Abstract: Describe herein are various embodiments of protected small logical qubit architectures and superconducting devices for use therewith. The disclosed architectures, methods, devices, and systems, using their most coherent component parts as a baseline, may be useful in suppress all single qubit error channels, and once calibrated can be operated in a fully autonomous manner with no measurement or feedback. Applicant's logical qubit may be compatible with strong, tunable interactions so that fast gates can be performed. In many embodiments, the control structure may be both simple, and robust. In many embodiments, the disclosed methods, devices, and systems are able to endure small variations in the device parameters, to ensure repeatability and scalability.

Abstract: An exemplary method for achieving an error divisible gate in a quantum system includes selecting an intrinsic gate error rate threshold for a gate coupled between a pair of qubits, and determining a first gate time to execute a full entangling gate rotation with a first error rate less than the intrinsic gate error rate threshold. The exemplary method further includes, based on the time to execute the full entangling gate, applying, to the gate, a second gate rotation having a second gate time less than the first gate time to determine a second error rate. The exemplary method further includes selecting the second gate time as a final gate time when the second error rate is smaller than the first error rate.

Abstract: An exemplary tundable capacitor in a quantum system includes a pair of qubits, and a capacitive coupling element coupled between the pair of qubits. The capacitive coupling element includes a plurality of gate terminals. The capacitive coupling element is configured to receive a respective gate voltage at each of the plurality of gate terminals and to adjust a capacitance of the capacitive coupling element in response to the respective gate voltage received at each of the plurality of gate terminals. The capacitance of the capacitive coupling element is configured to control a coupling strength between the pair of qubits.

Abstract: Embodiments herein implement quantum annealing with a driver Hamiltonian that uses oscillating fields to advantageously obtain a quantum speedup over classical computing techniques. For a many-body quantum system formed with qubits, the oscillating fields drive the qubits so as to independently modulate the magnitudes and/or directions of transverse terms of the driver Hamiltonian. In particular, embodiments provide a quantum speedup for two types of first-order phase transitions: the paramagnet-to-spin-glass transition, and transitions between distinct “bit string” states. The resulting speedup is robust against energy fluctuations (e.g., 1/f noise), in contrast to other strategies like variable-rate annealing. Each oscillating field may be an oscillating electric field or magnetic field. The oscillating fields can be implemented with superconducting flux qubits by coupling oscillating fluxes and/or voltages to the flux qubits.

Abstract: Example methods for quantum optimization include applying an optimization algorithm to a problem Hamiltonian (defined by qubit interaction constraint coefficients based on a binary optimization problem to find a local minimum state with initial total energy). The method further includes selecting a target energy that is less than the initial energy based on the binary optimization problem, modifying a subset of the qubit interaction constraint coefficient of the interaction constraint coefficients by a selected amount to reduce a total energy of the local minimum state to approximate the target total energy to provide an updated problem Hamiltonian, evolving a many-body quantum system (MBQS) based on the updated problem Hamiltonian by applying oscillating fields to single qubit transverse field terms and/or to transverse inter-qubit couplings of the MBQS for a time period, determining the total energy relative to the problem Hamiltonian based on the MBQS after expiration of the time period.

Abstract: Error-transparent quantum gates may be implemented with one or two logical qubits, each having a plurality of coupled physical qubits. Error-transparent quantum gates implement Hamiltonians that commute with the Hamiltonian for single errors in the logical qubits, and thus can operate successfully even in the presence of single errors. As a result, error-transparent quantum gates may operate with higher fidelity than their error-opaque counterparts. Each of the logical qubits may be, for example, a very small logical qubit (VSLQ) formed from a cluster of transmons or other superconducting qubits.

Abstract: Embodiments herein implement quantum annealing with a driver Hamiltonian that uses oscillating fields to advantageously obtain a quantum speedup over classical computing techniques. For a many-body quantum system formed with qubits, the oscillating fields drive the qubits so as to independently modulate the magnitudes and/or directions of transverse terms of the driver Hamiltonian. In particular, embodiments provide a quantum speedup for two types of first-order phase transitions: the paramagnet-to-spin-glass transition, and transitions between distinct “bit string” states. The resulting speedup is robust against energy fluctuations (e.g., 1/f noise), in contrast to other strategies like variable-rate annealing. Each oscillating field may be an oscillating electric field or magnetic field. The oscillating fields can be implemented with superconducting flux qubits by coupling oscillating fluxes and/or voltages to the flux qubits.

Abstract: Error-transparent quantum gates may be implemented with one or two logical qubits, each having a plurality of coupled physical qubits. Error-transparent quantum gates implement Hamiltonians that commute with the Hamiltonian for single errors in the logical qubits, and thus can operate successfully even in the presence of single errors. As a result, error-transparent quantum gates may operate with higher fidelity than their error-opaque counterparts. Each of the logical qubits may be, for example, a very small logical qubit (VSLQ) formed from a cluster of transmons or other superconducting qubits.