Quantum processing unit comprising one or more superconducting qubits based on phase-biased linear and non-linear inductive-energy elements

Abstract

A quantum processing unit is disclosed. The quantum processing unit includes at least one superconducting qubit based on phase-biased linear and non-linear inductive-energy elements. A superconducting phase difference across the linear and non-linear inductive-energy elements is biased, for example, by an external magnetic field, such that quadratic potential energy terms of the linear and non-linear inductive-energy elements are cancelled at least partly. In a preferred embodiment, such cancellation is at least 30%. The partial cancellation of the quadratic potential makes it possible to implement a high-coherence high-anharmonicity superconducting qubit design.

1 . A quantum processing unit comprising:
 a dielectric substrate; and   at least one superconducting qubit provided on the dielectric substrate, each of the at least one superconducting qubit comprising:
 a linear inductive-energy element that is superconductive; 
 a non-linear inductive-energy element; and 
 a phase-biasing element, 
   wherein the phase-biasing element is configured to bias a superconducting phase difference across the linear inductive-energy element and the non-linear inductive-energy element such that quadratic potential energy terms of the linear inductive-energy element and the non-linear inductive-energy element are at least partly cancelled by one another.   
     
     
         2 . The unit of  claim 1 , wherein the phase-biasing element is configured to bias the superconducting phase difference such that the quadratic potential energy terms of the linear inductive-energy element and the non-linear inductive-energy element are cancelled by one another by at least 30%. 
     
     
         3 . The unit of  claim 1 , wherein the linear inductive-energy element comprises one or more geometric inductors. 
     
     
         4 . The unit of  claim 1 , wherein the non-linear inductive-energy element comprises one or more Josephson junctions or kinetic inductors. 
     
     
         5 . The unit of  claim 1 , wherein each of the at least one superconducting qubit further comprises a capacitive-energy element. 
     
     
         6 . The unit of  claim 5 , wherein the capacitive-energy element comprises one or more interdigitated capacitors, gap capacitors, parallel-plate capacitors, or junction capacitors. 
     
     
         7 . The unit of  claim 1 , wherein the phase-biasing element is configured to bias the superconducting phase difference by generating and threading a magnetic field through the at least one superconducting qubit or by applying a predefined voltage to the non-linear inductive-energy element. 
     
     
         8 . The unit of  claim 7 , wherein the phase-biasing element comprises at least one of (i) one or more coils, or (ii) flux-bias lines. 
     
     
         9 . The unit of  claim 1 , wherein the at least one superconducting qubit comprises two or more superconducting qubits that are at least one of capacitively or inductively coupled to each other on the dielectric substrate. 
     
     
         10 . The unit of  claim 1 , wherein the at least one superconducting qubit comprises two or more superconducting qubits, and wherein the unit further comprises at least one of (i) one or more coupling resonators, or (ii) tunable couplers for coupling the superconducting qubits on the dielectric substrate. 
     
     
         11 . The unit of  claim 1 , further comprising signal lines provided on the dielectric substrate, the signal lines being configured to provide control signals to the at least one superconducting qubit. 
     
     
         12 . The unit of  claim 11 , wherein the signal lines comprise radio-frequency lines, and wherein the control signals comprise microwave pulses. 
     
     
         13 . The unit of  claim 1 , further comprising readout lines provided on the dielectric substrate, the readout lines being configured to measure a state of the at least one superconducting qubit. 
     
     
         14 . The unit of  claim 13 , further comprising readout resonators provided on the dielectric substrate, and wherein the readout lines are coupled to the at least one superconducting qubit via the readout resonators. 
     
     
         15 . The unit of  claim 1 ,
 wherein the at least one superconducting qubit is configured as a distributed-element resonator comprising at least two conductors separated by at least one gap,   wherein at least one of the at least two conductors serves as the linear inductive-energy element, and the non-linear inductive-energy element comprises at least one Josephson junction embedded in the distributed-element resonator, and   wherein the phase-biasing element is configured to bias the superconducting phase difference by generating and threading a magnetic field through the at least one gap of the distributed-element resonator.   
     
     
         16 . The unit of  claim 15 , wherein the distributed-element resonator is configured as a coplanar waveguide (CPW) resonator, wherein the at least two conductors comprise a center superconductor and a superconducting ground plane, the center superconductor serving as the linear inductive-energy element, and wherein the at least one Josephson junction is embedded in the CPW resonator such that the quantum processing unit is free of isolated superconducting islands. 
     
     
         17 . The unit of  claim 16 , wherein the center superconductor of the CPW resonator has a first pair of opposite sides and a second pair of opposite sides, and wherein the superconducting ground plane is formed on the dielectric substrate such that the center superconductor is galvanically connected to the superconducting ground plane on the first pair of opposite sides and separated by the gaps from the superconducting ground plane on the second pair of opposite sides. 
     
     
         18 . The unit of  claim 16 , wherein the superconducting ground plane comprises opposite portions physically separated from each other by the center superconductor and the gaps, the opposite portions being connected with each other via air bridges stretching over the gaps and the center superconductor. 
     
     
         19 . The unit of  claim 16 , wherein the at least one Josephson junction is embedded in the center superconductor. 
     
     
         20 . The unit of  claim 19 , wherein the at least one Josephson junction comprises a parallel connection of two Josephson junctions. 
     
     
         21 . The unit of  claim 19 , wherein the at least one Josephson junction is centrally arranged in the center superconductor. 
     
     
         22 . The unit of  claim 16 , wherein the at least one Josephson junction comprises:
 a first Josephson junction embedded in the center superconductor; and   at least one second Josephson junction arranged in one or more of the gaps in the vicinity of the first Josephson junction, each of the at least one second Josephson junction connecting the center superconductor to the superconducting ground plane via the corresponding gap.   
     
     
         23 . The unit of  claim 22 , wherein the at least one second Josephson junction comprises an even number of second Josephson junctions arranged symmetrically relative to the first Josephson junction. 
     
     
         24 . The unit of  claim 22 , wherein the first Josephson junction is centrally arranged in the center superconductor. 
     
     
         25 . The unit of  claim 16 , wherein the center superconductor has a linear or curved shape. 
     
     
         26 . The unit of  claim 1 , further comprising at least one 3D cavity, and wherein the dielectric substrate with the at least one superconducting qubit is provided in the at least one 3D cavity. 
     
     
         27 . A quantum computer comprising at least one quantum processing unit according to any one of  claims 1  to  26  and a control unit configured to perform computing operations by using the at least one quantum processing unit.