A Josephson voltage standard includes: electrical conductors that receive bias currents and radiofrequency biases; a first Josephson junction array that: includes a first Josephson junction and produces a first voltage reference from the first bias current and the third bias current; a second Josephson junction array in electrical communication with the first Josephson junction array and that: includes a second Josephson junction; receives the second bias current; receives the third bias current; receives the second radiofrequency bias; and produces a second voltage reference from the second bias current and the third bias current; a first voltage reference output tap in electrical communication with the first Josephson junction array and that receives the first voltage reference from the first Josephson junction array such that the first voltage reference is electrically available at the first voltage reference output tap; and a second voltage reference output tap.

A Josephson voltage standard includes: electrical conductors that receive bias currents and radiofrequency biases; a first Josephson junction array that: includes a first Josephson junction and produces a first voltage reference from the first bias current and the third bias current; a second Josephson junction array in electrical communication with the first Josephson junction array and that: includes a second Josephson junction; receives the second bias current; receives the third bias current; receives the second radiofrequency bias; and produces a second voltage reference from the second bias current and the third bias current; a first voltage reference output tap in electrical communication with the first Josephson junction array and that receives the first voltage reference from the first Josephson junction array such that the first voltage reference is electrically available at the first voltage reference output tap; and a second voltage reference output tap.

A silicon-based quantum device is provided. The device comprises: a first metallic structure (501); a second metallic structure (502) laterally separated from the first metallic structure; and an L-shaped elongate channel (520) defined by the separation between the first and second metallic structures; wherein the elongate channel has a vertex (505) connecting two elongate parts of the elongate channel. The device further comprises: a third metallic structure (518), mediator gate, positioned in the elongate channel; a fourth metallic structure (531) forming a first barrier gate, arranged at a first end of the third metallic structure; and a fifth metallic structure (532) forming a second barrier gate arranged at a second end of the third metallic structure. The first, second, third, fourth and fifth metallic structures are configured for connection to first, second, third, fourth and fifth electric potentials respectively. The first, second, fourth and fifth electric potentials are controllable to define an electrical potential well to confine quantum charge carriers in an elongate quantum dot beneath the elongate channel. The fourth and fifth electric potentials and the position of the fourth and fifth metallic structures define first and second ends of the elongate channel respectively. The width of the electrical potential well is defined by the position of the first and second metallic structures and their corresponding electric potentials; and the length of the electrical potential well is defined by the position of the fourth and fifth metallic structures and their corresponding electric potentials. The third electric potential is controllable to adjust quantum charge carrier energy levels in the electrical potential well.

A silicon-based quantum device is provided. The device comprises: a first metallic structure (501); a second metallic structure (502) laterally separated from the first metallic structure; and an L-shaped elongate channel (520) defined by the separation between the first and second metallic structures; wherein the elongate channel has a vertex (505) connecting two elongate parts of the elongate channel. The device further comprises: a third metallic structure (518), mediator gate, positioned in the elongate channel; a fourth metallic structure (531) forming a first barrier gate, arranged at a first end of the third metallic structure; and a fifth metallic structure (532) forming a second barrier gate arranged at a second end of the third metallic structure. The first, second, third, fourth and fifth metallic structures are configured for connection to first, second, third, fourth and fifth electric potentials respectively. The first, second, fourth and fifth electric potentials are controllable to define an electrical potential well to confine quantum charge carriers in an elongate quantum dot beneath the elongate channel. The fourth and fifth electric potentials and the position of the fourth and fifth metallic structures define first and second ends of the elongate channel respectively. The width of the electrical potential well is defined by the position of the first and second metallic structures and their corresponding electric potentials; and the length of the electrical potential well is defined by the position of the fourth and fifth metallic structures and their corresponding electric potentials. The third electric potential is controllable to adjust quantum charge carrier energy levels in the electrical potential well.

A coupler includes first and second electrodes and a nonlinear element including a Josephson junction. The first and second electrodes are spaced apart from a ground plane surrounding peripheries thereof and arranged opposed to each other. The first/second electrode includes two opposing portions extended toward first and second qubits/third and fourth qubits. At least either one of a gap between the first electrode and the ground plane facing the first electrode and a gap between the second electrode and the ground plane facing the second electrode, includes a gap width of at least a value of a same extent as or a fraction of a size of the first electrode or the second electrode.

A coupler includes first and second electrodes and a nonlinear element including a Josephson junction. The first and second electrodes are spaced apart from a ground plane surrounding peripheries thereof and arranged opposed to each other. The first/second electrode includes two opposing portions extended toward first and second qubits/third and fourth qubits. At least either one of a gap between the first electrode and the ground plane facing the first electrode and a gap between the second electrode and the ground plane facing the second electrode, includes a gap width of at least a value of a same extent as or a fraction of a size of the first electrode or the second electrode.

There is described herein a topologically protected quantum circuit with superconducting qubits and method of operation thereof. The circuit comprises a plurality of physical superconducting qubits and a plurality of coupling devices interleaved between pairs of the physical superconducting qubits. The coupling devices comprise at least one φ-Josephson junction, wherein a Josephson phase φ.sub.0 of the φ-Josephson junction is non-zero in a ground state, the coupling devices have a Josephson energy E.sub.Jφ, the physical superconducting qubits have a Josephson energy E.sub.Jq, and the circuit operates in a topological regime when $\frac{E_{Jq}}{2}>-E_{J\phi }\cos {\phi }_0>\frac{E_{Jq}}{3}.$

There is described herein a topologically protected quantum circuit with superconducting qubits and method of operation thereof. The circuit comprises a plurality of physical superconducting qubits and a plurality of coupling devices interleaved between pairs of the physical superconducting qubits. The coupling devices comprise at least one φ-Josephson junction, wherein a Josephson phase φ.sub.0 of the φ-Josephson junction is non-zero in a ground state, the coupling devices have a Josephson energy E.sub.Jφ, the physical superconducting qubits have a Josephson energy E.sub.Jq, and the circuit operates in a topological regime when $\frac{E_{Jq}}{2}>-E_{J\phi }\cos {\phi }_0>\frac{E_{Jq}}{3}.$

A closed-loop feedback system and method of active noise cancellation to maintain a desired operating frequency of a qubit during a quantum computation, even when that frequency is relatively sensitive to flux noise. A series of Ramsey experiments is performed on the qubit to estimate an offset between its actual and desired operating frequencies, and the error is accumulated. After the probing is complete, the accumulated error is supplied to an arbitrary waveform generator that produces a magnetic flux that is coupled to the qubit, thereby tuning the qubit and actively controlling its operating frequency. Having corrected the operating frequency of the qubit and extended its coherence time, the quantum state of the qubit is allowed to evolve according to the computation.

A closed-loop feedback system and method of active noise cancellation to maintain a desired operating frequency of a qubit during a quantum computation, even when that frequency is relatively sensitive to flux noise. A series of Ramsey experiments is performed on the qubit to estimate an offset between its actual and desired operating frequencies, and the error is accumulated. After the probing is complete, the accumulated error is supplied to an arbitrary waveform generator that produces a magnetic flux that is coupled to the qubit, thereby tuning the qubit and actively controlling its operating frequency. Having corrected the operating frequency of the qubit and extended its coherence time, the quantum state of the qubit is allowed to evolve according to the computation.