Efficient realization of quantum algorithms with qudits

Abstract

The development of a universal fault-tolerant quantum computer that can solve efficiently various difficult computational problems is an outstanding challenge for science and technology. In this work, we propose a technique for an efficient implementation of quantum algorithms with multilevel quantum systems (qudits). Our method uses a transpilation of a circuit in the standard qubit form, which depends on the parameters of a qudit-based processor, such as their number and the number of accessible levels. This approach provides a qubit-to-qudit mapping and comparison to a standard realization of quantum algorithms highlighting potential advantages of qudits. We provide an explicit scheme of transpiling qubit circuits into sequences of single-qudit and two-qudit gates taken from a particular universal set. We then illustrate our method by considering an example of an efficient implementation of a $6$-qubit quantum algorithm with qudits. We expect that our findings are of relevance for ongoing experiments with noisy intermediate-scale quantum devices that operate with information carrier allowing qudit encodings, such as trapped ions and neutral atoms as well as optical and solid-state systems.

14 pages, 10 figures; substantially extended discussion of technical aspects of realizing quantum algorithms with qudits and finding sub-optimal qubit-to-qudit mapping

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• Qudits for decomposing multiqubit gates and realizing quantum algorithms
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• Noise-adapted qudit codes for amplitude-damping noise
• Schwinger-Keldysh non-perturbative field theory of open quantum systems beyond the Markovian regime: Application to spin-boson and spin-chain-boson models
• Qudit low-density parity-check codes
• Barren plateaus are amplified by the dimension of qudits
• Transpiling quantum assembly language circuits to a qudit form
• Measurement-based quantum computing with qudit stabilizer states
• Single Qudit Control in ${}^{87}$Sr via Optical Nuclear Electric Resonance
• Heralded High-Dimensional Photon-Photon Quantum Gate
• Applying Grover-mixer quantum alternating operator ansatz algorithm to higher-order unconstrained binary optimization problems
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• Scalable platform for qudit-based quantum computing using polar molecules
• Blind quantum computing with different qudit resource state architectures
• Creating two-qudit maximally entangled quantum link through bulk