> VQE is a hybrid algorithm designed to use a Quantum Processing Unit (QPU) and a Classical Processing Unit (CPU) together to perform faster computations.
> Global research teams, including IBM and Google, are investigating it in a variety of quantum systems, including superconducting and trapped-ion systems. However, qubit-based VQE is currently only implemented up to 2 qubits in photonic systems and 12 qubits in superconducting systems, and is challenged by error issues that make it difficult to scale when more qubits and complex computations are required. [...]
> In this study, a qudit was implemented by the orbital angular momentum state of a single-photon, and dimensional expansion was possible by adjusting the phase of a photon through holographic images. This allowed for high-dimensional calculations without complex quantum gates, reducing errors.
> In this study, a qudit was implemented by the orbital angular momentum state of a single-photon, and dimensional expansion was possible by adjusting the phase of a photon through holographic images
> This means that hard-to-measure optical properties such as amplitudes, phases and correlations—perhaps even these of quantum wave systems—can be deduced from something a lot easier to measure: light intensity.
> [..] Qian's team interpreted the intensity of a light as the equivalent of a physical object's mass, then mapped those measurements onto a coordinate system that could be interpreted using Huygens' mechanical theorem. "Essentially, we found a way to translate an optical system so we could visualize it as a mechanical system, then describe it using well-established physical equations," explained Qian.
> Once the team visualized a light wave as part of a mechanical system, new connections between the wave's properties immediately became apparent—including the fact that entanglement and polarization stood in a clear relationship with one another.
Shouldn't that make holography and photonic phase sensors and light field cameras possible with existing photographic intensity sensors?
> Given a guess or ansatz, the quantum processor calculates the expectation value of the system with respect to an observable, often the Hamiltonian, and a classical optimizer is used to improve the guess. The algorithm is based on the variational method of quantum mechanics. [...] It is an example of a noisy intermediate-scale quantum (NISQ) algorithm
>> We fully resolve this problem, giving a polynomial time algorithm for learning H to precision ϵ from polynomially many copies of the Gibbs state at any constant β>0.
>> Our main technical contribution is a new flat polynomial approximation to the exponential function, and a translation between multi-variate scalar polynomials and nested commutators. This enables us to formulate Hamiltonian learning as a polynomial system. We then show that solving a low-degree sum-of-squares relaxation of this polynomial system suffices to accurately learn the Hamiltonian.
> VQE is a hybrid algorithm designed to use a Quantum Processing Unit (QPU) and a Classical Processing Unit (CPU) together to perform faster computations.
> Global research teams, including IBM and Google, are investigating it in a variety of quantum systems, including superconducting and trapped-ion systems. However, qubit-based VQE is currently only implemented up to 2 qubits in photonic systems and 12 qubits in superconducting systems, and is challenged by error issues that make it difficult to scale when more qubits and complex computations are required. [...]
> In this study, a qudit was implemented by the orbital angular momentum state of a single-photon, and dimensional expansion was possible by adjusting the phase of a photon through holographic images. This allowed for high-dimensional calculations without complex quantum gates, reducing errors.
ScholarlyArticle: "Qudit-based variational quantum eigensolver using photonic orbital angular momentum states" (2024) https://www.science.org/doi/10.1126/sciadv.ado3472
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