Methods, systems, and apparatus for implementing a unitary quantum gate on one or more qubits. In one aspect, a method includes the actions designing a control pulse for the unitary quantum gate, comprising: defining a universal quantum control cost function, wherein the control cost function comprises a qubit leakage penalty term representing i) coherent qubit leakage, and ii) incoherent qubit leakage across all frequency components during a time dependent Hamiltonian evolution that realizes the unitary quantum gate; adjusting parameters of the time dependent Hamiltonian evolution to vary a control cost according to the control cost function such that leakage errors are reduced; generating the control pulse using the adjusted parameters; and applying the control pulse to the one or more qubits to implement the unitary quantum gate.

A pulse generation circuit in a quantum controller operates synchronously with a pulse computation circuit. The pulse generation circuit generates a pulse associated with a quantum element operation. The pulse computation circuit is able to determine characteristics of a signal that is based on the pulse. These characteristics are used by the pulse generation circuit to modify the pulse.

A pulse generation circuit in a quantum controller operates synchronously with a pulse computation circuit. The pulse generation circuit generates a pulse associated with a quantum element operation. The pulse computation circuit is able to determine characteristics of a signal that is based on the pulse. These characteristics are used by the pulse generation circuit to modify the pulse.

Topologies for interconnecting capacitive and inductive elements in a capacitively-coupled rib are described. An example relates to a resonant clock network (RCN) that resonates in response to both a first clock signal having a first phase and a second clock signal having a second phase. The RCN includes at least one rib coupled to at least one spine. The rib includes a first capacitive line configured to receive the first clock signal and provide, via a first capacitor, a first bias current to a first superconducting circuit. The rib further includes a second capacitive line configured to receive the second clock signal and provide, via a second capacitor, a second bias current to a second superconducting circuit. The rib further includes at least one inductive line configured to connect the first capacitive line with the second capacitive line forming a direct connection between the two capacitive lines.

Topologies for interconnecting capacitive and inductive elements in a capacitively-coupled rib are described. An example relates to a resonant clock network (RCN) that resonates in response to both a first clock signal having a first phase and a second clock signal having a second phase. The RCN includes at least one rib coupled to at least one spine. The rib includes a first capacitive line configured to receive the first clock signal and provide, via a first capacitor, a first bias current to a first superconducting circuit. The rib further includes a second capacitive line configured to receive the second clock signal and provide, via a second capacitor, a second bias current to a second superconducting circuit. The rib further includes at least one inductive line configured to connect the first capacitive line with the second capacitive line forming a direct connection between the two capacitive lines.

The present disclosure relates to improved electronic structures for propagating logic states between superconducting digital logic gates using a three-junction interferometer in a receiver circuit to reduce reflecting signals that otherwise result in distortions in the signals being transmitted between the gates. Other improved electronic structures comprise passive transmission lines (PTLs) with transmission line matching circuitry that has previously been avoided. The matching circuity minimizes generation and propagation of spurious pulses emitted by Josephson junctions used in the digital logic gates.

A circuit can include a first sub-circuit, a second sub-circuit, and a third sub-circuit. The first sub-circuit can store a reset state or a set state, and can include a first Josephson junction (JJ), a second JJ, and a third JJ coupled in parallel using superconducting inductors. The first JJ, the second JJ, and the third JJ can be biased using a JJ-based current source. The second sub-circuit can switch the first sub-circuit to the set state in response to receiving a pulse. The third sub-circuit can switch the first sub-circuit to the reset state in response to receiving one or more pulses.

A circuit can include a first sub-circuit, a second sub-circuit, and a third sub-circuit. The first sub-circuit can store a reset state or a set state, and can include a first Josephson junction (JJ), a second JJ, and a third JJ coupled in parallel using superconducting inductors. The first JJ, the second JJ, and the third JJ can be biased using a JJ-based current source. The second sub-circuit can switch the first sub-circuit to the set state in response to receiving a pulse. The third sub-circuit can switch the first sub-circuit to the reset state in response to receiving one or more pulses.

A superconducting integrated circuit, comprising a plurality of superconducting circuit elements, each having a variation in operating voltage over time; a common power line; and a plurality of bias circuits, each connected to the common power line, and to a respective superconducting circuit element, wherein each respective bias circuit is superconducting during at least one time portion of the operation of a respective superconducting circuit element, and is configured to supply the variation in operating voltage over time to the respective superconducting circuit element.

A superconducting logic cell includes at least one quantum phase-slip junction (QPSJ) for receiving at least one input and responsively providing at least one output, each QPSJ being configured such that when an input voltage of an input voltage pulse exceeds a critical value, a quantized charge of a Cooper electron pair tunnels across said QPSJ as an output, when the input voltage is less than the critical value, no quantized charge of the Cooper electron pair tunnels across said QPSJ as the output, where the presence and absence of the quantized charge in the form of a constant area current pulse in the output form two logic states, and the at least one QPSJ is biased with a bias voltage. The superconducting logic cell further includes at least one Josephson junction (JJ) coupled with the at least one QPSJ to perform one or more logic operations.