Reducing spontaneous emission in circuit quantum electrodynamics by a combined readout and filter technique

A method of providing a superconductor circuit, the method comprising:

• providing a delta (Δ) circuit comprising a first node connecting a Purcell capacitor (CP) to a qubit coupling capacitor (Cq), a second node connecting the Purcell capacitor (CP) to a readout coupling capacitor (Cc), and a third node connecting the qubit coupling capacitor (Cq) to the readout coupling capacitor (Cc);
• providing a qubit connected to the first node, wherein the qubit has a qubit frequency;
• and
• forming a readout resonator connected to the third node, wherein the readout resonator combines with the Purcell capacitor (CP) to form a filter;
• wherein the second node is configured for connection to an external environment;
• wherein capacitance of the Purcell capacitor (CP) is determined as a factor of the qubit frequency of the qubit, such that the capacitance of the Purcell capacitor (CP) blocks emissions of the qubit at the qubit frequency to the external environment;
• and
• wherein the capacitance of the Purcell capacitor (CP) is set to cause destructive interference, between a first path containing the Purcell capacitor (CP) and a second path containing both the qubit coupling capacitor (Cq) and the readout coupling capacitor (Cc), at the qubit frequency in order to block the emissions of the qubit at the qubit frequency to the external environment.

A superconductor circuit comprising:

• a qubit connected to a qubit coupling capacitor (C′q), wherein the qubit has a qubit frequency;
• a combination readout resonator and filter including a Purcell capacitor (C′P), the Purcell capacitor (C′P) being connected to the qubit coupling capacitor (C′q);
• a readout coupling capacitor (C′c) connected to the Purcell capacitor (C′P) and the qubit coupling capacitor (C′q), the readout coupling capacitor (C′c) configured for connection to an external environment;
• wherein capacitance of the Purcell capacitor (C′P) is determined as a factor of the qubit frequency of the qubit, such that the capacitance of the Purcell capacitor (C′P) blocks emissions of the qubit at the qubit frequency to the external environment;
• and
• wherein the capacitance of the Purcell capacitor (C′P) is set to short the combination readout resonator and filter including the Purcell capacitor (C′P) to ground at the qubit frequency in order to block the emissions of the qubit at the qubit frequency to the external environment.

A method for a superconductor circuit, the method comprising:

• providing a qubit connected to a qubit coupling capacitor (C′q), wherein the qubit has a qubit frequency;
• forming a combination readout resonator and filter including a Purcell capacitor (C′P), the Purcell capacitor (C′P) being connected to the qubit coupling capacitor (C′q);
• and
• providing a readout coupling capacitor (C′c) connected to the Purcell capacitor (C′P) and the qubit coupling capacitor (C′q), the readout coupling capacitor (C′c) configured for connection to an external environment;
• wherein capacitance of the Purcell capacitor (C′P) is determined as a factor of the qubit frequency of the qubit, such that the capacitance of the Purcell capacitor (C′P) blocks emissions of the qubit at the qubit frequency to the external environment;
• and
• wherein the capacitance of the Purcell capacitor (C′P) is set to short the combination readout resonator and filter to ground at the qubit frequency in order to block the emissions of the qubit at the qubit frequency to the external environment.

A superconductor circuit comprising:

• a delta (Δ) circuit comprising a first node connecting a Purcell capacitor (CP) to a qubit coupling capacitor (Cq), a second node connecting the Purcell capacitor (CP) to a readout coupling capacitor (Cc), and a third node connecting the qubit coupling capacitor (Cq) to the readout coupling capacitor (Cc);
• a qubit connected to the first node, wherein the qubit has a qubit frequency;
• a readout resonator connected to the third node, wherein the readout resonator combines with the Purcell capacitor (CP) to form a filter;
• and
• the second node configured for connection to the external environment;
• wherein the delta circuit is equivalent to a Y circuit;
• wherein the Y circuit includes a qubit coupling capacitor (C′q), a Purcell capacitor (C′P), and a readout coupling capacitor (C′c);
• wherein capacitances of the Purcell capacitor (CP), the qubit coupling capacitor (Cq), and the readout coupling capacitor (Cc) are determined by a Δ-Y transformation as follows:
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