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Journal ArticleDOI

A cryogen-free dilution refrigerator based Josephson qubit measurement system

30 Mar 2012-Review of Scientific Instruments (American Institute of Physics)-Vol. 83, Iss: 3, pp 033907
TL;DR: A small-signal measurement system on cryogen-free dilution refrigerator which is suitable for superconducting qubit studies and shows that the measurements of Josephson junction's switching current distribution, quantum coherent Rabi oscillation and Ramsey interference of the superconducted qubit can be successfully performed.
Abstract: We develop a small-signal measurement system on cryogen-free dilution refrigerator which is suitable for superconducting qubit studies. Cryogen-free refrigerators have several advantages such as less manpower for system operation and large sample space for experiment, but concern remains about whether the noise introduced by the coldhead can be made sufficiently low. In this work, we demonstrate some effective approaches of acoustic isolation to reduce the noise impact. The electronic circuit that includes the current, voltage, and microwave lines for qubit coherent state measurement is described. For the current and voltage lines designed to have a low pass of dc-100 kHz, we show that the measurements of Josephson junction's switching current distribution with a width down to 1 nA, and quantum coherent Rabi oscillation and Ramsey interference of the superconducting qubit can be successfully performed.

Summary (2 min read)

A cryogen-free dilution refrigerator based Josephson qubit measurement system

  • The authors develop a small-signal measurement system on cryogen-free dilution refrigerator which is suitable for superconducting qubit studies.
  • The authors demonstrate some effective approaches of acoustic isolation to reduce the noise impact.
  • Experimental studies of superconducting qubits require mK temperature environment with extremely low electromagnetic (EM) noise level, so that coherent quantum states of qubits can be prepared, maintained, and controlled and their delicate coherent evolution can be monitored and measured.
  • For these dry systems, the above mentioned disadvantages are avoided.
  • A main concern about using pulse-tube based dilution refrigerators for sensitive small signal measurements is whether noises (vibration, electrical, and acoustic) introduced by the coldhead is sufficiently low.

II. MECHANICAL CONSTRUCTION

  • Figure 1(a) shows the front view of their system with the DR200 refrigerator installed on an aluminum-alloy frame near the center.
  • This setup proves significantly reducing the vibrations from the turbo pump.
  • The overall arrangements of the system are schematically shown and further explained in Fig.
  • The accelerometer is manufactured by Wilcoxon Research (Model 731) and its sensor is placed on the top of the refrigerator, as indicated by a thick red arrow in Fig. 1(b), which measures the vertical acceleration of the system.
  • Hz, which the authors call acceleration spectral density.

III. ELECTRONIC SETUP

  • The electrical measurement circuit includes three types of lines:.
  • These copper powder filters are mounted next to the sample platform which is at the mixing chamber temperature.
  • Low-noise preamplifiers are used in the voltage lines of the detector SQUIDs.
  • All coaxial cables and attenuators are thermally anchored to various temperature stages (namely, on the 70 K, 4 K, still, 100 mK, and mixing chamber plates).
  • As can be seen in Figs. 1(a) and 1(b), a smaller EM shielding box (Faraday cage) made of cold-rolled steel sheet is placed near the top of the fridge, in which EMI filters and preamplifiers are located.

IV. QUANTUM COHERENT-STATE MEASUREMENTS

  • As an initial characterization of the electronic system, the authors measured the switching current distribution P(I) of a Nb dc-SQUID with the loop inductance much smaller than the Josephson inductance of the junctions so that the SQUID behaves as a single junction with critical current Ic tunable by applying a magnetic field.
  • The flux biased phase qubit had similar layout and parameters as that described in Ref. 11 and was coupled to an asymmetric dc-SQUID to readout its quantum state.
  • For a given E10, a short resonant microwave pulse of variable length with frequency f10 = E10/h was applied, which coherently transfers population between the ground state and the first excited state.
  • Data obtained with microwave frequency of about 16 GHz are shown in Fig. 7(a) as symbols.
  • The linear dependence of the Ramsey frequency on detuning can be seen in Fig. 8(b).

ACKNOWLEDGMENTS

  • The authors are grateful to Junyun Li of Oxford Instruments Shanghai Office for his continuous support in this work and to H. J. Gao, L. Shan, and C. Ren for their kind help during vibration measurements.
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A cryogen-free dilution refrigerator based Josephson qubit measurement system
Ye Tian, H. F. Yu, H. Deng, G. M. Xue, D. T. Liu, Y. F. Ren, G. H. Chen, D. N. Zheng, X. N. Jing, Li Lu, S. P.
Zhao, and Siyuan Han
Citation: Review of Scientific Instruments 83, 033907 (2012); doi: 10.1063/1.3698001
View online: http://dx.doi.org/10.1063/1.3698001
View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/83/3?ver=pdfcov
Published by the AIP Publishing
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REVIEW OF SCIENTIFIC INSTRUMENTS 83, 033907 (2012)
A cryogen-free dilution refrigerator based Josephson qubit
measurement system
Ye Tian,
1
H. F. Yu,
1
H. Deng,
1
G. M. Xue,
1
D. T. Liu,
1
Y. F. Ren,
1
G. H. Chen,
1
D. N. Zheng,
1
X. N. Jing,
1
Li Lu,
1
S. P. Zhao,
1
and Siyuan Han
2
1
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of
Sciences, Beijing 100190, China
2
Department of Physics and Astronomy, University of Kansas, Lawrence, Kansas 66045, USA
(Received 14 January 2012; accepted 9 March 2012; published online 30 March 2012)
We develop a small-signal measurement system on cryogen-free dilution refrigerator which is suitable
for superconducting qubit studies. Cryogen-free refrigerators have several advantages such as less
manpower for system operation and large sample space for experiment, but concern remains about
whether the noise introduced by the coldhead can be made sufficiently low. In this work, we demon-
strate some effective approaches of acoustic isolation to reduce the noise impact. The electronic
circuit that includes the current, voltage, and microwave lines for qubit coherent state measurement is
described. For the current and voltage lines designed to have a low pass of dc-100 kHz, we show that
the measurements of Josephson junction’s switching current distribution with a width down to 1 nA,
and quantum coherent Rabi oscillation and Ramsey interference of the superconducting qubit can be
successfully performed. © 2012 American Institute of Physics.[http://dx.doi.org/10.1063/1.3698001]
I. INTRODUCTION
Experimental studies of superconducting qubits require
mK temperature environment with extremely low electro-
magnetic (EM) noise level, so that coherent quantum states
of qubits can be prepared, maintained, and controlled and
their delicate coherent evolution can be monitored and
measured.
14
So far, most of these experiments are performed
using dilution refrigerators that use liquid He
4
as cryogen
for the first-stage cooling. However, for such traditional wet
systems, there are several obvious disadvantages. For in-
stance, even “low-loss” Dewars require refilling every few
days, therefore it is not only more expensive but also re-
quires more manpower, infrastructure, and time to conduct
experiments. Also, the need for a narrow neck in the helium
Dewar to keep the boil-off to an acceptable level means that
the space available for experimental wiring and other exper-
imental services is limited. Moreover, the cold vacuum seal
also means hermetically sealed and cryogenically compatible
wiring feedthroughs are required in addition to the room tem-
perature fittings.
There has been much recent interest in the dry dilu-
tion refrigerators which use pulse-tube coolers to provide the
first-stage cooling instead of the liquid cryogen. For these
dry systems, the above mentioned disadvantages are avoided.
Namely, they need much less manpower to operate and have
a much larger sample space. The smaller overall size of the
systems is also convenient for magnetic shielding and other
lab-space arrangements. In addition, they do not rely on liq-
uid He
4
cryogen which is becoming a more expensive natural
resource.
Presently, there are still less users for the dry system
than those for the wet system. A main concern about using
pulse-tube based dilution refrigerators for sensitive small sig-
nal measurements is whether noises (vibration, electrical, and
acoustic) introduced by the coldhead is sufficiently low. In
this paper, we describe the design, construction, and charac-
terization of a system built on an Oxford DR200 cryogen-
free dilution refrigerator suitable for experiments that are ex-
tremely sensitive to their electromagnetic environments. The
paper is organized as follows. We first describe the mechan-
ical constructions which reduce the acoustic vibrations to a
very low level. We then present the electronic measurement
setup that includes various filtering, attenuation, and amplifi-
cation for different parts of the qubit quantum state prepara-
tion and measurement. Finally, we show that the system is
adequate for studying coherent quantum dynamics of su-
perconducting qubits by demonstrating Rabi oscillation and
Ramsey fringe in an Al superconducting phase qubit.
II. MECHANICAL CONSTRUCTION
Figure 1(a) shows the front view of our system with
the DR200 refrigerator installed on an aluminum-alloy frame
near the center. The refrigerator can reach its base tempera-
ture of 8 mK and temperatures below 20 mK, respectively,
before and after all electronic components and measurement
lines described below are installed. It has a prolonged ver-
sion compared to the Oxford’s standard design and has a large
sample space of 25 cm in diameter and 28 cm in height. To
reduce vibrations coupled from the floor, the aluminum-alloy
frame is placed on four 0.8 cm thick rubber stands. The re-
frigerator can be attached to the frame via an air-spring sys-
tem to provide further vibration isolation. The turbo pump,
originally placed on the t op of the refrigerator, is moved to
the other side of the wall in the next room and is connected
to the fridge by a stainless steel pipe and a 1 m long bellows
as can be seen in Fig. 1(b). Both the pipe and the bellows
have the same diameter as that of the inlet of the turbo pump.
This setup proves significantly reducing the vibrations from
the turbo pump. Furthermore, the rotary valve is separated
0034-6748/2012/83(3)/033907/5/$30.00 © 2012 American Institute of Physics83, 033907-1
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033907-2 Tian
et al.
Rev. Sci. Instrum. 83, 033907 (2012)
FIG. 1. Photos of the cryogen-free DR200 dilution refrigerator system suitable for qubit quantum-state measurements. (a) Front view. (b) Top view. The fridge
is installed on an aluminum-alloy frame with double acoustic isolation from the ground using rubber stands and air springs. The turbo pump and rotary valve are
mechanically decoupled from the fridge. The fridge is also electrically isolated from the pumps, the control instruments, and the gas lines. The thick red arrow
in (b) indicates where an accelerometer sensor is placed for vibration measurement.
from the insert and securely attached to the wall, as can also
be seen in Fig. 1(b). Soft plastic hoses are used for the connec-
tions to the DR unit wherever needed. Other equipments, in-
cluding the forepump, the compressor (dry pump), the pulse-
tube refrigerator (PTR) compressor, and a water cooler are all
located in the next room. The overall arrangements of the sys-
tem are schematically shown and further explained in Fig. 2.
Vibration levels of the system are measured using an ac-
celerometer in three cases: Namely, the whole system is off,
only the turbo pump is on, and both the turbo pump and the
PTR are on. The results are shown in Fig. 3. The accelerom-
eter is manufactured by Wilcoxon Research (Model 731) and
its sensor is placed on the top of the refrigerator, as indicated
by a thick red arrow in Fig. 1(b), which measures the verti-
cal acceleration of the system. The sensor is connected to a
preamplifier with a 450-Hz low-pass filter. The output volt-
age signal of the preamplifier (1 kV corresponds to 9.8 m/s
2
)
FIG. 2. Schematic overall arrangement of the cryogen-free DR200 dilution
refrigerator measurement system. (1) Aluminum-alloy frame; (2) PTR cold-
head; (3) and (4) pumping line; (5) bellows assembly; (6) turbo pump; (7)
rotary valve; (8) compressor; (9) forepump; (10) LN2 coldtrap; (11) PTR
compressor; (12) and (13) electrically isolated gas line and connecters; (14)
rubber stands; (15) air-spring system (optional); (16) sand bag; (17) trilayer
μ-metal shielding. Thin blue lines represent the gas lines.
is then measured by a spectrum analyzer. In its power spec-
tral density mode, we directly obtain the acceleration “power”
spectral density, which has the unit (m/s
2
)
2
/Hz, or the corre-
sponding data presented in unit (m/s
2
)/
Hz, which we call
acceleration spectral density. The velocity spectral density
shown in Fig. 3 in unit (m/s)/
Hz are the latter data divided
by ω and averaged over 400 measurements in each case.
The baseline in Fig. 3 (bottom line) decreases mono-
tonically from 10
6
(m/s)/
Hz at low frequency (<5Hz)
to 10
9
(m/s)/
Hz at high frequency (>200 Hz), which
is comparable to the data recorded in several scanning
tunneling microscopy (STM) labs around the world.
5
As
a result of the separation of the turbo pump from the
main body of the refrigerator, we see that the veloc-
ity spectral density increases only slightly when the turbo
FIG. 3. Velocity spectral density of the dilution refrigerator system measured
under three conditions: The whole system is off (bottom line), only the turbo
pump is on (middle line), and both the turbo pump and the PTR are on (top
line), respectively. See text for measurement details. Peaks at 50 Hz and its
harmonics and subharmonics are due to power line interference (not due to
mechanical vibrations).
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033907-3 Tian
et al.
Rev. Sci. Instrum. 83, 033907 (2012)
FIG. 4. Diagram of the electronic measurement system. Typical three kinds of the measurement lines are shown starting from the left side of the diagram:The
qubit flux bias and SQUID-detector current lines, the SQUID-detector voltage lines, and the microwave/fast-pulse lines.
pump is switched on (middle line). On the other hand, it
increases significantly, especially above about 100 Hz, when
the PTR is also running (top line). This is unavoidable since
the PTR is mechanically integrated to the body of the fridge.
At f > 200 Hz, the data are approximately two orders of
magnitude higher than the baseline. The results presented in
Sec. IV below show that this level of vibration has negligible
effect on the control and measurement of the coherent quan-
tum dynamics of superconducting phase qubits.
III. ELECTRONIC SETUP
The electrical measurement circuit includes three types
of lines: The current bias lines, the voltage sensing lines, and
the microwave/fast-pulse lines, which are shown schemat-
ically in Fig. 4. The current and voltage lines from room
temperature to low temperature, which are used for the
qubit flux bias or superconducting quantum interference
device (SQUID)-detector current bias and the SQUID-
detector voltage measurement, are composed of flexible coax-
ial cables, electromagnetic interference (EMI) filters, resis-
tance/capacitance (RC) filters, and copper powder filters
6, 7
down to the sample platform. Flexible coaxial cables man-
ufactured by GVL Cryoengineering with a bandwidth of dc
to 300 MHz are used. The cables have φ 0.65 mm CuNi outer
conductor, teflon dielectric, and central conductors made of
ultra-low-temperature-coefficient φ 0.1 mm brass Ms63 (used
above the 4 K plate) and of φ 0.1 mm superconducting NbTi
(used below the 4 K plate). EMI filters placed outside the
fridge at the room temperature are VLFX-470 (VLFX) low-
pass filters manufactured by MiniCircuits, which are used to
filtering out high frequency noises from room temperature
lines. The characteristic impedance of the coaxial filter VLFX
is 50 and the passing band of the filter is dc to 470 MHz
with attenuation greater than 40 dB between 2 and 20 GHz.
RC filters are inserted into the coaxial cables and are ther-
mally anchored to the 4 K plate. All RC filters have a 3 dB
cutoff frequency of 100 kHz. To reduce joule heating R (C) is
chosen to be 1 k (2040 pF) and 10 k (204 pF) for t he cur-
rent and voltage leads, respectively. The copper powder filters
are made following the technique developed by Lukashenko
and Ustinov.
7
Their 3 dB cutoff frequency is around 80 MHz
and has more than 60 dB attenuation at 1 GHz. Their typ-
ical characteristic and final appearance of these filters are
shown in Fig. 5 and the inset. These copper powder filters are
mounted next to the sample platform which is at the mixing
chamber temperature.
Low-noise preamplifiers are used in the voltage lines of
the detector SQUIDs. These preamplifiers, with a gain of
1000, are made using two “analog devices” AD624 instru-
mentation amplifiers (gains set to 10 and 100, respectively) in
series. The bandwidth of these preamps is 100 kHz and the
noise characteristic is shown in Fig. 6. Finally, the microwave
lines, shown schematically in Fig. 4, are composed of 2.2 mm
diameter semirigid coaxial cables manufactured by Keycom
with non-magnetic stainless steel inner/outer conductors with
MiniCircuits attenuators (frequency range 0–18 GHz) to in-
crease signal-to-noise ratio. The total attenuation coefficient
in each line is typically 40 dB.
FIG. 5. Typical attenuation versus frequency characteristic of the copper
powder filters. The attenuation at 120 MHz is about 3 dB, and is more than
60 dB above 1 GHz. The length of filter is 7 cm as is shown in the inset.
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033907-4 Tian
et al.
Rev. Sci. Instrum. 83, 033907 (2012)
FIG. 6. Noise characteristic of a voltage preamplifier with gain of 1000 made
from two AD624 instrumentation amplifiers in series. The noise spectrum
density is less than 10 nV rms/
Hz (refer to input) above 10 Hz up to
100 kHz (flat part above 1.6 kHz not shown). The inset shows the final as-
sembly (the longer one) together with that of an isolation amplifier with unity
gain (the shorter one).
All coaxial cables and attenuators are thermally anchored
to various temperature stages (namely, on the 70 K, 4 K, still,
100 mK, and mixing chamber plates). The thermal anchors for
the flexible coaxial cables are made by two copper plates with
a 3.5 cm section of coaxial cables clamped between them. As
can be seen in Figs. 1(a) and 1(b), a smaller EM shielding
box (Faraday cage) made of cold-rolled steel sheet is placed
near the top of the fridge, in which EMI filters and pream-
plifiers are located. A trilayer μ-metal magnetic shield, also
illustrated in Fig. 2, is used to reduce the ambient static field
to about 20 nT. The sample holder has twelve 50 coplanar
waveguides (CPWs) allowing signals with frequencies up to
18 GHz to pass through with minimal reflections. The fridge
is galvanically isolated from the vacuum pumps, the control
instruments, and gas lines so that the system can be electri-
cally connected to a dedicated ground post. We also use an
optical coupler in the control line to achieve galvanic isola-
tion between the refrigerator and the control rack (see Fig.
1). Our tests showed that this setup is adequate for measur-
ing coherent quantum dynamics of Josephson qubit circuits
as described in detail below.
IV. QUANTUM COHERENT-STATE MEASUREMENTS
In order to qualify our system for qubit experiments, we
chose to measure coherent dynamics of a superconducting
phase qubit, which is extremely sensitive to its EM environ-
ment. As an initial characterization of the electronic system,
we measured the switching current distribution P(I )ofaNb
dc-SQUID with the loop inductance much smaller than the
Josephson inductance of the junctions so that the SQUID be-
haves as a single junction with critical current I
c
tunable by
applying a magnetic field.
8
From the measured width σ of
P(I) versus temperature, we found that σ continuously de-
crease to as low as 4 nA at 20 mK by reducing I
c
and as low as
1 nA near 1 K due to phase diffusion
9, 10
indicating a current
noise level below 1 nA in our measurement circuit.
The flux biased phase qubit had similar layout and pa-
rameters as that described in Ref. 11 and was coupled to an
asymmetric dc-SQUID to readout its quantum state. A current
bias line was used to apply an external magnetic flux to the
qubit loop which controls the shape of the potential energy
landscape and the level separation E
10
between the ground
and first excited states of the qubit. For a given E
10
, a short res-
onant microwave pulse of variable length with frequency f
10
= E
10
/h was applied, which coherently transfers population
between the ground state and the first excited state. Conse-
quently, we observed Rabi oscillations by keeping the ampli-
tude of the microwave field constant while varying the dura-
tion of the modulation pulses. Data obtained with microwave
frequency of about 16 GHz are shown in Fig. 7(a) as symbols.
A simple fit to an exponentially damped sinusoidal function
yields a decay time of 70 ns. In Fig. 7(b), the Rabi frequency
versus microwave amplitude, which shows the expected linear
dependence, is displayed.
FIG. 7. (a) Rabi oscillation measured from an rf-SQUID type phase qubit made of Al Josephson junction (symbols). The applied microwave frequency is
16 GHz and a decay time of 70 ns is obtained from the exponentially damped sinusoidal oscillation fit (line). (b) Rabi frequency versus microwave amplitude
(symbols). The line is a guide to the eye.
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Cites methods from "A cryogen-free dilution refrigerato..."

  • ...Figure 4(d) shows the experimental PswðIÞ which is obtained using the conventional time-of-flight technique [43–45] with a constant current sweeping rate of 5 mA=s in a very well-filtered and shielded cryostat suitable for coherent quantum dynamics of Josephson qubits [45,46]....

    [...]

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1,132 citations

Journal ArticleDOI
TL;DR: For an underdamped junction in the quantum regime, \ensuremath{\Gamma} became independent of temperature at low temperatures with a value that, with no adjustable parameters, was in excellent agreement with predictions for macroscopic quantum tunneling at T=0.
Abstract: Experiments are described that demonstrate the quantum behavior of a macroscopic degree of freedom, namely the phase difference \ensuremath{\delta} across a current-biased Josephson tunnel junction. The behavior of \ensuremath{\delta} was deduced from measurements of the escape rate \ensuremath{\Gamma} of the junction from its zero-voltage state. The relevant parameters of the junction, that is, its critical current and shunting admittance, were determined in situ in the thermal regime from the dependence of \ensuremath{\Gamma} on bias current and from resonant activation in the presence of microwaves. It was found that the shunting capacitance was dominated by the self-capacitance of the junction while the shunting conductance was dominated by the bias circuitry. For an underdamped junction in the quantum regime, \ensuremath{\Gamma} became independent of temperature at low temperatures with a value that, with no adjustable parameters, was in excellent agreement with predictions for macroscopic quantum tunneling at T=0. When the critical current was reduced with a magnetic field so that the junction remained in the thermal regime at low temperatures, \ensuremath{\Gamma} followed the predictions of the thermal model, thereby showing the influence of extraneous noise to be negligible. In a further series of experiments, the existence of quantized energy levels in the potential well of the junction was demonstrated spectroscopically. The positions of the energy levels agreed quantitatively with quantum-mechanical predictions involving junction parameters measured in the thermal regime. The relative heights and widths of the resonances are in reasonable agreement with the predictions of a simple model.

455 citations

Journal ArticleDOI
30 Sep 2010-Nature
TL;DR: The operation of three coupled superconducting phase qubits are demonstrated and used to create and measure |GHZ〉 and |W〉 states and are shown to satisfy entanglement witnesses, confirming that they are indeed examples of three-qubitEntanglement and are not separable into mixtures of two-qubits.
Abstract: Quantum entanglement, in which the states of two or more particles are inextricably linked, is a key requirement for quantum computation. In superconducting devices, two-qubit entangled states have been used to implement simple quantum algorithms. The availability of three-qubit states, which can be entangled in two fundamentally different ways (the GHZ and W states), would be a significant advance because they should make it possible to perform error correction and infer scalability to the higher numbers of qubits needed for a practical quantum-information-processing device. Two groups now report the generation of three-qubit entanglement. John Martinis and colleagues create and measure both GHZ and W-type states. Leonardo DiCarlo and colleagues generate the GHZ state and demonstrate the first step of basic quantum error correction by encoding a logical qubit into a manifold of GHZ-like states using a repetition code. Quantum entanglement is one of the key resources required for quantum computation. In superconducting devices, two-qubit entangled states have been used to implement simple quantum algorithms, but three-qubit states, which can be entangled in two fundamentally different ways, have not been demonstrated. Here, however, three superconducting phase qubits have been used to create and measure these two entangled three-qubit states. Entanglement is one of the key resources required for quantum computation1, so the experimental creation and measurement of entangled states is of crucial importance for various physical implementations of quantum computers2. In superconducting devices3, two-qubit entangled states have been demonstrated and used to show violations of Bell’s inequality4 and to implement simple quantum algorithms5. Unlike the two-qubit case, where all maximally entangled two-qubit states are equivalent up to local changes of basis, three qubits can be entangled in two fundamentally different ways6. These are typified by the states |GHZ〉 = (|000〉 + |111〉)/ and |W〉 = (|001〉 + |010〉 + |100〉)/ . Here we demonstrate the operation of three coupled superconducting phase qubits7 and use them to create and measure |GHZ〉 and |W〉 states. The states are fully characterized using quantum state tomography8 and are shown to satisfy entanglement witnesses9, confirming that they are indeed examples of three-qubit entanglement and are not separable into mixtures of two-qubit entanglement.

349 citations