A quantum computing system for converting Pauli errors of one or more qubits to erasure errors in a photonic quantum computing architecture. Two or more photonic qubits may be input to a quantum computing system, where at least one first qubit of the two or more qubits has experienced a Pauli error. A sequence of linear optical circuitry operations may be performed on the two or more qubits to generate two or more modified qubits, wherein the sequence of operations transforms one or more of the first qubits from a logical subspace of a Fock space to an erasure subspace of the Fock space. A cluster state for universal quantum computing may be generated from the two or more modified qubits using probabilistic entangling gates. A quantum computational algorithm may be performed using the quantum cluster state generated from the two or more modified qubits.

An analog computing system with coupled non-linear oscillators can solve complex combinatorial optimization problems using the weighted Ising model. The system is composed of a fully-connected LC oscillator network with low-cost electronic components and compatible with traditional integrated circuit technologies. Each LC oscillator, or node, in the network can be coupled to each other node in the array with a multiply and accumulate crossbar array or optical interconnects. When implemented with four nodes, the system performs with single-run ground state accuracies of 98% on randomized MAX-CUT problem sets with binary weights and 84% with five-bit weight resolutions. The four-node system can obtain solutions within five oscillator cycles with a time-to-solution that scales directly with oscillator frequency. A scaling analysis suggests that larger coupled oscillator networks may be used to solve computationally intensive problems faster and more efficiently than conventional algorithms.

An analog computing system with coupled non-linear oscillators can solve complex combinatorial optimization problems using the weighted Ising model. The system is composed of a fully-connected LC oscillator network with low-cost electronic components and compatible with traditional integrated circuit technologies. Each LC oscillator, or node, in the network can be coupled to each other node in the array with a multiply and accumulate crossbar array or optical interconnects. When implemented with four nodes, the system performs with single-run ground state accuracies of 98% on randomized MAX-CUT problem sets with binary weights and 84% with five-bit weight resolutions. The four-node system can obtain solutions within five oscillator cycles with a time-to-solution that scales directly with oscillator frequency. A scaling analysis suggests that larger coupled oscillator networks may be used to solve computationally intensive problems faster and more efficiently than conventional algorithms.

In response to a request to pull over an ADV at a destination point at a side of a lane, a path including a first segment, a second segment and a transition point is planned. The transition point is determined based on at least one of a distance to the destination point or a predetermined distance to a boundary of the side of the lane. The first segment from a start point to the transition point is generated by using a quadratic programming (QP) operation. The second segment from the transition point to the destination is generated based on a shape of the boundary. The ADV is controlled to pull over to the destination point according to the planned path.

In response to a request to pull over an ADV at a destination point at a side of a lane, a path including a first segment, a second segment and a transition point is planned. The transition point is determined based on at least one of a distance to the destination point or a predetermined distance to a boundary of the side of the lane. The first segment from a start point to the transition point is generated by using a quadratic programming (QP) operation. The second segment from the transition point to the destination is generated based on a shape of the boundary. The ADV is controlled to pull over to the destination point according to the planned path.

A computer-implemented method comprises receiving a plurality of sampled data points, each data point including a y value and a t value; defining a plurality of bins; defining an array of elements; dividing the sampled data points into a plurality of sections; assigning a plurality of polynomial equations, one polynomial equation to each section, each polynomial equation having a waveform that fits the data points of the associated section; determining a plurality of section bin times, one section bin time for each bin in each section, each section bin time determined using the polynomial equation and indicating an amount of time that the waveform has values in the range of one of the bins; and adding the section bin time for each bin in each section to the histogram data in the array element pointed to by the number of the bin.

A computer-implemented method comprises receiving a plurality of sampled data points, each data point including a y value and a t value; defining a plurality of bins; defining an array of elements; dividing the sampled data points into a plurality of sections; assigning a plurality of polynomial equations, one polynomial equation to each section, each polynomial equation having a waveform that fits the data points of the associated section; determining a plurality of section bin times, one section bin time for each bin in each section, each section bin time determined using the polynomial equation and indicating an amount of time that the waveform has values in the range of one of the bins; and adding the section bin time for each bin in each section to the histogram data in the array element pointed to by the number of the bin.

Embodiments use quantum conditional logic in the Quantum Phase Estimation Algorithm (QPEA) to compute eigenvalues prior to inversion. Embodiments estimate the eigenvalues of a unitary, U=e.sup.iÂt, generated by a N×N Hermitian matrix Â. The binary representations of the n-bit estimations of eigenvalues of  may be encoded in these states: |λ.sub.i=|b.sub.1b.sub.2 . . . b.sub.n; λ.sub.i is an estimation of the i-th eigenvalue, excluding degeneracy, and .b.sub.1b.sub.2 . . . b.sub.n is its binary representation. To perform the eigenvalue inversion, an n-qubit controlled Ry rotation with angle λ.sub.i/2.sup.(n−1) conditioned on seeing |b.sub.1b.sub.2 . . . b.sub.n is applied for each possible n-bit binary string b.sub.1b.sub.2 . . . b.sub.n (2.sup.n values). The overall unitary is called a “uniformly controlled Ry rotation” in literature.

Embodiments use quantum conditional logic in the Quantum Phase Estimation Algorithm (QPEA) to compute eigenvalues prior to inversion. Embodiments estimate the eigenvalues of a unitary, U=e.sup.iÂt, generated by a N×N Hermitian matrix Â. The binary representations of the n-bit estimations of eigenvalues of  may be encoded in these states: |λ.sub.i=|b.sub.1b.sub.2 . . . b.sub.n; λ.sub.i is an estimation of the i-th eigenvalue, excluding degeneracy, and .b.sub.1b.sub.2 . . . b.sub.n is its binary representation. To perform the eigenvalue inversion, an n-qubit controlled Ry rotation with angle λ.sub.i/2.sup.(n−1) conditioned on seeing |b.sub.1b.sub.2 . . . b.sub.n is applied for each possible n-bit binary string b.sub.1b.sub.2 . . . b.sub.n (2.sup.n values). The overall unitary is called a “uniformly controlled Ry rotation” in literature.

A method and system are disclosed for automatic replenishment of a retail enterprise store, and a computer-readable storage medium. In the method of the present disclosure, historical operational transaction data of at least one store of the same type as the retail enterprise store is used to obtain four indicators of each product of the at least one store, a plurality of target features having an impact on an indicator matrix composed of the four indicators are extracted to provide replenishment suggestions, and the indicator matrix composed of the four indicators is automatically adjusted to update a replenishment model. In the embodiments of the present disclosure, a set of algorithm models can be optimized and customized according to the historical operational transaction data of the store and external environments such as weather changes, business circle customer flow, discount events, etc., so that each store can be provided with SKU-level high-precision demand prediction and replenishment suggestions to generate replenishment suggestions, improving the processing efficiency of the server, and further realizing the artificially controllable intelligent replenishment decision-making function.