(light electronic music) - Hello, I'm Steve Girvin, professor of physics and applied
physics at Yale University, and Director of the Co-design
Center for Quantum Advantage at Brookhaven National Laboratory. I'm going to talk to you about the history of superconducting qubits, a challenging task, because
of the explosion of activity in the last quarter century. So I won't be able to
cover all of the threads, but I'll pick a few of them to illustrate the tremendous
advances that have occurred. So let's start at the beginning. Information is physical. Quantum information is stored in the states of quantum
objects called qubits, and can be represented as superpositions of the occupation of the
two lowest energy levels among the quantized energy
levels of any quantum system. You can see on the right
an experiment I did with a compact fluorescent light bulb, sending the light through a slit, bouncing off a compact disc. You can see the discrete
colors in the spectrum representing the transitions, the quantum jumps of the
electrons in the atom, among the different levels. It's very important that
the colors of these, the light emitted in these
transitions is different, that the energy level
spacing is not uniform. In this case, the blue light, if you have blue light from
a laser to match the color of the fluorescent blue
light that you see, you can control the superposition of the zero and one states, and not excite the atom
into higher states, because that takes a
different color of light, green in this case. So the minimal engineering
requirement for a qubit is to be able to control
the superposition state of the two lowest levels, and this requires the
spectrum to be anharmonic. So this is all about engineering, and I'll give a simple
definition of engineering, optimization subject to constraints. What other skill in life do you need? Unfortunately, for the case of qubits, we have severe conflicting constraints. In order to have very long coherence times for the qubits to remember
the quantum information, they have to be completely
isolated from the outside world and from each other,
and remain unobserved, because in quantum mechanics, the act of observing a state changes it. In complete conflict with this constraint that will give us long coherence time is the constraint that we have to be able to change the state of
the qubit very rapidly. We need fast control, and we need strong and accurate readout of
the state of the system. Both of these requirements require very strong coupling of the qubits to the outside world. So the history of the
field, so far at least, is the story of this
struggle to optimize systems in the face of these
conflicting constraints. So one choice you can make
in the optimization is between using natural atoms and ions, and synthetic atoms,
superconducting qubits. Synthetic atoms are very nice, of course. They're not simply identical, but they're literally indistinguishable in a deep quantum mechanical sense. They have very long coherence times. They generally work well
at room temperature, but at the same time, because they have long coherence times, because they do not couple very strongly to electromagnetic radiation,
and therefore to each other, and therefore to the readout system. Also, you have to deal with lasers and their amplitude and phase noise, and control of the spatial
modes of the lasers, all of which are
expensive and challenging. Synthetic atoms,
superconducting qubits have nice engineering properties. They can be individually designed, engineered, and optimized. They're a bit like people from California, each one is their own distinct individual. Unlike people from California, they work best near absolute zero, and one has to have an
expensive refrigerator to achieve that condition. They have modest, but strongly
improved, coherence times over what they were at the
beginning of the field. A very powerful advantage is that they're natural for use in
electronic circuits and chips. And their macroscopic size, they're typically a millimeter in size, implies strong coupling
to electromagnetic fields for fast control and multi-qubit gates. Also, at least those of
us who work with radios, feel that the microwave amplitude phase and spatial mode control
with off-the-shelf equipment is much easier for microwaves
than it is for lasers. So let's go back now to the pre-history, which is the discovery
of the Josephson effect, a prediction by Brian Josephson, which is related to what happens in a Josephson tunnel
junction to metal electrodes that are superconducting separated by a few atom
thick insulating barrier. And the state, the macroscopic state, into which Cooper pairs of electrons in a superconductor condense
is defined by a phase phi, and it's related to a microscopic property of the quantum field amplitude for pairs of up and down-spin electrons. But it is itself effectively
a classical property. It is connected. It determines the current
through the junction, and its time rate of change
controls the voltage, as you can see in these
Josephson equations up here. It's been known since the 1960s that this phase variable phi acts
like the position of a particle that obeys Newton's equations of motion for classical particles, F equals M A. In this case, the mass
of the particle is played by the capacitance in the circuit, and the force acting on the particle comes from the bias current, which is supplied to the junction. And there's an oscillating term, which produces a tilted washboard potential, as
you see in the graph. There's also a viscous damping term, the third term in the equation, and it's inversely proportional to the resistance in the circuit. I should perhaps stop at this point, and quote the late, great Mike Tinkham. For you young people in the audience who don't know what a washboard is, it's a classical analog
of a Josephson junction that used to be used for cleaning clothes. So the key thing you
need to know about this is what happens if the
particle should escape one of these wells, potential
wells in the washboard, and begin rolling downhill. You can see from the
Josephson equation up here that the velocity of the particle produces an external easily measured
voltage in the circuit proportional to the time rate of change of the position of the particle. And that can be used to detect the escape of the particle from the
well, and we will use that, that will appear in a later
discussion of early experiments. So Tony Leggett in the 1980s began to ask the question, well, if this phase across
the Josephson junction acts like the position
of a classical particle, and it's in a, bound in a potential well, is there any possibility that
that particle could itself exhibit macroscopic quantum behavior? That is, its position could be uncertain. It should be described by a wave function with a probability amplitude
for different positions. A second important
question that Tony asked was just how macroscopic
would this object be if it's quantum mechanical? And what do these words even mean? And so, I will try to
illustrate them with an analogy developed by my colleague, Michel Devoret. So the phase of a
superconducting condensate is a macroscopic, but
classical, manifestation of quantum order, just as
the discrete facet angles of a crystal are macroscopic manifestation of the existence of quantum-ordered
microscopic objects, the individual atoms. And these beautiful, right
angle cleavage planes in this pyrite crystal are there because they are a reflection
of the right angles that exist in the microscopic
simple cubic packing of the atoms in this compound. And this is the first
experimental evidence for the existence of atoms, and was known to the ancient Greeks. This is sort of level one of the way that macroscopic manifestations of quantum mechanics can occur, but there's a second and deeper level, which is that the orientation
of the crystal in space depends on the collective
center of mass motion of the entire crystal, and only under very special circumstances do quantum effects of this
collective coordinate, which is rather massive, become visible. But this is exactly what we need in order to build a superconducting qubit. So Tony had asked this question in 1980 and the group of John Clark at Berkeley, together with young
post-doc Michel Devoret and beginning student John Martinis, decided to try to experimentally verify the quantization of the energy
levels of this phase particle trapped in one of the wells of the tilted washboard potential, and they succeeded in a
series of landmark papers beginning in 1985. And the way they did it
was to do spectroscopy on this artificial atom. Just as I showed you the visible spectrum of the light from the atoms
in a compact fluorescent bulb on the first slide, here,
they sent in microwave tones to create excitations between the discrete
quantized levels of the atom, and then to detect the quantization of the energy levels of these particles, they used spectroscopy,
much like the spectrum I showed you of optical
light on the first slide. But here they used microwave
radiation to excite the atom, or the phase particle, from one quantized energy
level to the second. And then to detect that that happened, it's impossible to really
see that tiny amount of energy absorbed, but
once the particle's excited, then a second quantum effect, namely quantum tunneling,
through this barrier takes place at an increased rate,
because it's near the top of the barrier, and the
phase particle begins to slide downhill in
the washboard potential, producing a macroscopically
observable voltage, as I mentioned previously. And here you can see
the discrete transitions at effectively different frequencies. This is actually for a
different tilt of the washboard, but it's effectively the same. And as Leggett pointed out,
it's extremely important that this is an anharmonic potential, so that the energy levels
are unequally spaced, and you evade the
correspondence principle. You're able to address the
individual transitions, and see sharp peaks at
different frequencies corresponding to the
quantized energy levels. So this was the beginning. It led to the creation now
of a whole periodic table of the artificial elements, charge qubits, phase qubits, flux qubits, and other types of qubits. But they're all made of the same three non-dissipative elements, a capacitor, which is a linear circuit element, an inductor, which is a
linear circuit element, and the Josephson junction, which is the only non-linear, non-dissipative circuit
element that we know of. Hence, every superconducting
qubit involves a Josephson junction. Here's the Cooper pair box. It's a small, mesoscopic
scale piece of superconductor, which has a very small capacitance, so small that if you
add a single electron, or a single Cooper pair of electrons, it costs a significant amount of energy. You can add and subtract Cooper pairs by tunneling them through this
very thin insulating barrier of the Josephson junction. And then to adjust the cost, how much it costs in Coulomb
energy to add a pair, you have an adjustable bias
voltage here, a gate voltage. And as a function of that gate voltage, you can cause a level
crossing between the state, which has roughly a billion
Cooper pairs on the box, and the state that has a billion plus one, and at a certain special bias voltage, those two states are degenerate in energy, and that degeneracy is lifted by the coherent Josephson
tunneling back and forth of one single Cooper pair, connecting coherence between a billion and a billion plus one pairs. So as you slowly change this bias voltage, the average charge on the island slowly evolves from a billion
to a billion plus one. And the Saclay group in Paris, led by Michel Devoret and Daniel Esteve, it built a single-electron
transit electrometer very sensitive to measure
this average charge. And here you can see in this
curve the smooth transition of the charge one Cooper pair at a time as the voltage is slowly ramped up, whereas if you had a normal,
non-superconducting island, there's no coherent tunneling,
only incoherent hopping, and there's no coherent
broadening of the transition. So this was very strong,
but indirect, evidence that the Cooper pair box was existing in a coherent superposition. This broadening was clearly shown not to be due to temperature, and the only possible source would be the coherent Josephson tunneling. Meanwhile, in Japan, Yasunobu
Nakamura and collaborators were doing spectroscopy
on a Cooper pair box, shining in microwaves
to cause a transition between these quantized energy levels, and then using a subsequent
complicated process in which Cooper pairs could tunnel, and pieces of broken Cooper
pairs, Josephson quasiparticles, could also tunnel into an external probe, creating a current. And with that, they were
able to perform spectroscopy, and see directly in the frequency domain the quantized energy levels. My entry in the field
came with this paper. I had no idea that there
were people thinking about building quantum computers. I knew nothing about the concept
of superconducting qubits. I was busy thinking about the fractional quantum
hall effect in those days. And Nakamura and collaborators
decided to do an experiment in which they change the gate
voltage not adiabatically, but as close to
instantaneously as they could. This required purchasing
a $500,000 pulse generator that could change the
voltage in 40 picoseconds. But because it was, the
change was so rapid, the quantum state did not smoothly follow the ground state as it
would adiabatically, but it stayed in state N, but the Hamiltonian now suddenly changed. It was a superposition of
the coherent eigenstates, and therefore it began to evolve in time, as you can see from these ripples in the measured current
detecting the state of the qubit. Notice the timescale is picoseconds. These are effectively Rabi oscillations in the language of atomic physics, and they lasted a few nanoseconds, very, very short length of time. But the fact that you could see direct time domain evidence
of quantum coherence in a macroscopic electrical
circuit was just stunning. And when I saw this paper, I said, "It's time to change fields," and began thinking about
superconducting qubits. It was a really exciting
moment in my life. At the same time, the Saclay
group was busy working with their Cooper pair box, and extended it to a new type of qubit, which they dubbed quantronium. Quantronium is a
beautifully designed qubit with special symmetry
properties that give it what atomic physicists
call a clock transition. There exists a regime of gate voltage and magnetic field where the frequency of the
transition is insensitive to the precise values of those parameters, and therefore unaffected
by accidental noise in those parameters. And Michel Devoret and
Daniel Esteve and Denis Vion published in 2002 a spectacular experiment showing the first first
Ramsey interference fringes, which is the acid test of coherence needed to satisfy atomic physicists
that this is real, real true coherence
observed in the time domain. There are a number of technical
innovations in this qubit. It was a kind of a hybrid
charge-phase qubit. You wrote in the charge mode, and read out in the phase mode, and that orthogonality of the
modes turned out to be useful. There was a latching
readout which they invented to help with the signal to noise, and of course the main
thing was this sweet spot, because now you can see these
Ramsey interference fringes going out to microsecond timescales at least a factor of 100 greater than the initial work from Japan. It's a really exciting,
and wonderful experiment. Meanwhile, in Europe, in Delft, Hans Mooij and collaborators
were thinking about something dual to the charge qubit. Instead of a superposition of a billion and a billion plus one Cooper pairs, you could have, on an island, you could have a closed
loop carrying current, and the current could
be in a superposition of going clockwise and counterclockwise, or equivalently magnetic
flux could be tunneling in and out of this loop. And they developed this proposal for a three-junction flux qubit in 1999, and began publishing
experiments on it in 2000. Finally, there was the phase qubit. John Martinis went back to his PhD thesis, and constructed this
tilted washboard potential, but now arranged for the barrier for tunneling out of the lowest
two levels to be very large, but tunneling out of the
third level to be more rapid, so by he could manipulate
the lowest two levels of the artificial atom, and then read it out by applying a tone such that if it were in the excited state it would go up to the next
excited state, tunnel out, and produce a large voltage. This large voltage gave
amazingly high readout fidelity of about 85% in a single shot, which was very, very impressive
for these early days. But it was later realized
that that large voltage spike was destructive of the coherent
states of nearby qubits once they began experimenting
with more than one qubit, and this method was eventually abandoned for the dispersive readout,
which I'll talk about. The qubit in widest use
today is the transmon qubit. It's sort of the world's simplest qubit. It just consists of two pieces of aluminum film evaporated
on a sapphire substrate making a dipole antenna
about a millimeter long, and the two halves are connected
by a Josephson junction to give you the anharmonic
spectrum that you need. So the theory paper led by Jens Koch was soon followed by the
first experimental paper led by Andrew Houck, and
the advantage of this, this is basically just a Cooper pair box, but with a large shunting capacitance in the form of this antenna, and this makes it
exponentially insensitive to noise in the charge channel at the cost of only a modest
reduction in the anharmonicity, and the very large dipole
moment of this artificial atom, it's about 100,000 times
larger than the dipole moment of natural atom, gives
this artificial atom extremely strong coupling
to microwave photons, which we will take advantage of. So you can think of this
as an artificial atom with atomic number 10 to the 12. There are roughly 10 of the
12 pairs of electrons in here. You might think that the spectrum
would then be a nightmare, but at low energies, the
spectrum is just that of an anharmonic oscillator. It's even simpler than hydrogen, and it has a comparable quality factor to the Lyman-alpha transition in hydrogen. So we're starting to catch
up with the natural atoms. There's been orders of magnitude progress in improving the qubit coherence lifetimes over the last 20 years
based on new designs, better microwave hygiene, we call it, minimizing the sources of dissipation at microwave frequencies,
and better materials. So the coherence times have increased by about six orders of magnitude
in recent developments. For example, the Maryland group has achieved coherence times
north of a millisecond, and using improved materials. This is in the fluxonium qubit. The Princeton group using a transmon, but changing some of the materials, has increased their coherence time to about 1/3 of a millisecond. It's now possible because
of all these advances in the field to do very high
fidelity two-qubit gates that you need for quantum computation. Here's just one of many recent examples, some nice progress from
Will Oliver's group at MIT doing controlled phase gates
in about 60 nanoseconds with a almost three nines
fidelity in an iSWAP gate and 30 nanoseconds, again, with almost three nines in fidelity. One of the crucial enabling technologies for reading out data and reading out error syndromes to do quantum error correction
is the development of quantum limited amplifiers, which have made tremendous progress, both motivated by their need for superconducting qubit circuits, but able to be improved dramatically because of the progress in creating superconducting circuits. And so, Irfan Siddiqi observed
the first quantum jumps in a superconducting
artificial atom in 2011. Zlatko Minev and Michel
Devoret recently caught a quantum jump in mid-flight
and showed to people's surprise that it's much more coherent
than people realized. And Konrad Lehnert at JILA is supplying amazing amplifiers that do two-mode squeezing to the HAYSTAC dark matter search at Yale, searching for, which will
accelerate that search for axions. So this kind of technology is assisting both the development of quantum
computers and in cosmology. So there are two
experiments now in cosmology that use squeezing. One is LIGO, the
gravitational wave detector, and the other is this HAYSTAC experiment. So that brings us now to the quantum electrodynamics
of electrical circuits. QED is the study of atoms and
electrons coupled to photons and the effect of the fact
that the electromagnetic field is quantized, that it has
zero-point fluctuations, and how these so-called
vacuum fluctuations affect atomic spectrum. Cavity QED engineers
those vacuum fluctuations by putting the atom in, not in free space, but inside some sort of resonator that makes the
electromagnetic modes discrete instead of continuous. In the microwave domain,
we have the luxury of completely surrounding the box by superconducting mirrors that almost perfectly
reflect the microwaves. One of the things you can do with this is the Purcell effect. You can choose the cavity
frequency to be different than the qubit's frequency at which it would spontaneously fluoresce. And this can enhance the
lifetime by a factor of 1,000. A transmon, the large dipole
moment of the transmon qubit means that in free space it
would spontaneously decay by emitting a microwave photon in about 100 nanoseconds. Putting it in a box gives
you the 100 microseconds, so a gain of a factor of 1,000. So this is where the story
becomes more personal, and I got interested, and moved to Yale, and began working with Rob
Schoelkopf and Michel Devoret, thinking about how to apply
ideas from quantum optics and cavity QED to microwave
electrical circuits. This was a new field for me. I hadn't studied this, and it took me a couple of years to learn some quantum optics, and
the first thing I learned is that people in atomic physics know much more quantum
mechanics than those of us who came from condensed matter theory. So that was very interesting. And we had the idea that if you could put an
artificial atom in a cavity, you could perhaps see
what's called the vacuum Rabi splitting the coherent
motion of one excitation coherently going back and
forth between the qubit and the single photon in the cavity. And I struggled and
struggled to figure out exactly how big is the
zero-point fluctuations of the electric field in
these small resonators. It turns out to be amazingly large. It produces about a microvolt
of potential across the qubit, and it turned out to be possible to achieve vacuum Rabi
couplings of 100 megahertz. And when I realized that, I
realized there was a chance to actually do the experiment. It was still not obvious, because in those bad,
old days the line widths of these qubits could
be 100 megahertz wide due to their short coherence time. So the theory paper developing this circuit QED, we called
it, was led by Alexandre Blais, and then the experiment
led by Andreas Wallraff, who was a post-doc at Yale with Schoelkopf and Dave Schuster and a
student soon followed. And one of the things which
eventually we were able to do was show that you could go
to a strong dispersive limit, where the qubit is
detuned from the cavity, and yet still have such
strong dispersive coupling that each time you added
a single microwave photon, which has 100,000 times less
energy than an optical photon, but despite that you
could see a distinct shift in the frequency of the qubit by, of order of 1,000 line widths. So this is very, very strong
coupling, unavailable, completely unavailable with natural atoms. That experiment was carried
out by, led by Dave Schuster, and theoretical work was
done by Jay Gambetta. Later, we made, this work was first done with 2D planar resonators. Later, we moved to these 3D resonators that completely surround the qubit with superconducting aluminum, and produce a much quieter environment, and Hanhee Paik did the
first experiment there showing the great benefits
on the lifetime of the qubit, and later Matt Raygor developed
some very high-Q resonators that could be used for quantum memories. Andrew Cleveland and Martinis at UCSB did a remarkable experiment synthesizing arbitrary quantum states in a superconducting resonator in a Max Hofheinz-led experiment. Here, you see the theoretical and experimental Wigner functions, the state tomography for
completely non-classical states, such as a superposition
of zero and five photons, exhibiting the complete quantum control that's available in this system, which has such strong
coupling between the qubits and the harmonic oscillator, the cavity. Here's a picture of the first crude, all-electronic quantum processor constructed in 2009 using this circuit QED architecture, and it's the first
all-electronic processor able to run quantum algorithms. It only had two qubits, but it was able to do the Grover search and Deutsch-Jozsa algorithms. And all the current industrial systems based on superconducting qubits are really massive engineering
scale-ups of this, inspired by this first crude device. And here you see some pictures of some of the current
amazing industrial systems with 50 and 60 qubits at Google and IBM. Here's Chad Rigetti, who is a
graduate student in our group, and it's wonderful to see
the sum of these ideas going out into the world, and allowing tremendous
engineering advances in the field. I'll mention here just one highlight, which is quantum error correction at, or even slightly beyond,
the break-even point, using not superconducting qubits to hold the information, but rather, that hasn't succeeded yet, but rather, succeeding by
putting the quantum information into these superposition states of different numbers of microwave photons. The first to break the,
reach the break-even point is the Schrodinger cat code
developed in this theory paper, and executed in this experiment in 2016. More recently, people have
made experimental progress at long last on a fascinating code developed by Gottesman,
Kitaev, and Preskill in 2001 in which the stabilizers, the errors, and the logical gates are
all simple displacements of the oscillator in phase space. But it was such an exotic
state, quantum state, that no one could imagine that it would be possible to produce. But due to recent progress
in superconducting qubits, and in trapped ion experiments, there are now two
realizations of these states, and here you see not
quite the Wigner function, but the so-called characteristic function, a different kind of tomogram, and effectively, this is
a Schrodinger cat state living in 35 places at
once in phase space, so really demonstration of
remarkable quantum control of an oscillator. Finally, here's a recent
interesting result that got some press from Andreas Wallraff, who was on the first circuit QED paper. He has now entangled a qubit system separated by five meters using a cryogenically cooled wave
guide to connect the two qubits in each of these refrigerators, and achieved a fidelity of
state transfer of about 80%. So this talk has covered
a few of the threads in this now exploding field. It's necessarily I've given
you a very incomplete list of topics and key players, and I apologize for leaving
many important things out. I'd like to thank my colleagues who've shared some of their slides, and thank everyone in the
Yale Quantum Institute who have made doing physics and exploring this field so much fun. And I'll close with a picture from 2007 when we first did the two-qubit dance, and got entangled states
in the circuit QED setup. Thank you very much for listening.
