Time-efficient implementation of quantum search with qudits

Abstract

We propose a simpler and more efficient scheme for the implementation of the multi-valued Grover's quantum search. The multi-valued search generalizes the original Grover's search by replacing qubits with qudits --- quantum systems of $d$ discrete states. The qudit database is exponentially larger than the qubit database and thus it requires fewer particles to control. The Hadamard gate, which is the key elementary gate in the qubit implementation of Grover's search, is replaced by a $d$-dimensional (complex-valued) unitary matrix $F$, the only condition for which is to have a column of equal moduli elements irrespective of their phases; it can be realized through any physical interaction, which achieves an equal-weight superposition state. An example of such a transformation is the $d$-dimensional discrete Fourier transform, used in earlier proposals; however, its construction is much more costly than that of the far simpler matrix $F$. We present examples of how such a transform $F$ can be constructed in realistic qudit systems in a \emph{single} interaction step.

5 pages, 2 figures

References in corpus (33)

• Quantum Mechanics helps in searching for a needle in a haystack
• Security of quantum key distribution using d-level systems
• Experimental One-Way Quantum Computing
• Bell inequalities for arbitrarily high dimensional systems
• Implementation of a Quantum Search Algorithm on a Nuclear Magnetic Resonance Quantum Computer
• Quantum cryptography with 3-state systems
• Violations of local realism by two entangled quNits are stronger than for two qubits
• Grover Algorithm with zero theoretical failure rate
• Optimal eavesdropping in cryptography with three-dimensional quantum states
• Multi-valued Logic Gates for Quantum Computation
• Measuring Entangled Qutrits and Their Use for Quantum Bit Commitment
• Quantum non-locality in two three-level systems
• A Bell-type test of energy-time entangled qutrits
• Quantum communication complexity protocol with two entangled qutrits
• Implementation of Grover's Quantum Search Algorithm in a Scalable System
• A Quantum Adiabatic Algorithm for Factorization and Its Experimental Implementation
• Implementation of quantum search algorithm using classical Fourier optics
• On Arbitrary Phases in Quantum Amplitude Amplification
• Phase matching in quantum searching
• Experimental Quantum Coin Tossing
• Implementation of a three-quantum-bit search algorithm
• A Magnetic Resonance Realization of Decoherence-Free Quantum Computation
• Nested quantum search and NP-complete problems
• Qutrit Entanglement
• Maximizing the Hilbert space for a finite number of distinguishable quantum states
• A quantum protocol for cheat-sensitive weak coin flipping
• Coherent pulsed excitation of degenerate multistate systems: Exact analytic solutions
• Violations of local realism with quNits up to N=16
• Entangled qutrits violate local realism stronger than qubits - an analytical proof
• Experimental realization of a continuous version of the Grover algorithm
• Implementing Grover's Quantum Search on a Para-Hydrogen based Pure State NMR Quantum Computer
• Scalable quantum search using trapped ions
• Simple implementation of a quantum search with trapped ions

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• Generalized Toffoli gate decomposition using ququints: Towards realizing Grover's algorithm with qudits
• Towards multiqudit quantum processor based on a ${}^{171}$Yb${}^{+}$ ion string: Realizing basic quantum algorithms
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• Fault-tolerant composite Householder reflection
• Optimizing the walk coin in the quantum random walk search algorithm through machine learning
• Moving Quantum States without SWAP via Intermediate Higher Dimensional Qudits
• Phase context decomposition of diagonal unitaries for higher-dimensional systems
• Demonstration of Discrete-Time Quantum Walks and Observation of Topological Edge States in a Superconducting Qutrit Chain
• Ab Initio Polaritonic Chemistry on Diverse Quantum Computing Platforms: Qubit, Qudit, and Hybrid Qubit-Qumode Architectures
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