Quantum systems are provided, including a qubit and a transmission line resonator having an associated resonant wavelength. A coupling capacitor is configured to capacitively couple the qubit to the transmission line resonator. A transformer is configured to inductively couple the qubit to the transmission line resonator. A selected one of an associated capacitance of the coupling capacitor and an associated mutual inductance of the transformer is a function of a location of the qubit along the transmission line resonator.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A quantum system comprising: a qubit; a transmission line resonator having an associated resonant wavelength; a coupling capacitor configured to capacitively couple the qubit to the transmission line resonator; and a transformer configured to inductively couple the qubit to the transmission line resonator; wherein a selected one of an associated capacitance of the coupling capacitor and an associated mutual inductance of the transformer is a function of a location of the qubit along the transmission line resonator. 2. The quantum system of claim 1, wherein an associated capacitance of the coupling capacitor is a function of a location of the coupling capacitor along the transmission line resonator. 3. The quantum system of claim 2, wherein the associated capacitance of the coupling capacitor is substantially equal to C 0  1 - sin   ( θ )  cos   ( θ )  , where θ is a distance along the transmission line resonator in radians of a resonant wavelength of the transmission line resonator and C0 is a capacitance that would provide a desired total amount of coupling at an antinode of the transmission line resonator. 4. The quantum system of claim 1, wherein an associated mutual inductance of the transformer is a function of a location of the coupling capacitor along the transmission line resonator. 5. The quantum system of claim 4, wherein an associated capacitance of the coupling capacitor is a function of a location of the coupling capacitor along the transmission line resonator. 6. The quantum system of claim 5, wherein the associated capacitance of the coupling capacitor is substantially equal to C0 cos(θ) and an associated mutual inductance of the transformer is substantially equal to M0 sin(θ), where θ is a distance along the transmission line resonator in radians of a resonant wavelength of the transmission line resonator, C0 is a capacitance that would provide a desired total amount of coupling at an antinode of the transmission line resonator, and M0 is a mutual inductance that would provide a desired total amount of coupling at a node of the transmission line resonator. 7. The quantum system of claim 6, wherein M0 is equal to the product of an impedance of the qubit, an impedance of the transmission line resonator, and C0. 8. The quantum system of claim 1, wherein the transformer comprises a portion of the transmission line resonator arranged in parallel with a portion of the qubit in an edge-coupled stripline geometry. 9. The quantum system of claim 1, wherein the qubit is a first qubit, the coupling capacitor is a first coupling capacitor, and the transformer is a first transformer, the system further comprising: a second qubit; a second coupling capacitor configured to capacitively couple the second qubit to the transmission line resonator; and a second transformer configured to inductively couple the second qubit to the transmission line resonator; wherein a selected one of an associated capacitance of the second coupling capacitor and an associated mutual inductance of the second transformer is a function of a location of the second qubit along the transmission line resonator, a location of the second qubit being different that a location of the first qubit. 10. The quantum system of claim 9, wherein a sum of a capacitive coupling between the first qubit and the transmission line resonator and an inductive coupling between the first qubit and the transmission line resonator is substantially equal in magnitude to a sum of a capacitive coupling between the second qubit and the transmission line resonator and an inductive coupling between the second qubit and the transmission line resonator. 11. The quantum system of claim 9, wherein the capacitive coupling between the first qubit and the transmission line resonator differs substantially from the capacitive coupling between the second qubit and the transmission line resonator. 12. The quantum system of claim 9, wherein the location of the second qubit is neither a voltage node nor a voltage antinode of the transmission line resonator. 13. The quantum system of claim 1, wherein the qubit is a transmon qubit. 14. A quantum system comprising: a transmission line resonator having an associated resonant wavelength; and a plurality of qubits comprising: a first qubit capacitively coupled to the transmission line resonator with a first capacitive coupling strength at a first location of the transmission line resonator; and a second qubit capacitively coupled to the transmission line resonator with a second capacitive coupling strength at a second location of the transmission line resonator; the first location being different from the second location, and the first capacitive coupling strength being different from the second capacitive coupling strength. 15. The quantum system of claim 14, wherein the first location is remote from any voltage nodes or antinodes of the transmission line resonator. 16. The quantum system of claim 14, wherein each of the first qubit and the second qubit are also inductively coupled to the transmission line resonator with respective first and second inductive coupling strengths. 17. The quantum system of claim 16, wherein a sum of the first inductive coupling strength and the first capacitive coupling strength is substantially equal in magnitude to a sum of the second inductive coupling strength and the second capacitive coupling strength. 18. The quantum system of claim 14, further comprising: a first coupling capacitor, configured to provide the capacitive coupling between the first qubit and the transmission line resonator; and a second coupling capacitor, configured to provide the capacitive coupling between the second qubit and the transmission line resonator; wherein the capacitance of each of the first coupling capacitor and the second coupling capacitor is selected as a function of the first and second locations, respectively. 19. A quantum system comprising: a first qubit; a second qubit; a transmission line resonator having an associated resonant wavelength; a first coupling capacitor, configured to provide capacitive coupling between the first qubit and the transmission line resonator at a first location remote from any nodes or antinodes of the transmission line resonator, the first coupling capacitor providing a first capacitive coupling strength; and a second coupling capacitor, configured to provide capacitive coupling between the second qubit and the transmission line resonator at a second location remote from the first location of the transmission line resonator, the second coupling capacitor providing a second capacitive coupling strength that is different from first capacitive coupling strength; a first transformer configured to inductively couple the first qubit to the transmission line resonator at the first location with a first inductive coupling strength; a second transformer configured to inductively couple the second qubit to the transmission line resonator at the second location with a second inductive coupling strength; and wherein either or both of the capacitances of the first and second coupling capacitors and the mutual inductances of the first and second transformers are a function of a location of their associated qubits along the transmission line resonator. 20. The quantum system of claim 19, wherein the function of the location of the qubits along the transmission line resonator is selected such that a sum of the first inductive coupling strength and the first capacitive coupling strength is substantially equal in magnitude to a sum of the second inductive coupling strength and the second capacitive coupling strength.