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6 results for POVM

New learning rule for quantum measurement classes overcomes uniform convergence issues.

problem Characterizing learnability of POVM hypothesis classes in quantum settings.
method Introduced a new learning rule called denoised ERM to address uniform convergence issues.
result Characterized learnability conditions and sample complexity bounds for POVM classes.

A single qubit may be represented on the Bloch sphere or similarly on the 33-sphere S3S^3. Our goal is to dress this correspondence by converting the language of universal quantum computing (UQC) to that of 33-manifolds. A magic state and the Pauli group acting on it define a model of UQC as a positive operator-value…

2018-02-12abs ↗pdf ↗

Quantum circuits learn to classify non-orthogonal quantum states.

problem Classifying non-orthogonal quantum states is crucial in quantum information.
method Trained quantum circuits using Adam optimization to discover parameters of unknown POVMs.
result Shallow quantum circuits can learn to discriminate among various quantum states with comparable performance to optimal POVMs.

We classify SIC-POVMs of rank one in CP^2, or equivalently sets of nine equally-spaced points in CP^2, without the assumption of group covariance. If two points are fixed, the remaining seven must lie on a pinched torus that a standard moment mapping projects to a circle in R^3. We use this approach to prove that any S…

2014-10-21abs ↗pdf ↗

New proof shows 11 measurements needed for phase retrieval in 4D complex space.

problem Determining the minimal number of intensity measurements for phase retrieval in 4D complex space.
method Leveraged characteristic classes and cohomology groups from differential topology.
result Proved that 11 is the exact minimum number of measurements required for phase retrieval in 4D complex space.