A quantum computing system and methods for performing fault-tolerant quantum computing. A fusion controller sequentially performs a series of fusion measurements on different fusion sites of a plurality of fusion sites to obtain a respective series of classical measurement results. The series of fusion measurements is performed on quantum modes of a logical qubit. For respective fusion measurements of the series of fusion measurements, a basis for performing the respective fusion measurement is selected based on classical measurement results of previous fusion measurements. The series of classical measurement results are in the memory medium.

A novel and useful system and method of quantum stochastic rounding using silicon based quantum dot arrays. Unitary noise is derived from a probability of detecting a particle within a quantum dot array structure comprising position based charge qubits with two time independent basis states |0> and |1>. A two level electron tunneling device such as an interface device, qubit or other quantum structure is used to generate quantum noise. The electron tunneling device includes a reservoir of particles, a quantum dot, and a barrier that is used to control tunneling between the reservoir and the quantum dot. A detector circuit connected to the device outputs a digital stream corresponding to the probability of a particle of being detected. Controlling the bias applied to the barrier controls the probability of detection. Thus, the probability density function (PDF) of the output unitary noise can be controlled to correspond to a desired probability. The unitary noise is used to perform stochastic rounding by controlling the bias applied to the barrier in accordance with a remainder of numbers to be rounded.

A novel and useful system and method of accelerated learning in neural networks using silicon based quantum dot arrays. Unitary noise is derived from a probability of detecting a particle within a quantum dot array structure comprising position based charge qubits with two time independent basis states |0> and |1>. A two level electron tunneling device such as an interface device, qubit or other quantum structure is used to generate quantum noise. The electron tunneling device includes a reservoir of particles, a quantum dot, and a barrier that is used to control tunneling between the reservoir and the quantum dot. Controlling the bias applied to the barrier controls the probability of detection. Thus, the probability density function (PDF) of the output unitary noise can be controlled to correspond to a desired probability. The quantum unitary noise is injected into one or more layers of an artificial neural network (ANN) to improve the learning and training process. The quantum noise source is also used to perform stochastic rounding in the ANN. The PDF of the quantum noise source output is set to a desired value in accordance with the remainder portion of input numbers within the layers of the ANN to be rounded.

A quantum computing system and methods for performing fusion based quantum computing on encoded qubits. A fusion controller sequentially performs a series of fusion measurements on respective physical qubits of first and second encoded qubits to obtain a respective series of classical measurement results. For respective fusion measurements of the series of fusion measurements, a basis for performing the respective fusion measurement is selected based on classical measurement results of previous fusion measurements. An encoded fusion measurement result is determined based on the classical measurement results, and the encoded fusion measurement result is stored in a memory medium.

A system and method for storing information in a quantum computer using a quantum storage ring. The method comprises cooling ions in the quantum storage ring to a low temperature; and binding the ions into a lattice structure, forming an ion Coulomb crystal.

Apparatus, methods, and systems are disclosed for robust scalable topological quantum computing. Quantum dots are fabricated as van der Waals heterostructures, supporting localized topological phases and non-Abelian anyons (quasiparticles). Large bandgaps provide noise immunity. Three-dot structures include an intermediate quantum dot between two computational quantum dots. With the intermediate quantum dot in an OFF state, quasiparticles at the computational quantum dots can be isolated, with long lifetimes. Alternatively, the intermediate quantum dot can be controlled to decrease the quasiparticle tunneling barrier, enabling fast computing operations. A computationally universal suite of operations includes quasiparticle initialization, braiding, fusion, and readout of fused quasiparticle states, with, optionally, transport or tunable interactions—all topologically protected. Robust qubits can be operated without error correction. Quasilinear arrays of quantum dots or qubits can be scaled arbitrarily, up to resource limits, and large-scale topological quantum computers can be realized. Extensive two-dimensional arrays can also be used.

Apparatus, methods, and systems are disclosed for robust scalable topological quantum computing. Quantum dots are fabricated as van der Waals heterostructures, supporting localized topological phases and non-Abelian anyons (quasiparticles). Large bandgaps provide noise immunity. Three-dot structures include an intermediate quantum dot between two computational quantum dots. With the intermediate quantum dot in an OFF state, quasiparticles at the computational quantum dots can be isolated, with long lifetimes. Alternatively, the intermediate quantum dot can be controlled to decrease the quasiparticle tunneling barrier, enabling fast computing operations. A computationally universal suite of operations includes quasiparticle initialization, braiding, fusion, and readout of fused quasiparticle states, with, optionally, transport or tunable interactions—all topologically protected. Robust qubits can be operated without error correction. Quasilinear arrays of quantum dots or qubits can be scaled arbitrarily, up to resource limits, and large-scale topological quantum computers can be realized. Extensive two-dimensional arrays can also be used.

Apparatus, methods, and systems are disclosed for robust scalable topological quantum computing. Quantum dots are fabricated as van der Waals heterostructures, supporting localized topological phases and non-Abelian anyons (quasiparticles). Large bandgaps provide noise immunity. Three-dot structures include an intermediate quantum dot between two computational quantum dots. With the intermediate quantum dot in an OFF state, quasiparticles at the computational quantum dots can be isolated, with long lifetimes. Alternatively, the intermediate quantum dot can be controlled to decrease the quasiparticle tunneling barrier, enabling fast computing operations. A computationally universal suite of operations includes quasiparticle initialization, braiding, fusion, and readout of fused quasiparticle states, with, optionally, transport or tunable interactions—all topologically protected. Robust qubits can be operated without error correction. Quasilinear arrays of quantum dots or qubits can be scaled arbitrarily, up to resource limits, and large-scale topological quantum computers can be realized. Extensive two-dimensional arrays can also be used.

A qubit array reparation system includes a reservoir of ultra-cold particle, a detector that determines whether or not qubit sites of a qubit array include respective qubit particles, and a transport system for transporting an ultra-cold particle to a first qubit array site that has been determined by the probe system to not include a qubit particle so that the ultra-cold particle can serve as a qubit particle for the first qubit array site. A qubit array reparation process includes maintaining a reservoir of ultra-cold particles, determining whether or not qubit-array sites contain respective qubit particles, each qubit particle having a respective superposition state, and, in response to a determination that a first qubit site does not contain a respective qubit particle, transporting an ultracold particle to the first qubit site to serve as a qubit particle contained by the first qubit site.

A security test logic system can include a non-transitory memory configured to store measurements from a measurement apparatus, the measurement outputs comprising indications of presence or absence of coincidences where particles are detected at more than one detector at substantially the same time, the detectors being at the end of different channels from a particle source and having substantially the same length. The system can include a processor configured to compute a test statistic from the stored measurements. The test statistic may express a Bell inequality, and the system can compare the test statistic with a threshold. The processor can be configured to generate and output a certificate certifying that the measurements are from a quantum system if the value of the computed test statistic passes the threshold.