Qudit-Basis Universal Quantum Computation using ${\chi }^{(2)}$ Interactions

Abstract

We prove that universal quantum computation can be realized---using only linear optics and ${\chi }^{(2)}$ (three-wave mixing) interactions---in any $(n+1)$-dimensional qudit basis of the $n$-pump-photon subspace. First, we exhibit a strictly universal gate set for the qubit basis in the one-pump-photon subspace. Next, we demonstrate qutrit-basis universality by proving that ${\chi }^{(2)}$ Hamiltonians and photon-number operators generate the full $\mathfrak{u}(3)$ Lie algebra in the two-pump-photon subspace, and showing how the qutrit controlled-$Z$ gate can be implemented with only linear optics and ${\chi }^{(2)}$ interactions. We then use proof by induction to obtain our general qudit result. Our induction proof relies on coherent photon injection/subtraction, a technique enabled by ${\chi }^{(2)}$ interaction between the encoding modes and ancillary modes. Finally, we show that coherent photon injection is more than a conceptual tool in that it offers a route to preparing high-photon-number Fock states from single-photon Fock states.

9 pages, 3 figures

References in corpus (15)

• Optical Quantum Computing
• Silica-on-Silicon Waveguide Quantum Circuits
• Resource-efficient linear optical quantum computation
• From three-photon GHZ states to ballistic universal quantum computation
• Direct generation of photon triplets using cascaded photon-pair sources
• Direct generation of three-photon polarization entanglement
• Continuous-time cross-phase modulation and quantum computation
• Nonlinear interaction between two heralded single photons
• Efficient generation and spectral characterization of spectrally factorable biphotons
• Deterministic Generation of Entangled Photons in Superconducting Resonator Arrays
• Hardware-Efficient Bosonic Quantum Error-Correcting Codes Based on Symmetry Operators
• Near-deterministic creation of universal cluster states with probabilistic Bell measurements and 3-qubit resource states
• Converting one photon into two via four-wave mixing in optical fibers
• Power-efficient production of photon pairs in a tapered chalcogenide microwire
• Parametric four-wave mixing toolbox for superconducting resonators

Cited by in corpus (28)

• Bosonic quantum error correction codes in superconducting quantum circuits
• Hardware-efficient quantum random access memory with hybrid quantum acoustic systems
• Pair-cat codes: autonomous error-correction with low-order nonlinearity
• Room-Temperature Photonic Logical Qubits via Second-Order Nonlinearities
• Conditional $\pi$-Phase Shift of Single-Photon-Level Pulses at Room Temperature
• Wave Function Engineering for Spectrally-Uncorrelated Biphotons in the Telecommunication Band based on a Machine-Learning Framework
• Recent advances in high-dimensional mode-locked quantum frequency combs
• Randomized benchmarking for qudit Clifford gates
• Protecting qudit operations from noise by continuous dynamical decoupling
• A cavity-enhanced broadband photonic Rabi oscillation
• Certifying dimension of quantum systems by sequential projective measurements
• Qubit representation of qudit states: correlations and state reconstruction
• Implementing positive-operator-valued-measurement elements in photonic circuits for performing minimum quantum state tomography of path qudits
• Optical frequency tweezers
• Wave-Shape-Tolerant Photonic Quantum Gates
• Adaptive State Fidelity Estimation for Higher Dimensional Bipartite Entanglement
• Strong coupling between a single-photon and a two-photon Fock state
• Experimental entanglement swapping through single-photon ${\chi }^{(2)}$ nonlinearity
• Complete conversion between one and two photons in nonlinear waveguides with tailored dispersion
• CNOT gate on reverse photon modes in ring cavity
• Time-dependent Rabi frequencies to protect quantum operations on an atomic qutrit by continuous dynamical decoupling
• Quantum computation with charge-and-color permuting twists in qudit color codes
• Unconditional remote entanglement using second-harmonic generation and twin two-mode squeezed vacuum states
• Quantum Computation and Communication in Bosonic Systems
• Experimental Approach to Demonstrating Contextuality for Qudits
• Constructing Qudits from Infinite Dimensional Oscillators by Coupling to Qubits
• Physically motivated decompositions of single-qutrit gates
• Gaussian Amplitude Amplification for Quantum Pathfinding