For 45° and 90°, it is equal to the expected accidental rate. For a 25° angle, it only about 15% greater than the accidental rate, which is still statistically significant, if barely. When I rotate one of the Geigers out of alignment, the coincidence rate drops precipitously. There are various subtleties in separating accidental and genuine coincidence rates and in estimating statistical errors, but the signal I observe is something like 10 standard deviations above the noise. This is about 40% greater than the expected rate of accidental coincidences. When the Geigers are pointing straight at each other, each clicks about 900 times per minute and both do so in unison about 4 times per minute. If gamma-ray photons are indeed emerging two by two in opposite directions, the coincidence rate should vary strongly when I change the alignment of the two Geigers. It is not done well but you are surprised to find it done at all.”Īs a warm-up exercise, I sandwich my source of entangled photons-a disk of radioactive sodium-22-between my two Geiger counters (see diagram and photo below) and leave the system to run overnight, measuring how often the Geigers click at the same time. It doesn’t give publishable results, but, to appropriate a line from Samuel Johnson, a homebrew entanglement experiment is “like a dog’s walking on his hinder legs. To my knowledge, it’s the cheapest and simplest such experiment ever done. The answers to these open research questions will determine the routes for the VQE to achieve quantum advantage as the quantum computing hardware scales up and as the noise levels are reduced.In my last post, I scrounged the parts for a very crude, but very cool, experiment you can do in your basement to demonstrate quantum entanglement. We identify four main areas of future research: (1) optimal measurement schemes for reduction of circuit repetitions required (2) large scale parallelization across many quantum computers (3) ways to overcome the potential appearance of vanishing gradients in the optimization process for large systems, and how the number of iterations required for the optimization scales with system size (4) the extent to which VQE suffers for quantum noise, and whether this noise can be mitigated in a tractable manner. These include the representation of Hamiltonians and wavefunctions on a quantum computer, the optimization process to find ground state energies, the post processing mitigation of quantum errors, and suggested best practices. All the different components of the algorithm are reviewed in detail. This review aims at disentangling the relevant literature to provide a comprehensive overview of the progress that has been made on the different parts of the algorithm, and to discuss future areas of research that are fundamental for the VQE to deliver on its promises. Despite strong theoretical underpinnings suggesting excellent scaling of individual VQE components, studies have pointed out that their various pre-factors could be too large to reach a quantum computing advantage over conventional methods. The potential practical advantages of the algorithm are also widely discussed in the literature, but with varying conclusions. Finding a path to navigate the relevant literature has rapidly become an overwhelming task, with many methods promising to improve different parts of the algorithm, but without clear descriptions of how the diverse parts fit together. One important advantage is that variational algorithms have been shown to present some degree of resilience to the noise in the quantum hardware. The VQE may be used to model these complex wavefunctions in polynomial time, making it one of the most promising near-term applications for quantum computing. Conventional computing methods are constrained in their accuracy due to the computational limits facing exact modeling of the exponentially growing electronic wavefunction for these many-electron systems. It uses the variational principle to compute the ground state energy of a Hamiltonian, a problem that is central to quantum chemistry and condensed matter physics. (2014), has received significant attention from the research community in recent years. The variational quantum eigensolver (or VQE), first developed by Peruzzo et al.
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