1. Chernogolovka, Oct. 12, 2009Vasili.Semenov@StonyBrook.edu1 Reversible Computing with nSQUID Arrays Vasili K. Semenov, Jie Ren, Yuri Polyakov, Dmitri V. Averin Department of Physics and Astronomy Stony Brook University (SUNY) This work was supported in part by the National Security Agency (NSA) under Army Research Office (ARO) contract number W911NF-06-1-217 and by JST/CREST.

2. Chernogolovka, Oct. 12, 2009Vasili.Semenov@StonyBrook.edu2 Clock Frequency of Modern Semiconductor Gates and Circuits Could Be rather High (There is no dramatic advantage in speed)

3. Chernogolovka, Oct. 12, 2009Vasili.Semenov@StonyBrook.edu3 The leakage (or static power consumption) is now responsible for less than 10% of total power dissipation

4. Chernogolovka, Oct. 12, 2009Vasili.Semenov@StonyBrook.edu4 Irreversibility is the major dissipation factor of Modern CMOS gates Vb C C For a typical parasitic capacitance C (~ 10 fF) and bias voltage Vb (~1V) recharging energy E C is about 5. 10 -15 J Total powers (will be) burned, for example, by supercomputers “Dawn” and “Sequoia” are 1.13 and 6.6 mega Watts. At a realistically modest electricity rate (10 cents per kW x hour) these figures lead to over $1,000,000 and $6,000,000 annual energy costs.

5. Chernogolovka, Oct. 12, 2009Vasili.Semenov@StonyBrook.edu5 Theoretically an AC Multiphase Bias Would Allow a Lower Power Dissipation Vb C C Time Vb C However, for any (semiconductor or superconductor) electronics a multiphase AC bias is an engineering nightmare!

6. Chernogolovka, Oct. 12, 2009Vasili.Semenov@StonyBrook.edu6 Logic Reversibility and Thermodynamics Set Limitations on Energy Dissipation R. Landauer, “Irreversibility and heat generation in the computing process,” IBM J. of Res. and Devel., vol. 3, pp. 183-191, 1961. C. Bennett, “Logical reversibility of computation”, IBM J. of Res. and Devel., vol. 17, p. 525, 1973 Only erasure of the information costs energy [R. Landauer]. This conclusion leads to the concept of logically reversible computation which avoids erasure of the information [C. Bennett]. Our real goal is to experimentally cross thermodynamic threshold for energy dissipation per logic operation: k B Tln2 (~4  10 -23 J at T=4.2 K)

7. Chernogolovka, Oct. 12, 2009Vasili.Semenov@StonyBrook.edu7 Josephson Junction Technology Is the Best Candidate for a Reversible Computing K.K. Likharev, “Classical and quantum limitations on energy consumption in computation,” Int. J. Theor. Phys., vol. 21, p. 311, 1982. -No energy dissipation in superconducting state; -Very convenient and accurate energy potential: E(  )=I C  0  cos(  ); -Developed technology: CAD tools, fabrication, measurement.

8. Chernogolovka, Oct. 12, 2009Vasili.Semenov@StonyBrook.edu8 Our First Try: Externally (AC) Clocked Parametric Quantrons K.K. Likharev, S.V. Rylov, and V.K. Semenov, Reversible conveyer computation in arrays of parametric quantrons, IEEE Trans. on Magn., vol. 21, pp. 947-950, March 1985. The energy flow in and out of a quantron through AC bias lines is about four order of magnitude larger than the proposed energy dissipation. Unexceptionally high energy dissipation in AC power lines.

9. Chernogolovka, Oct. 12, 2009Vasili.Semenov@StonyBrook.edu9 nSQUID is the New Basic Gate of DC-Biased Reversible JJ Circuits The cell is a symmetric 2-junction SQUID (Ic1=Ic2=Ic; L1=L2=L) with a negative mutual coupling (m=M/L ~  ) between the SQUID arms. (V.K. Semenov, G.V. Danilov, and D.V. Averin, “Negative-inductance SQUID as the basic element of reversible Josephson-junction circuits”, IEEE Trans. Appl. Supercond., vol. 13, pp. 938-943, June 2003) Large effective inductance l + for circulating current allows 2 stable states at negative cos(   , while small effective inductance l - for bias current provides a smooth (quasi-linear) evolution of   with time.

10. Chernogolovka, Oct. 12, 2009Vasili.Semenov@StonyBrook.edu10 Evolution of the Ongoing Project 1.Initially we have been asked to develop support circuitry for superconducting qubits. The main goal was to reduce the energy dissipation as much as possible. Physically and logically reversible circuits are definitely the best candidates for such ultimate reduction of power 2.Rather soon we discovered that experimental works with superconducting qubits is limited by one or two physical qubits. In particular, the result of one quantum operation can not be used as the input for the other operation. As a result, we have been “forced” to suggest any QC architecture simply to start the development of classical circuitry supporting this architecture. 3.Fortunately we found that our nSQUID based circuits allow a straightforward extension for quantum mode of operation. 4.In this report we present operational nSQUID circuits operating in a classical mode with extremely low energy dissipation that might be below thermodynamic threshold k B Tln2. In other words, we are transferring a QC approach to conventional electronics!

11. Chernogolovka, Oct. 12, 2009Vasili.Semenov@StonyBrook.edu11 Our reversible circuits are “derived” from two known components: nSQUID is a 2-junction SQUID (with a negative mutual coupling between the inductive arms and). (V.K. Semenov, G.V. Danilov, and D.V. Averin, IEEE Trans. Appl. Supercond., vol. 13, pp. 938-943, June 2003) Fluxons or Josephson vortices can freely move along long Josephson junctions with arbitrary speed V that depends only on initial and boundary conditions..

12. Chernogolovka, Oct. 12, 2009Vasili.Semenov@StonyBrook.edu12 The Final Step: a String of Mutually Coupled nSQUIDs Bi-stable flux domain behaves as a flux qubit but in contrast with conventional qubits it can freely move along the circuit. An Intermediate step: a String of Uncoupled nSQUIDs

13. Chernogolovka, Oct. 12, 2009Vasili.Semenov@StonyBrook.edu13 Comparison of Data presentations in RSFQ and nSQUID Circuits In RSFQ presentation logic data are coded by presence (“1”) absence (“0”) of Josephson vertices travelling along “a long Josephson junction”. Such presentation must be accompanied by a separate clock line with a uniform sequence of “clock” vertices. In nSQUID presentation data are sitting on the top of flying “clock” vortices. RSFQ nSQUIDs

14. Chernogolovka, Oct. 12, 2009Vasili.Semenov@StonyBrook.edu14 Dynamics of a Linear nSQUD Array (numerical simulations) There is a strong overlapping of bi-stable states of adjacent cells. At the selected 8-phase timing all cells are organized into bi-stable domains consisting of 3 to 4 cells and isolated by 5 to 4 mono-stable cells. Pictures illustrate the evolution of differential phase with time. The upper plot shows that domains occupy about 4 cells and move along the array with a constant speed (strictly proportional to the applied DC voltage). The lower plot shows evolutions of differential phases in 4 different nSQUIDs.

15. Chernogolovka, Oct. 12, 2009Vasili.Semenov@StonyBrook.edu15 Schematics and Layouts of nSQUIDs (type c) with Galvanic Coupling Year 2004 Year 2007-08 0.01 mA

16. Chernogolovka, Oct. 12, 2009Vasili.Semenov@StonyBrook.edu16 The Latest Design with 2 Reversible Shift Registers We run 8 revisions of 5 mm x 5 mm design with 2 nSQUID shift registers sharing a common clock ring. Each shift register contains 8 nSQUIDs, 2 readout SQUIDs and 2 inputs/outputs. Besides, the circuit contains “a magnetic bias” cell injecting into the clock ring 2 Josephson vortices (or 2  0  phase shift) and a voltage (power) source. The (bias) current flowing via the shift register is measured by a SQIF. Two stand-alone cells (nSQUID and SQIF) are used for calibration. 2 Shift RegistersVoltage Source 2020 2 SQIFs (  A-meters) Dummy cells

17. Chernogolovka, Oct. 12, 2009Vasili.Semenov@StonyBrook.edu17 Two Shift Registers with a Common Clock Ring Target critical current density jc=30 A/cm2; Pitch – 170  m, Each register contains 8 nSQUIDs; Reading of data is provided by DC SQUIDs. (Coupling factor with the nSQUID is about 3 %.)

18. Chernogolovka, Oct. 12, 2009Vasili.Semenov@StonyBrook.edu18 N  0 generator Josephson vortices are “injected” into the clock ring by applying a corresponding magnetic flux to one of ring inductances.

19. Chernogolovka, Oct. 12, 2009Vasili.Semenov@StonyBrook.edu19 Data Input/Output and Readout SQUID Differential phase of nSQUID is measured by a readout SQUID. (Effective coupling ~3%)

20. Chernogolovka, Oct. 12, 2009Vasili.Semenov@StonyBrook.edu20 Superconductor (SQIF Based) micro Ampere-meter with a low crosstalk

21. Chernogolovka, Oct. 12, 2009Vasili.Semenov@StonyBrook.edu21 Measurement of Bias Current I. SQIF

22. Chernogolovka, Oct. 12, 2009Vasili.Semenov@StonyBrook.edu22 Operation of Shift Registers Digitization of analog input magnetic flux and transfer it on about 2 mm distance, where the digitized signal is measured by a dc SQUID. Legends show clock frequencies in GHz. 2 vortices in the clock loop. Frequency range 0.05 GHz to 7.1 GHz 3 vortices in the clock loop. Frequency range 6.1 GHz to 9.1 GHz

23. Chernogolovka, Oct. 12, 2009Vasili.Semenov@StonyBrook.edu23 Measurements of Energy Dissipation At Temp=4.2 K I th =0.02  A

24. Chernogolovka, Oct. 12, 2009Vasili.Semenov@StonyBrook.edu24 Measurement of Bias Current II.

25. Chernogolovka, Oct. 12, 2009Vasili.Semenov@StonyBrook.edu25 Discussion of Results We measured that two shift registers operate at bias current as low as ~0.14  A. It means one shift register consumes ~0.07  A or 3.5 x k B Tln2! This figure is still above 0.02  A thermodynamic threshold. But scaling of power dissipated in best CMOS gates (about 1.7. 10 6 k B Tln2) converts, say, 1 mega Watt of energy to less than 3 Watts at room temperature or less than 0.1 Watt at helium temperature! It is possible to say that this remarkable result is achieved simply by removing the quantum mechanics from our prospective quantum computer architecture suggested in the framework of this project. In other words, we experimentally illustrated potential advantages of quantum computing.

26. Chernogolovka, Oct. 12, 2009Vasili.Semenov@StonyBrook.edu26 Mutual Magnetic Shielding of Cells (Qubits) Is Vitally Important Two layer circuits (typical for QC experiments) Three layer circuits (our first nSQUID circuits) Four layer circuits (our recent nSQUID circuits)

27. Chernogolovka, Oct. 12, 2009Vasili.Semenov@StonyBrook.edu27 Superconducting Quantum Interference Filter (SQIF) Could be Used for an Active Compensation of Residual Magnetic Field (This part of the project is supported by ONR) On SQIF chip being mounted in the vicinity of the investigated circuit allows to measure the residual magnetic field. A corresponding feedback coil could be used to set the residual field to zero. In fact, now we can easily see a single Abrikosov vortex frozen in the integrated circuit.

28. Chernogolovka, Oct. 12, 2009Vasili.Semenov@StonyBrook.edu28 Prospective Primitive Cells Two shift registers with opposite direction of data transfer (a, b), Similar cell but with one dummy register (a), memory or delay cell (c).

29. Chernogolovka, Oct. 12, 2009Vasili.Semenov@StonyBrook.edu29 2/3 Majority Gate The logic function is defined by interactions of inputs/outputs of the shift registers The gates

30. Chernogolovka, Oct. 12, 2009Vasili.Semenov@StonyBrook.edu30 Composite XOR Gate Calculation of XOR(A,B) Erasure of B

31. Chernogolovka, Oct. 12, 2009Vasili.Semenov@StonyBrook.edu31 A Prospective more complex nSQUID Circuit Operating in a Classical Mode The functions are programmed by the presence, sign, and strength of corresponding links. Notations =>

32. Chernogolovka, Oct. 12, 2009Vasili.Semenov@StonyBrook.edu32 The Simplest Quantum Experiment CL/Q “Natural” z (or  ) rotation If the effective qubit parameters (in particular  U~3 GHz) are similar to those in “typical” modern experiments then the total propagation delay along the quantum fraction of the nSQUID array should be about 300 ps. It means that that 1 ns decoherence time would be large for the experiment!

33. Chernogolovka, Oct. 12, 2009Vasili.Semenov@StonyBrook.edu33 nSQUID Circuits Could be Used as Flying Qubits (old slide) Three first devices that could be useful for any quantum computer

34. Chernogolovka, Oct. 12, 2009Vasili.Semenov@StonyBrook.edu34 nSQUID Circuits Could be Used as Flying Qubits II (old slide) Another 3 important devices utilizing Flying Qubit approach

35. Chernogolovka, Oct. 12, 2009Vasili.Semenov@StonyBrook.edu35 Two Input Gate Domains motion is only slightly distorted by inductive coupling between nSQUID array. However the coupling create a temporal misbalance of the energy profiles. This effect could be described as  (or XY) rotation. The rotation angle is proportional to the “area” under the interaction energy:. Note that the area is reversely proportional to domains speed.

36. Chernogolovka, Oct. 12, 2009Vasili.Semenov@StonyBrook.edu36 Possible Structure of nSQUID Based Quantum Computer Vertical arrows note two input quantum gates (rotations). Due to inherent reversibility Inputs and Outputs are interchangeable.