Systems and methods for the optical control of qubits and other quantum particles with spatial light modulators (SLM) for quantum computing and quantum simulation are disclosed herein. The system may include a particle system configured to provide an ordered array comprising a multiplicity of quantum particles or a multiplicity of qubits, an optical source, a SLM configured to project a structured illumination pattern capable of individually addressing one or more quantum particles or qubits of the ordered array, and a SLM controller.

In a general aspect, a quantum error-correction technique includes applying a first set of two-qubit gates to qubits in a lattice cell, and applying a second, different set of two-qubit gates to the qubits in the lattice cell. The qubits in the lattice cell include data qubits and ancilla qubits, and the ancilla qubits reside between respective nearest-neighbor pairs of the data qubits. After the first and second sets of two-qubit gates have been applied, measurement outcomes of the ancilla qubits are obtained, and the parity of the measurement outcomes is determined.

In a general aspect, a quantum error-correction technique includes applying a first set of two-qubit gates to qubits in a lattice cell, and applying a second, different set of two-qubit gates to the qubits in the lattice cell. The qubits in the lattice cell include data qubits and ancilla qubits, and the ancilla qubits reside between respective nearest-neighbor pairs of the data qubits. After the first and second sets of two-qubit gates have been applied, measurement outcomes of the ancilla qubits are obtained, and the parity of the measurement outcomes is determined.

A transmission line has a first conductor layer extending in a first direction, a second conductor layer disposed on a side of a first surface of the first conductor layer via a first dielectric layer, the second conductor layer extending in the first direction, and a third conductor layer disposed on a side of a second surface of the first conductor layer opposite to the first surface, via a second dielectric layer, the third conductor layer extending in the first direction, wherein a width, in a second direction intersecting the first direction, of each of the second conductor layer and the third conductor layer is different at a plurality of locations in the first direction, and the first conductor layer, the second conductor layer, and the third conductor layer at least partially overlap each other in a plan view from a normal direction of the first surface.

A transmission line has a first conductor layer extending in a first direction, a second conductor layer disposed on a side of a first surface of the first conductor layer via a first dielectric layer, the second conductor layer extending in the first direction, and a third conductor layer disposed on a side of a second surface of the first conductor layer opposite to the first surface, via a second dielectric layer, the third conductor layer extending in the first direction, wherein a width, in a second direction intersecting the first direction, of each of the second conductor layer and the third conductor layer is different at a plurality of locations in the first direction, and the first conductor layer, the second conductor layer, and the third conductor layer at least partially overlap each other in a plan view from a normal direction of the first surface.

A hybrid computing system for solving a computational problem includes a digital processor, a quantum processor having qubits and coupling devices that together define a working graph of the quantum processor, and at least one nontransitory processor-readable medium communicatively coupleable to the digital processor which stores at least one of processor-executable instructions or data. The digital processor receives a computational problem, and programs the quantum processor with a first set of bias fields and a first set of coupling strengths. The quantum processor generates samples as potential solutions to an approximation of the problem. The digital processor updates the approximation by determining a second set of bias fields based at least in part on the first set of bias fields and a first set of mean fields that are based at least in part on the first set of samples and coupling strengths of one or more virtual coupling devices.

A hybrid computing system for solving a computational problem includes a digital processor, a quantum processor having qubits and coupling devices that together define a working graph of the quantum processor, and at least one nontransitory processor-readable medium communicatively coupleable to the digital processor which stores at least one of processor-executable instructions or data. The digital processor receives a computational problem, and programs the quantum processor with a first set of bias fields and a first set of coupling strengths. The quantum processor generates samples as potential solutions to an approximation of the problem. The digital processor updates the approximation by determining a second set of bias fields based at least in part on the first set of bias fields and a first set of mean fields that are based at least in part on the first set of samples and coupling strengths of one or more virtual coupling devices.

A quaternion deep neural network (QTDNN) includes a plurality of modular hidden layers, each comprising a set of QT computation sublayers, including a quaternion (QT) general matrix multiplication sublayer, a QT non-linear activations sublayer, and a QT sampling sublayer arranged along a forward signal propagation path. Each QT computation sublayer of the set has a plurality of QT computation engines. In each modular hidden layer, a steering sublayer precedes each of the QT computation sublayers along the forward signal propagation path. The steering sublayer directs a forward-propagating quaternion-valued signal to a selected at least one QT computation engine of a next QT computation subsequent sublayer.

A quaternion deep neural network (QTDNN) includes a plurality of modular hidden layers, each comprising a set of QT computation sublayers, including a quaternion (QT) general matrix multiplication sublayer, a QT non-linear activations sublayer, and a QT sampling sublayer arranged along a forward signal propagation path. Each QT computation sublayer of the set has a plurality of QT computation engines. In each modular hidden layer, a steering sublayer precedes each of the QT computation sublayers along the forward signal propagation path. The steering sublayer directs a forward-propagating quaternion-valued signal to a selected at least one QT computation engine of a next QT computation subsequent sublayer.

An apparatus includes a light source to provide a plurality of input optical modes in a squeezed state. The apparatus also includes a network of interconnected reconfigurable beam splitters (RBSs) configured to perform a unitary transformation of the plurality of input optical modes to generate a plurality of output optical modes. An array of photon counting detectors is in optical communication with the network of interconnected RBSs and configured to measure the number of photons in each mode of the plurality of the output optical modes after the unitary transformation. The apparatus also includes a controller operatively coupled to the light source and the network of interconnected RBSs. The controller is configured to control at least one of the squeezing factor of the squeezed state of light, the angle of the unitary transformation, or the phase of the unitary transformation.