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Scaling On-Chip Entangled Photon States to Higher Dimensions

Michael Kues, Christian Reimer, Piotr Roztocki, Luis Romero Cortés, Stefania Sciara, José Azaña, Yanbing Young Zhang, R. Morandotti, Benjamin Wetzel, A. Cino, S. T. Chu, Brent E. Little, D. Moss, Lucia Caspani

Published Jan 1, 2017• 0 citations
OpenAlex

Abstract

Considerable efforts have recently focused on advancing quantum information processing by increasing the number of qubits (the simplest unit of quantum information) in nonclassical systems such as ultracold atoms and superconducting circuits. A complementary approach to scale up information content is to move from two-level (qubit) to multilevel (quDit) systems.

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Stochastic Model of Qudit Measurement for Superconducting Quantum Information Processing

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The field of superconducting quantum computing, based on Josephson junctions, has recently seen remarkable strides in scaling the number of logical qubits. In particular, the fidelities of one- and two-qubit gates are close to the breakeven point with the novel error mitigation and correction methods. Parallel to these advances is the effort to expand the Hilbert space within a single device by employing high-dimensional qubits, otherwise known as qudits. Research has demonstrated the possibility of driving higher-order transitions in a transmon or designing innovative multimode superconducting circuits, termed multimons. These advances can significantly expand the computational basis while simplifying the interconnects in a large-scale quantum processor. This thesis provides a detailed introduction to the superconducting qudit and demonstrates a comprehensive analysis of decoherence in an artificial atom with more than two levels using Lindblad master equations and stochastic master equations (SMEs). After extending the theory of the design, control, and readout of a conventional superconducting qubit to that of a qudit, the thesis focuses on modeling the dispersive measurement of a transmon qutrit in an open quantum system using quadrature detections. Under the Markov assumption, master equations with different levels of abstraction are proposed and solved; in addition, both the ensemble-averaged and the quantum-jump approach of decoherence analysis are presented and compared analytically and numerically. The thesis ends with a series of experimental results on a transmon-type qutrit, verifying the validity of the stochastic model.

arXiv:2312.03754•Dec 3, 2023•0 citations

Entanglement Levels Up

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Extending a key resource of quantum technology, entanglement—either by having more than two quantum objects or using "qudits" instead of "qubits"-offers prospects for improvements in quantum communications, computation and other technologies.

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Fluxonium Qudits in Hybrid Circuits

Pamela B. Rambow

As quantum computing progresses into the new Quantum Utility era—marked by the ca- pability to execute increasingly complex computations with improved fault tolerance—systems exceeding 1,000 qubits have already been demonstrated by Atom Computing and IBM. While the majority of academic and industrial efforts remain focused on qubit-based archi- tectures, built on decades of work in two-state computational logic and algorithms, growing attention is now turning to the untapped potential of qudits—quantum units that ex- tend beyond the binary nature of qubits. Research into qudits is gaining momentum, as increasing the number of computational states per unit can significantly enhance compu- tational power and reduce circuit complexity. This paradigm shift opens the door to more efficient quantum algorithms and hardware architectures. Moreover, hybrid systems that integrate qubits and qudits may provide a powerful bridge between existing technologies and next-generation performance—making qudit research a critical frontier in unlocking the full potential of quantum computing.This dissertation presents a comprehensive framework for implementing a hybrid quan- tum architecture using fluxonium-based qudits. Fluxonium circuits, constructed from a superconducting loop interrupted by a Josephson junction and a large inductance, exhibit strong anharmonicity and non-fixed selection rules. These features enable multiple direct transitions between quantum states, which can be precisely tuned through a set of circuit parameters known as fluxonium characteristic values. A detailed study of these parameters was conducted to identify optimal qudit systems within a ten-dimensional Hilbert space (D = 10), with estimated coherence times comparable to those of conventional qubit sys- tems. Theoretical and numerical tools were developed to extend the approach to higher dimensions. A set of universal qudit logic gates was designed for arbitrary dimensions D = 2^n, as well as some gates and gate combinations in high dimension Hilbert space. The study demonstrates a significant reduction in gate complexity—particularly in the number of driving pulses required for multiply-controlled gates. Additionally, hybrid logic circuits using D = 8 and D = 4 qudits were analyzed, revealing reduced circuit complexity com- pared to qubit-only implementations. In summary, this work shows that fluxonium superconducting circuits are well-suited systems extending the traditional two-level qubit into multi-level qudit operation, where accessing higher energy levels can enhance computational capacity, reduce gate overhead, and enable more efficient quantum algorithms compared to standard qubit architectures.

•Jan 1, 2025•0 citations

Generalized Toffoli Gate Decomposition Using Ququints: Towards Realizing Grover’s Algorithm with Qudits

Anastasiia S. Nikolaeva, Evgeniy O. Kiktenko, Aleksey K. Fedorov

Qubits, which are the quantum counterparts of classical bits, are used as basic information units for quantum information processing, whereas underlying physical information carriers, e.g., (artificial) atoms or ions, admit encoding of more complex multilevel states—qudits. Recently, significant attention has been paid to the idea of using qudit encoding as a way for further scaling quantum processors. In this work, we present an efficient decomposition of the generalized Toffoli gate on five-level quantum systems—so-called ququints—that use ququints’ space as the space of two qubits with a joint ancillary state. The basic two-qubit operation we use is a version of the controlled-phase gate. The proposed N-qubit Toffoli gate decomposition has O(N) asymptotic depth and does not use ancillary qubits. We then apply our results for Grover’s algorithm, where we indicate on the sizable advantage of using the qudit-based approach with the proposed decomposition in comparison to the standard qubit case. We expect that our results are applicable for quantum processors based on various physical platforms, such as trapped ions, neutral atoms, protonic systems, superconducting circuits, and others.

arXiv:2212.12505•Entropy•Feb 20, 2023•16 citations

Quantum Computation

Richard Hughes

In a conventional computer, information is represented by quantities that obey the laws of classical physics, such as the voltage levels in a logic circuit. But as the size of microelectronics shrinks, quantum physics becomes increasingly important.

Computing in Science & Engineering•Mar 1, 2001•3 citations
Considerable efforts have recently focused on advancing quantum information processing by increasing the number of qubits (the simplest unit of quantum information) in nonclassical systems such as ultracold atoms and superconducting circuits. A complementary approach to scale up information content is to move from two-level (qubit) to multilevel (quDit) systems.
The field of superconducting quantum computing, based on Josephson junctions, has recently seen remarkable strides in scaling the number of logical qubits. In particular, the fidelities of one- and two-qubit gates are close to the breakeven point with the novel error mitigation and correction methods. Parallel to these advances is the effort to expand the Hilbert space within a single device by employing high-dimensional qubits, otherwise known as qudits. Research has demonstrated the possibility of driving higher-order transitions in a transmon or designing innovative multimode superconducting circuits, termed multimons. These advances can significantly expand the computational basis while simplifying the interconnects in a large-scale quantum processor. This thesis provides a detailed introduction to the superconducting qudit and demonstrates a comprehensive analysis of decoherence in an artificial atom with more than two levels using Lindblad master equations and stochastic master equations (SMEs). After extending the theory of the design, control, and readout of a conventional superconducting qubit to that of a qudit, the thesis focuses on modeling the dispersive measurement of a transmon qutrit in an open quantum system using quadrature detections. Under the Markov assumption, master equations with different levels of abstraction are proposed and solved; in addition, both the ensemble-averaged and the quantum-jump approach of decoherence analysis are presented and compared analytically and numerically. The thesis ends with a series of experimental results on a transmon-type qutrit, verifying the validity of the stochastic model.
As quantum computing progresses into the new Quantum Utility era—marked by the ca- pability to execute increasingly complex computations with improved fault tolerance—systems exceeding 1,000 qubits have already been demonstrated by Atom Computing and IBM. While the majority of academic and industrial efforts remain focused on qubit-based archi- tectures, built on decades of work in two-state computational logic and algorithms, growing attention is now turning to the untapped potential of qudits—quantum units that ex- tend beyond the binary nature of qubits. Research into qudits is gaining momentum, as increasing the number of computational states per unit can significantly enhance compu- tational power and reduce circuit complexity. This paradigm shift opens the door to more efficient quantum algorithms and hardware architectures. Moreover, hybrid systems that integrate qubits and qudits may provide a powerful bridge between existing technologies and next-generation performance—making qudit research a critical frontier in unlocking the full potential of quantum computing.This dissertation presents a comprehensive framework for implementing a hybrid quan- tum architecture using fluxonium-based qudits. Fluxonium circuits, constructed from a superconducting loop interrupted by a Josephson junction and a large inductance, exhibit strong anharmonicity and non-fixed selection rules. These features enable multiple direct transitions between quantum states, which can be precisely tuned through a set of circuit parameters known as fluxonium characteristic values. A detailed study of these parameters was conducted to identify optimal qudit systems within a ten-dimensional Hilbert space (D = 10), with estimated coherence times comparable to those of conventional qubit sys- tems. Theoretical and numerical tools were developed to extend the approach to higher dimensions. A set of universal qudit logic gates was designed for arbitrary dimensions D = 2^n, as well as some gates and gate combinations in high dimension Hilbert space. The study demonstrates a significant reduction in gate complexity—particularly in the number of driving pulses required for multiply-controlled gates. Additionally, hybrid logic circuits using D = 8 and D = 4 qudits were analyzed, revealing reduced circuit complexity com- pared to qubit-only implementations. In summary, this work shows that fluxonium superconducting circuits are well-suited systems extending the traditional two-level qubit into multi-level qudit operation, where accessing higher energy levels can enhance computational capacity, reduce gate overhead, and enable more efficient quantum algorithms compared to standard qubit architectures.
Qubits, which are the quantum counterparts of classical bits, are used as basic information units for quantum information processing, whereas underlying physical information carriers, e.g., (artificial) atoms or ions, admit encoding of more complex multilevel states—qudits. Recently, significant attention has been paid to the idea of using qudit encoding as a way for further scaling quantum processors. In this work, we present an efficient decomposition of the generalized Toffoli gate on five-level quantum systems—so-called ququints—that use ququints’ space as the space of two qubits with a joint ancillary state. The basic two-qubit operation we use is a version of the controlled-phase gate. The proposed N-qubit Toffoli gate decomposition has O(N) asymptotic depth and does not use ancillary qubits. We then apply our results for Grover’s algorithm, where we indicate on the sizable advantage of using the qudit-based approach with the proposed decomposition in comparison to the standard qubit case. We expect that our results are applicable for quantum processors based on various physical platforms, such as trapped ions, neutral atoms, protonic systems, superconducting circuits, and others.