated only constant factor improvements, owing to the log2(3) binary-to-ternary compression factor. We present a novel technique using qutrits to achieve a logarithmic depth (runtime) decomposition of the Generalized Toffoli gate using no ancilla-a significant improvement over linear depth for the best qubit-only equivalent. Our circuit construction also features a 70x improvement in two-qudit gate count over the qubit-only equivalent decomposition. This results in circuit cost reductions for important algorithms like quantum neurons and Grover search. We develop an open-source circuit simulator for qutrits, along with realistic near-term noise models which account for the cost of operating qutrits. Simulation results for these noise models indicate over 90% mean reliability (fidelity) for our circuit construction, versus under 30% for the qubit-only baseline. These results suggest that qutrits offer a promising path towards scaling quantum computation. 

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5. Speed limits of two-qubit gates with qudits

   Basyildiz, Bora; Jameson, Casey; Gong, Zhexuan (December 2023, arXiv)

   The speed of elementary quantum gates ultimately sets the limit on the speed at which quantum circuits can operate. For a fixed physical interaction strength between two qubits, the speed of any two-qubit gate is limited even with arbitrarily fast single-qubit gates. In this work, we explore the possibilities of speeding up two-qubit gates beyond such a limit by expanding our computational space outside the qubit subspace, which is experimentally relevant for qubits encoded in multi-level atoms or anharmonic oscillators. We identify an optimal theoretical bound for the speed limit of a two-qubit gate achieved using two qudits with a bounded interaction strength and arbitrarily fast single-qudit gates. In addition, we find an experimentally feasible protocol using two parametrically coupled superconducting transmons that achieves this theoretical speed limit in a non-trivial way. We also consider practical scenarios with limited single-qudit drive strengths and off-resonant transitions. For such scenarios, we develop an open-source, machine learning assisted, quantum optimal control algorithm that can achieve a speedup close to the theoretical limit with near-perfect gate fidelity. This work opens up a new avenue to speed up two-qubit gates when the physical interaction strength between qubits cannot be easily increased while extra states outside the qubit subspace can be well controlled. 

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