Generalized Toffoli gate decomposition using ququints: Towards realizing Grover's algorithm with qudits

Abstract

Qubits, which are 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 is 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 the five-level quantum systems, so-called ququints, that uses ququints' space as the space of two qubits with a joint ancillary state. The basic two-qubit operation that we use is a version of controlled-phase gate. The proposed $N$-qubit Toffoli gate decomposition has $O(N)$ asymptotic depth using no ancillary qubits. We then apply our results for Grover's algorithm, where we indicate on the sizable advantage of the using qudit-based approach with the proposed decomposition. We expect that our results are applicable for quantum processors based on various physical platforms.

arXiv comment10 pages, 4 figures

References in corpus (53)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Quantum Mechanics helps in searching for a needle in a haystack
• Elementary gates for quantum computation
• Quantum computational advantage using photons
• Security of quantum key distribution using d-level systems
• Strong quantum computational advantage using a superconducting quantum processor
• Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator
• Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator
• Programmable quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms
• Quantum optimization using variational algorithms on near-term quantum devices
• High-dimensional quantum cryptography with twisted light
• Demonstration of multi-qubit entanglement and algorithms on a programmable neutral atom quantum computer
• Computing with spin qubits at the surface code error threshold
• Fast universal quantum control above the fault-tolerance threshold in silicon
• Quantum computing with neutral atoms
• Quantum Optimization of Maximum Independent Set using Rydberg Atom Arrays
• Quantum teleportation in high dimensions
• Multi-valued Logic Gates for Quantum Computation
• Implementation of a Toffoli Gate with Superconducting Circuits
• A universal qudit quantum processor with trapped ions
• Operating Quantum States in Single Magnetic Molecules: Implementation of Grover's Quantum Algorithm
• Efficient Toffoli Gates Using Qudits
• Precision tomography of a three-qubit donor quantum processor in silicon
• Coherence and Decay of Higher Energy Levels of a Superconducting Transmon Qubit
• Manipulating biphotonic qutrits
• Ultracold polar molecules as qudits
• Fluxonium: an alternative qubit platform for high-fidelity operations
• Hardware efficient quantum simulation of non-abelian gauge theories with qudits on Rydberg platforms
• High-Fidelity Qutrit Entangling Gates for Superconducting Circuits
• Universal simulation of Hamiltonian dynamics for qudits
• High fidelity two-qubit gates on fluxoniums using a tunable coupler
• Practical trapped-ion protocols for universal qudit-based quantum computing
• Factoring with Qutrits: Shor's Algorithm on Ternary and Metaplectic Quantum Architectures
• Single qudit realization of the Deutsch algorithm using superconducting many-level quantum circuits
• Asymptotic Improvements to Quantum Circuits via Qutrits
• Maximizing the Hilbert space for a finite number of distinguishable quantum states
• Multilevel superconducting circuits as two-qubit systems: Operations, state preparation, and entropic inequalities
• Entangling power and operator entanglement in qudit systems
• Scalable quantum computing with qudits on a graph
• Parallelism for Quantum Computation with Qudits
• Generalized Toffoli gates using qudit catalysis
• Multiqubit Spin
• Geometry of Quantum Computation with Qutrits
• Multi-photon dressing of an anharmonic superconducting many-level quantum circuit
• Time-efficient implementation of quantum search with qudits
• Decomposing the generalized Toffoli gate with qutrits
• Arithmetic Circuits for Multilevel Qudits Based on Quantum Fourier Transform
• Control of inhomogeneous atomic ensembles of hyperfine qudits
• Schemes of implementation in NMR of quantum processors and Deutsch-Jozsa algorithm by using virtual spin representation
• Minimal measurements of the gate fidelity of a qudit map
• Three-Qubit Gate Realization Using Single Quantum Particle
• Adaptive Compilation of Multi-Level Quantum Operations
• Determining quantum correlations in bipartite systems - from qubit to qutrit and beyond

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