Reciprocal quantum logic based circuits for an A-and-not-B gate

1. A circuit for an A-and-not-B gate comprising:

an output terminal;

a first input terminal for receiving a first set of single flux quantum (SFQ) pulses;

a second input terminal for receiving a second set of SFQ pulses;

a first Josephson junction (JJ) coupled to receive the first set of SFQ pulses; and

a second JJ coupled to the first JJ, wherein the second JJ is configured to negatively bias the first JJ such that the circuit is configured to not pass the first set of SFQ pulses to the output terminal only when the second set of SFQ pulses have arrived at the second input terminal prior to an arrival of the first set of SFQ pulses at the first input terminal.

2. The circuit of claim 1 , wherein the first JJ is coupled to the output terminal, and wherein the circuit further comprises a first inductor coupled between the first input terminal and the output terminal.

3. The circuit of claim 2 , wherein the circuit further comprises a third JJ coupled to a first node, and wherein the circuit further comprises a second inductor coupled between the second input terminal and the first node.

4. The circuit of claim 3 further comprising a third inductor coupled to a second node, wherein the second node is further coupled to the second JJ and a fourth inductor.

5. The circuit of claim 4 , wherein the fourth inductor is coupled to receive both an alternating current bias and a direct current bias via a transformer.

6. The circuit of claim 5 further comprising a fifth inductor coupled between the output terminal and a ground terminal and a sixth inductor coupled between the second node and the ground terminal.

7. The circuit of claim 2 , wherein the second JJ is directly coupled to the output terminal resulting in a stacked arrangement of the first JJ and the second JJ.

8. A circuit for an A-and-not-B gate comprising:

an output terminal;

a first input terminal for receiving a first set of single flux quantum (SFQ) pulses;

a second input terminal for receiving a second set of SFQ pulses;

a first Josephson junction (JJ) coupled to receive the first set of SFQ pulses, wherein the first JJ having a first end coupled to a first node and having a second end coupled to a ground terminal; and

a second JJ having a first end directly coupled to the output terminal, wherein the second JJ is configured to negatively bias the first JJ such that the circuit is configured to not pass the first set of SFQ pulses to the output terminal only when the second set of SFQ pulses have arrived at the second input terminal prior to an arrival of the first set of SFQ pulses at the first input terminal.

9. The circuit of claim 8 further comprising a first inductor coupled between the first input terminal and the output terminal.

10. The circuit of claim 9 , wherein the circuit further comprises a third JJ coupled to a first node, and wherein the circuit further comprises a second inductor coupled between the second input terminal and the first node.

11. The circuit of claim 10 further comprising a third inductor coupled to a second node, wherein the second node is further coupled to the second JJ and a fourth inductor.

12. The circuit of claim 11 , wherein the fourth inductor is coupled to receive both an alternating current bias and a direct current bias via a transformer.

13. The circuit of claim 12 further comprising a fifth inductor coupled between the output terminal and a ground terminal and a sixth inductor coupled between the second node and the ground terminal.

14. The circuit of claim 13 , wherein the sixth inductor is coupled to receive an additional direct current bias.

15. A method of operating a circuit for an A-and-not-B gate, wherein the circuit including an output terminal, the method comprising:

receiving a first set of single flux quantum (SFQ) pulses via a first input terminal;

receiving a second set of SFQ pulses via a second input terminal; and

passing the first set of SFQ pulses to the output terminal in response to a triggering of a first Josephson junction (JJ), coupled to the output terminal, unless negative biasing of the first JJ because of triggering of a second JJ coupled to the first JJ prevents the first JJ from triggering, wherein the triggering of the second JJ is caused at least by an arrival of the second set of SFQ pulses at the second input terminal prior to an arrival of the first set of SFQ pulses at the first input terminal.

16. The method of claim 15 , wherein the circuit further comprises a first inductor coupled between the first input terminal and the output terminal.

17. The method of claim 16 , wherein the circuit further comprises a third JJ coupled to a first node, and wherein the circuit further comprises a second inductor coupled between the second input terminal and the first node.

18. The method of claim 17 , wherein the circuit further comprises a third inductor coupled to a second node, wherein the second node is further coupled to the second JJ and a fourth inductor.

19. The method of claim 18 , wherein the fourth inductor is coupled to receive both an alternating current bias and a direct current bias via a transformer.

20. The method of claim 19 , wherein the circuit further comprises a fifth inductor coupled between the output terminal and the ground terminal and a sixth inductor coupled between the second node and the ground terminal.