Quantum Phase Estimation with Time-Frequency Qudits in a Single Photon

Abstract

The Phase Estimation Algorithm (PEA) is an important quantum algorithm used independently or as a key subroutine in other quantum algorithms. Currently most implementations of the PEA are based on qubits, where the computational units in the quantum circuits are two-dimensional states. Performing quantum computing tasks with higher dimensional states -- qudits -- has been proposed, yet a qudit-based PEA has not been realized. Using qudits can reduce the resources needed for achieving a given precision or success probability. Compared to other quantum computing hardware, photonic systems have the advantage of being resilient to noise, but the probabilistic nature of photon-photon interaction makes it difficult to realize two-photon controlled gates that are necessary components in many quantum algorithms. In this work, we report an experimental realization of a qudit-based PEA on a photonic platform, utilizing the high dimensionality in time and frequency degrees of freedom (DoFs) in a single photon. The controlled-unitary gates can be realized in a deterministic fashion, as the control and target registers are now represented by two DoFs in a single photon. This first implementation of a qudit PEA, on any platform, successfully retrieves any arbitrary phase with one ternary digit of precision.

arXiv comment7 pages, 4 figures

References in corpus (29)

• Quantum Computing in the NISQ era and beyond
• Quantum Machine Learning
• Quantum Computing
• Quantum algorithm for solving linear systems of equations
• Probing many-body dynamics on a 51-atom quantum simulator
• Simulated Quantum Computation of Molecular Energies
• Scalable Quantum Simulation of Molecular Energies
• Towards Quantum Chemistry on a Quantum Computer
• Cloud Quantum Computing of an Atomic Nucleus
• Provably-Secure and High-Rate Quantum Key Distribution with Time-Bin Qudits
• Security Proof for Quantum Key Distribution Using Qudit Systems
• High-Dimensional Single-Photon Quantum Gates: Concepts and Experiments
• Arbitrary accuracy iterative phase estimation algorithm as a two qubit benchmark
• Experimental Bayesian Quantum Phase Estimation on a Silicon Photonic Chip
• Electro-Optic Frequency Beamsplitters and Tritters for High-Fidelity Photonic Quantum Information Processing
• Review of Decoherence Free Subspaces, Noiseless Subsystems, and Dynamical Decoupling
• High-dimensional frequency-bin entangled photons in an optical microresonator on a chip
• High-dimensional optical quantum logic in large operational spaces
• Deterministic Controlled-NOT gate for single-photon two-qubit quantum logic
• Controllable two-photon interference with versatile quantum frequency processor
• Quantum Algorithm for Obtaining the Energy Spectrum of Molecular Systems
• Quantum gates on hybrid qudits
• Calculating Unknown Eigenvalues with a Quantum Algorithm
• Decomposition of Unitary Matrices for Finding Quantum Circuits: Application to Molecular Hamiltonians
• Quantum Circuit Design for Solving Linear Systems of Equations
• Generation and distribution of high-dimensional frequency-entangled qudits
• All-optical frequency processor for networking applications
• Implementation of quantum state tomography for time-bin qudits
• Reconfigurable generation and measurement of mutually unbiased bases for time-bin qudits

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• Complete unitary qutrit control in ultracold atoms
• Qudit entanglers using quantum optimal control
• Asymptotically Improved Circuit for $d$-ary Grover's Algorithm with Advanced Decomposition of $n$-qudit Toffoli Gate
• Emulating two qubits with a four-level transmon qudit for variational quantum algorithms
• Hybrid controlled-SUM gate with one superconducting qutrit and one cat-state qutrit and application in hybrid entangled state preparation
• The Basics of Quantum Computing for Chemists
• A chip-scale polarization-spatial-momentum quantum SWAP gate in silicon nanophotonics
• A hybrid-qudit representation of digital RGB images
• Statistical Approach to Quantum Phase Estimation
• Qudit-inspired optimization for graph coloring
• The noisy Werner-Holevo channel and its properties
• Spatial-spectral mapping to prepare the frequency entangled qudits
• Outcome determinism in measurement-based quantum computation with qudits
• The Synthetic Hilbert Space of Laser-Driven Free-Electrons
• Generalized phase estimation in noisy quantum gates
• Experimental study of quantum uncertainty from lack of information
• Dissipative phase transition: from qubits to qudits
• Resource Reduction in Multiplexed High-Dimensional Quantum Reed-Solomon Codes
• Ab Initio Polaritonic Chemistry on Diverse Quantum Computing Platforms: Qubit, Qudit, and Hybrid Qubit-Qumode Architectures
• Quantum computation with charge-and-color permuting twists in qudit color codes
• Minimal orthonormal bases for pure quantum state estimation
• Qudit low-density parity-check codes
• Gaussian Amplitude Amplification for Quantum Pathfinding
• Entanglement swapping for partially entangled qudits and the role of quantum complementarity