Download Semenov

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.
Chernogolovka, Oct. 12, 2009
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Clock Frequency of Modern Semiconductor Gates and
Circuits Could Be rather High
(There is no dramatic advantage in speed)
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The leakage (or static power consumption) is now responsible
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less than 10% of
total power dissipation
Irreversibility is the major dissipation factor
of Modern CMOS gates
Vb
Vb
EC  C  Vb 2 / 2
C
C
For a typical parasitic capacitance C (~ 10 fF) and bias voltage Vb (~1V)
recharging energy EC is about 5.10-15J
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.
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Theoretically an AC Multiphase Bias Would Allow a Lower
Power Dissipation
Vb
Time
Vb
Vb
Vb
C
C
However, for any (semiconductor or
superconductor) electronics
a multiphase AC bias
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is an engineering
nightmare!
C
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Logic Reversibility and Thermodynamics Set Limitations
on Energy Dissipation
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: kBTln2
(~4 10-23 J at T=4.2 K)
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
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Josephson Junction Technology Is the Best Candidate
for a Reversible Computing
-No energy dissipation in
superconducting state;
-Very convenient and accurate
energy potential:
E()=IC0cos();
-Developed technology: CAD
tools, fabrication, measurement.
K.K. Likharev, “Classical and quantum limitations on energy
consumption in computation,” Int. J. Theor. Phys., vol. 21, p. 311, 1982.
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Our First Try: Externally (AC)
Clocked Parametric Quantrons
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.
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.
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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 ~ 0.75) 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)
U ( ,  )  (  c ) 2 (  e ) 2 
  2 cos  cos  l  l (1  m)
 

 0 I c / 2π 
l
l

  1   2
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.
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Evolution of the Ongoing Project
1.
2.
3.
4.
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
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.
Fortunately we found that our nSQUID based circuits allow a
straightforward extension for quantum mode of operation.
In this report we present operational nSQUID circuits operating in a
classical mode with extremely low energy dissipation that might be
below thermodynamic threshold kBTln2. In other words, we are
transferring a QC approach to conventional electronics!
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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..
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An Intermediate step:
a String of Uncoupled
nSQUIDs
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.
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Comparison of Data presentations
in RSFQ and nSQUID Circuits
RSFQ
nSQUIDs
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.
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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.
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Schematics and Layouts of nSQUIDs (type c) with
Galvanic Coupling
0.01 mA
Year 2004
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Year 2007-08
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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.
20
2 Shift Registers
Voltage Source
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.
Dummy
cells
2 SQIFs (mA-meters)
Two stand-alone cells (nSQUID and
SQIF) are used for calibration.
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Two Shift Registers with a Common Clock Ring
Target critical current
density jc=30 A/cm2;
Pitch – 170 mm,
Each register contains 8
nSQUIDs;
Reading of data is
provided by DC
SQUIDs. (Coupling
factor with the nSQUID
is about 3 %.)
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N 0 generator
Josephson vortices
are “injected” into
the clock ring by
applying a
corresponding
magnetic flux to
one of ring
inductances.
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Data Input/Output
and Readout SQUID
Differential phase of nSQUID is
measured by a readout SQUID.
(Effective coupling ~3%)
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Superconductor (SQIF Based) micro Ampere-meter
with a low crosstalk
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Measurement of Bias Current I.
SQIF
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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
Chernogolovka,
range
0.05 GHzOct.
to 12,
7.12009
GHz
3 vortices in the clock loop.
Frequency range 6.1 GHz to 9.1 GHz
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Measurements of Energy Dissipation
I j  Ic  sin(2π  f  t )
E  V  I  Period
Eth  k BT ln 2
I th  (ln 2 /  0 )  k BTemp
1 / Period  (1 /  0 )  V At Temp=4.2 K
Ith=0.02mA
E  0  I
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Measurement of Bias Current II.
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Discussion of Results
• We measured that two shift registers operate at bias
current as low as ~0.14 mA. It means one shift register
consumes ~0.07 mA or 3.5 x kBTln2!
• This figure is still above 0.02 mA thermodynamic
threshold. But scaling of power dissipated in best CMOS
gates (about 1.7.106 kBTln2) 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
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computing.
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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)
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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.
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Prospective Primitive Cells
Two shift registers with
opposite direction of data
transfer (a, b),
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Similar cell but with one dummy
register (a), memory or delay cell
(c).
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2/3 Majority Gate
The logic function is defined by interactions of
inputs/outputs of the shift registers
The gates
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Composite XOR Gate
Calculation of XOR(A,B)
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Erasure of B
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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 =>
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The Simplest
Quantum Experiment
“Natural” z (or q) rotation
CL/Q
CL/Q
If the effective qubit parameters (in particular DU~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!
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nSQUID Circuits
Could be Used
as Flying Qubits
(old slide)
Three first devices that could be useful for any quantum computer
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nSQUID Circuits Could be Used
as Flying Qubits II (old slide)
Another 3 important
devices utilizing Flying
Qubit approach
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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
f (or XY) rotation. The rotation angle is proportional to the “area” under the interaction energy:


DE
dt . Note that the area is reversely proportional to domains speed.

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Possible Structure of
nSQUID Based Quantum Computer
Vertical arrows note two input quantum gates (rotations). Due to
inherent reversibility Inputs and Outputs are interchangeable.
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