Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physics

Measuring Higher Dimensional “Qudits” for Computation

Erika K. Carlson

Published Mar 10, 2021• 0 citations
Publisher

Abstract

Measuring Higher Dimensional "Qudits" for ComputationWith a technique called self-guided tomography, researchers accurately measure the states of qudits-quantum systems like qubits but with more than two dimensions.
DOI
10.1103/physics.14.s34

Related papers

Robust and Efficient High-Dimensional Quantum State Tomography

Markus Rambach, Mahdi Qaryan, Michael J. Kewming +3 more

The exponential growth in Hilbert space with increasing size of a quantum system means that accurately characterizing the system becomes significantly harder with system dimension d. We show that self-guided tomography is a practical, efficient, and robust technique of measuring higher-dimensional quantum states. The achieved fidelities are over 99.9% for qutrits (d=3) and ququints (d=5), and 99.1% for quvigints (d=20)-the highest values ever realized for qudit pure states. We also show excellent performance for mixed states, achieving average fidelities of 96.5% for qutrits. We demonstrate robustness against experimental sources of noise, both statistical and environmental. The technique is applicable to any higher-dimensional system, from a collection of qubits through to individual qudits, and any physical realization, be it photonic, superconducting, ionic, or spin.

arXiv:2010.00632•Physical Review Letters•Mar 10, 2021•77 citations

High-dimensional quantum process tomography with undetected photons

Salini Rajeev, Mayukh Lahiri

The goal of quantum process tomography is to fully characterize an operation performed on a quantum state. By considering high-dimensional quantum states (qudit), we show that it is possible to fully reconstruct an arbitrary operation without performing any measurement on the transformed qudit. Our method is interferometric and conceptually different from existing techniques of quantum process tomography that must perform a measurement on the transformed qudit.

quant-pharXiv:2608.02490•Aug 4, 2026•0 citations

Self-Guided Quantum Tomography in High-Dimensional Systems

Laura Serino, Markus Rambach, Benjamin Brecht +3 more

Quantum tomography-characterising a quantum system by assigning it a quantum state-is an essential building block for future technologies like quantum metrology or quantum computation. Ideal quantum tomography is accurate and robust to noise while being quick and efficient. The standard technique for decades, full quantum tomography (FQT), only fulfils parts of these criteria and quickly becomes unfeasible, even for medium-sized systems. As the number of possible states increases, the amount of measurements to characterise the system grows exponentially. The very feature that gives quantum physics immense possibilities hinders our ability to describe it. Additionally, FQT is neither robust to noise nor experimental errors and generally fails in the presence of these environmental perturbations unless additional resources are used.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jun 23, 2025•0 citations

Self-Guided Quantum Tomography

Christopher Ferrie

We introduce a self-learning tomographic technique in which the experiment guides itself to an estimate of its own state. Self-guided quantum tomography uses measurements to directly test hypotheses in an iterative algorithm which converges to the true state. We demonstrate through simulation on many qubits that Self-guided quantum tomography is a more efficient and robust alternative to the usual paradigm of taking a large amount of informationally complete data and solving the inverse problem of postprocessed state estimation.

arXiv:1406.4101•Physical Review Letters•Nov 7, 2014•124 citations

Optimal qudit overlapping tomography and optimal measurement order

Shuowei Ma, Qianfan Wang, Lvzhou Li +1 more

Quantum state tomography is essential for characterizing quantum systems, but it becomes infeasible for large systems due to exponential resource scaling. Overlapping tomography addresses this challenge by reconstructing all $k$-body marginals using few measurement settings, enabling the efficient extraction of key information for many quantum tasks. While optimal schemes are known for qubits, the extension to higher-dimensional qudit systems remains largely unexplored. Here, we investigate optimal qudit overlapping tomography, constructing local measurement settings from generalized Gell-Mann matrices. By establishing a correspondence with combinatorial covering arrays, we present two explicit constructions of optimal measurement schemes. For $n$-qutrit systems, we prove that pairwise tomography requires at most $8 + 56\left\lceil \log_{8} n \right\rceil$ measurement settings, and provide an explicit scheme achieving this bound. Furthermore, we develop an efficient algorithm to determine the optimal order of these measurement settings, minimizing the experimental overhead associated with switching configurations. Compared to the worst-case ordering, our optimized schedule reduces switching costs by approximately 50\%. These results provide a practical pathway for efficient characterization of qudit systems, facilitating their application in quantum communication and computation.

quant-pharXiv:2601.10059•Jan 16, 2026•0 citations

Entangled Solid-State Circuits

Irfan A. Siddiqi, John L. Clarke

Quantum tomography is used to determine the entangled state of two coupled superconducting qubits, a step forward for solid-state quantum computing.

Science•Sep 7, 2006•4 citations
The exponential growth in Hilbert space with increasing size of a quantum system means that accurately characterizing the system becomes significantly harder with system dimension d. We show that self-guided tomography is a practical, efficient, and robust technique of measuring higher-dimensional quantum states. The achieved fidelities are over 99.9% for qutrits (d=3) and ququints (d=5), and 99.1% for quvigints (d=20)-the highest values ever realized for qudit pure states. We also show excellent performance for mixed states, achieving average fidelities of 96.5% for qutrits. We demonstrate robustness against experimental sources of noise, both statistical and environmental. The technique is applicable to any higher-dimensional system, from a collection of qubits through to individual qudits, and any physical realization, be it photonic, superconducting, ionic, or spin.
Quantum tomography-characterising a quantum system by assigning it a quantum state-is an essential building block for future technologies like quantum metrology or quantum computation. Ideal quantum tomography is accurate and robust to noise while being quick and efficient. The standard technique for decades, full quantum tomography (FQT), only fulfils parts of these criteria and quickly becomes unfeasible, even for medium-sized systems. As the number of possible states increases, the amount of measurements to characterise the system grows exponentially. The very feature that gives quantum physics immense possibilities hinders our ability to describe it. Additionally, FQT is neither robust to noise nor experimental errors and generally fails in the presence of these environmental perturbations unless additional resources are used.
We introduce a self-learning tomographic technique in which the experiment guides itself to an estimate of its own state. Self-guided quantum tomography uses measurements to directly test hypotheses in an iterative algorithm which converges to the true state. We demonstrate through simulation on many qubits that Self-guided quantum tomography is a more efficient and robust alternative to the usual paradigm of taking a large amount of informationally complete data and solving the inverse problem of postprocessed state estimation.
Quantum state tomography is essential for characterizing quantum systems, but it becomes infeasible for large systems due to exponential resource scaling. Overlapping tomography addresses this challenge by reconstructing all kkk-body marginals using few measurement settings, enabling the efficient extraction of key information for many quantum tasks. While optimal schemes are known for qubits, the extension to higher-dimensional qudit systems remains largely unexplored. Here, we investigate optimal qudit overlapping tomography, constructing local measurement settings from generalized Gell-Mann matrices. By establishing a correspondence with combinatorial covering arrays, we present two explicit constructions of optimal measurement schemes. For nnn-qutrit systems, we prove that pairwise tomography requires at most 8+56⌈log⁡8n⌉8 + 56\left\lceil \log_{8} n \right\rceil8+56⌈log8​n⌉ measurement settings, and provide an explicit scheme achieving this bound. Furthermore, we develop an efficient algorithm to determine the optimal order of these measurement settings, minimizing the experimental overhead associated with switching configurations. Compared to the worst-case ordering, our optimized schedule reduces switching costs by approximately 50\%. These results provide a practical pathway for efficient characterization of qudit systems, facilitating their application in quantum communication and computation.