Solid State Quantum Bits

Abstract

We present the solid-state quantum circuits that have been developed in order to implement quantum bits suitable for a quantum processor. These qubits are either based on the quantum state of a single particle (semiconductor qubits), or on the quantum state of the global circuit (superconducting qubits). We discuss more in detail the superconducting qubits, and present results on qubit manipulation and readout. We explain the main strategies used to improve and tio maintain quantum coherence.

Full text

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SOLID STATE QUANTUM BIT CIRCUITS
Daniel Esteve and Denis Vion
Quantronics, SPEC, CEA-Saclay,
91191 Gif sur Yvette, France
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Contents
1. Why solid state quantum bits?
1.1. From quantum mechanics to quantum machines
1.2. Quantum processors based on qubits
1.3. Atom and ion versus solid state qubits
1.4. Electronic qubits
2. qubits in semiconductor structures
2.1. Kane’s proposal: nuclear spins of P impurities in silicon
2.2. Electron spins in quantum dots
2.3. Charge states in quantum dots
2.4. Flying qubits
3. Superconducting qubit circuits
3.1. Josephson qubits
3.1.1. Hamiltonian of Josephson qubit circuits
3.1.2. The single Cooper pair box
3.1.3. Survey of Cooper pair box experiments
3.2. How to maintain quantum coherence?
3.2.1. Qubit-environment coupling Hamiltonian
3.2.2. Relaxation
3.2.3. Decoherence: relaxation + dephasing
3.2.4. The optimal working point strategy
4. The quantronium circuit
4.1. Relaxation and dephasing in the quantronium
4.2. Readout
4.2.1. Switching readout
4.2.2. AC methods for QND readout
5. Coherent control of the qubit
5.1. Ultrafast ’DC’ pulses versus resonant microwave pulses
5.2. NMR-like control of a qubit
6. Probing qubit coherence
6.1. Relaxation
6.2. Decoherence during free evolution
6.3. Decoherence during driven evolution
7. Qubit coupling schemes
7.1. Tunable versus fixed couplings
7.2. A tunable coupling element for Josephson qubits
7.3. Fixed coupling Hamiltonian
7.4. Control of the interaction mediated by a fixed Hamiltonian
7.5. Running a simple quantum algorithm
8. Conclusions and perspectives
References
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1. Why solid state quantum bits?
Solid state quantum bit circuits are a new type of electronic circuit that aim to
implement the building blocks of quantum computing processors, namely the
quantum bits or qubits. Quantum computing [1] is a breakthrough in the field
of information processing because quantum algorithms could solve some math-
ematical tasks presently considered as intractable, such as the factorisation of
large numbers, exponentiallyfaster than classicalalgorithms operated on sequen-
tial Von Neumann computers. Among the various implementations envisioned,
solid state circuits have attracted a large interest because they are considered as
more versatile and more easily scalable than qubits based on atoms or ions, de-
spite worse quantumness. The 2003 Les Houches School devoted to Quantum
Coherence and Information Processing [2] has covered many aspects of quan-
tum computing [3], including solid state qubits [4–7]. Superconducting circuits
were in particular thoroughly discussed. Our aim is to provide in this course a
rational presentation of all solid state qubits. The course is organised as follows:
we first introduce the basic concepts underlying quantum bit circuits. We clas-
sify the solid state systems considered for implementing quantum bits, starting
with semiconductor circuits, in which a qubit is encoded in the quantum state
of a single particle. We then discuss superconducting circuits, in which a qubit
is encoded in the quantum state of the whole circuit. We detail the case of the
quantronium circuit that exemplifies the quest for quantum coherence.
1.1. From quantum mechanics to quantum machines
Quantum Computing opened a new field in quantum mechanics, that of quan-
tum machines, and a little bit of history is useful at this point. In his seminal
work, Max Planck proved that the quantisation of energy exchanges between
matter and the radiation field yields a black-body radiation law free from the di-
vergence previously found in classical treatments, and in good agreement with
experiment. This success led to a complete revision of the concepts of physics.
It took nevertheless about fifty years to tie together the new rules of physics in
what is now called quantum mechanics. The most widely accepted interpretation
of quantum mechanics was elaborated by a group physicists around Niels Bohr
in Copenhagen. Whereas classical physics is based on Newtonian mechanics for
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D. Esteve and Denis Vion
the dynamics of any system, and on fields, such as the electromagnetic field de-
scribed by Maxwell’s equations, quantum mechanics is based on the evolution
of a system inside a Hilbert space associated to all its physically possible states.
For example, localised states at all points in a box form a natural basis for the
Hilbert space of a particle confined in this box. Any superposition of the basis
states is a possible physical state. The evolution inside this Hilbert space follows
a unitary operator determined by the Hamiltonian of the system. Finally, when a
measurement is performed on a system, an eigenvalue of the measured variable
(operator) is found, and the state is projected on the corresponding eigenspace.
Although these concepts seem at odds with physical laws at our scale, the quan-
tum rules do lead to the classical behavior for a system coupled to a sufficiently
complex environment. More precisely, the theory of decoherence in quantum
mechanics predicts that the entanglement between the system and its environ-
ment suppresses coherence between system states (interferences are no longer
possible), and yields probabilities for the states that can result from the evolu-
tion. Classical physics does not derive from quantum mechanics in the sense that
the state emerging from the evolution of the system coupled to its environment
is predicted only statistically. As a result, quantum physics has been mainly
considered as relevant for the description of the microscopic world, although no
distinction exists in principle between various kinds of degrees of freedom: their
underlying complexity does not come into play within the standard framework of
quantum mechanics.
This blindness explains the fifty years delay between the establishment of
quantummechanics, and thefirstproposalsof quantummachinesinthenineteen-
eighties. On the experimental side, the investigation of quantum effects in elec-
troniccircuitscarriedoutduringthelastthirtyyearspavedthewaytothisconcep-
tual revolution. The question of the quantumness of a collective variable involv-
ing a large number of microscopic particles, such as the current in a supercon-
ducting circuit, was raised. The quantitative observation of quantum effects such
as macroscopic quantum tunneling [8] contributed to establishing the confidence
that quantum mechanics can be brought in the realm of macroscopic objects.
Before embarking on the description of qubits, it is worth noticing that quan-
tum machines offer a new direction to probe quantum mechanics. Recently, the
emphasis has been put on the entanglement degree rather than on the mere size of
a quantum system. Probing entanglement between states of macroscopic circuits,
or reaching quantum states with a high degree of entanglement are now major
issues in quantum physics. This is the new border, whose exploration started
by the demonstration of the violation of Bell’s inequalities for entangled pairs
of photons [9]. This research direction, confined for a long time in Byzantine
discussions about the EPR and Schrödinger cat paradoxes, is now accesible to
experimental tests [10].

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First proposals of quantum machines
such as the laser only involve quantummechanics at the microscopic level, atom-
field interactions in this case. A true quantum machine is a system in which
machine-state variables are ruled by quantum mechanics. One might think that
quantum machines more complex than molecules could not exist because the
interactions between any complex system and the numerous degrees of freedom
of its environment tend to drive it into the classical regime. Proposing machines
that could benefit from the quantumrules was thus a bold idea. Such propositions
appeared in the domain of processors after Deutsch and Josza showed that the
concept of algorithmic complexity is hardware dependent. More precisely, it was
provedthatasimplesetofunitaryoperationsonanensembleofcoupledtwolevel
systems, called qubits, is sufficient to perform some specific computing tasks in
a smaller number of algorithmic steps than with a classical processor [1].
Although the first problem solved ”more efficiently” by a quantum algorithm
was not of great interest, it initiated great discoveries. Important results were
obtained [1], culminating with the factorisation algorithm discovered by Shor
in 1994, and with the quantum error correction codes [1] developed by Shor,
Steane, Gottesman and others around 1996. These breakthroughs should not
hide the fact that the number of quantum algorithms is rather small. But since
many problems in the same complexity class can be equivalent, solving one of
them can provide a solution to a whole class of problems. Pessimists see in this
lack of algorithms a major objection to quantum computing. Optimists point
out that simply to simulate quantum systems, it is already worthwhile to develop
quantum processors, since this task is notoriously difficult for usual computers.
A more balanced opinion might be that more theoretical breakthroughs are still
needed before quantum algorithms are really worth the effort of making quantum
processors. How large does a quantum processor need to be to perform a useful
computation? It is considered that a few tens of robust qubits would already be
sufficient for performing interesting computations. Notice that the size of the
Hilbert space of such a processor is already extremely large.
Commonly accepted quantum machines
1.2. Quantum processors based on qubits
A sketch of a quantum processor based on quantum bits is shown in Fig. 1. It
consists of an array of these qubits, which are two level systems. Each qubit
is controlled independently, so that any unitary operation can be applied to it.
Qubits are coupled in a controlled way so that all the two qubit gate operations
required by algorithms can be performed. As in Boolean logic, a small set of
gates is sufficient to form a universal set of operations, and hence to operate a
quantum processor. A two-qubit gate is universal when, combined with a subset
of single qubit gates, it allows implemention of any unitary evolution [1]. For

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D. Esteve and Denis Vion
0
1
0
1
0
1
U1
U1
0
1
?
Fig. 1. Sketch of a quantum processor based on qubits. Each qubit is here a robust qubit, with its
error correction circuitry. The detailed architecture of a quantum processor strongly depends on the
set of gates that can be implemented. The single two qubit gates, combined with single qubit gates,
should form a universal set of gates, able to process any quantum algorithm.
instance, the control-not gate (C-NOT), which applies a not operation on qubit 2
when qubit1 is in state 1, is universal.
Criteria required for qubits
menting qubits. A series of points, summarised by DiVicenzo, need to be ad-
dressed (see chapter 7 in [1]):
1) The level spectrum should be sufficiently anharmonic to provide a good
two level system.
2) An operation corresponding to a ’reset’ is needed.
3) The quantum coherence time must be sufficient for the implementation of
quantum error correction codes.
4) The qubits must be of a scalable design with a universal set of gates.
5) A high fidelity readout method is needed.
These points deserve further comments:
The requirement on the coherence is measured by the number of gate opera-
tions that can be performed with an error small enough so that error correcting
codes can be used. This requirement is extremely demanding: less than one er-
ror in ???gate operations. Qubits rather better protected from decoherence than
those available today will be needed for this purpose.
If a readout step is performed while running the algorithm, a perfect read-
out system should provide answers with the correct probabilities, and project
the register on the state corresponding to the outcome read.The state can then
Not all two level systems are suitable for imple-

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be stored for other purpose. This is the definition of a quantum non demolition
(QND) measurement. Such a QND readout would be useful to measure quan-
tum correlations in coupled qubit circuits and to probe whether or not Bell’s
inequalities are violated as predicted by quantum mechanics like in the micro-
scopic world [9]. However, non QND readout systems could provide answers
with the correct probabilities, but fail to achieve the projection afterwards. Note
that QND readout is not essential for quantum algorithms? although the factor-
ization algorithm is often presented with intermediate projection step, it is not
necessary.
1.3. Atom and ion versus solid state qubits
Ontheexperimentalside, implementingquantumprocessorsisaformidabletask,
and no realistic scalable design presently exists. The activity has been focused
on the operation of simple systems, with at most a few qubits. Two main roads
have been followed. First, microscopic quantum systems like atoms [10] and
ions [11] have been considered. Their main advantage is their excellent quantum-
ness, but their scalability is questionable. The most advanced qubit implemen-
tation is based on ions in linear traps, coupled to their longitudinal motion [11]
and addressed optically. Although the trend is to develop atom-chips, these im-
plementations based on microscopic quantum objects still lack the ?exibility of
microfabricated electronic circuits, which constitute the second main road in-
vestigated. Here, quantumness is limited by the complexity of the circuits that
always involve a macroscopic number of atoms and electrons. We describe in the
following this quest for quantumness in electronic solid state circuits.
1.4. Electronic qubits
Two main strategies based on quantum states of either single particles or of the
whole circuit, have been followed for making solid-state qubits.
In the first strategy, the quantum states are nuclear spin states, single electron
spin states, or single electron orbital states. The advantage of using microscopic
states is that their quantumness has already been probed and can be good at low
temperature. The main drawback is that qubit operations are difficult to perform
since single particles are not easily controlled and read out.
The second strategy has been developed in superconducting circuits based on
Josephson junctions, which form a kind of artificial atoms. Their Hamiltonian
can be tailored almost at will, and a direct electrical readout can be incorporated
in the circuit. On the other hand, the quantumness of these artificial atoms does
not yet compare to that of natural atoms or of spins.

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2. qubits in semiconductor structures
Microscopic quantum states suitable for making qubits can be found in semi-
conductor nanostructures, but more exotic possibilities such as Andreev states
at a superconducting quantum point contact [12] have also been proposed. Sin-
gle particle quantum states with the best quantumness have been selected, and a
few representative approaches are described below. Two families can be distin-
guished: the first one being based on quantum states of nuclear spins, or of lo-
calised electrons, while the second one is based on propagating electronic states
(?ying qubits).
2.1. Kane’s proposal: nuclear spins of P impurities in silicon
The qubits proposed by Kane are the S=1/2 nuclear spins of ???impurities in
silicon [13]. Their quantumness is excellent, and rivals that of atoms in vacuum.
In the ref. [13], the author has proposed a scheme to control, couple and readout
such spins. A huge effort has been started in Australia in order to implement
this proposal sketched in Fig. 2. The qubits are controlled through the hyperfine
interaction between the nucleus of the ???impurity and the bound electron
around it. The effective Hamiltonian of two neighboring nucleus bound electron
spins:
? ? ????????? ????????? ????????
where the subscripts ? and ? refer to nuclei and bound electrons respectively.
The transition frequency of each qubit is determined by the magnetic field ap-
plied to it, and by its hyperfine coupling ? controlled by the gate voltage applied
to the A gate electrode, which displaces the wavefunction of the bound electron.
Single qubit gates would be performed by using resonant pulses, like in NMR,
while two qubit gates would be performed using the J gates, which tune the ex-
change interaction between neighboring bound electrons. The readout would be
performed by transfering the information on the qubit state to the charge of a
quantum dot, which would then be read using an rf-SET. Although the feasibility
of Kane’s proposal has not yet been demonstrated, it has already yielded signif-
icant progress in high accuracy positioning of a single impurity atom inside a
nanostructure.
2.2. Electron spins in quantum dots
Usingelectronspinsforthequbitsisattractivebecausethespinisweaklycoupled
to the other degrees of freedom of the circuit, and because the spin state can be
transferredtoachargestateforthepurposeofreadout(see[14]andrefs. therein).

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Fig. 2. Kane’s proposal: nuclear spins of phosphorus impurities form the qubits.The control is pro-
vided by the hyperfine interaction with a bound electron around each impurity. Each qubit level
scheme is controlled by applying a voltage to an A gate (labelled A) electrode that displaces slightly
the wavefunction of the bound electron, and thus modifies the hyperfine interaction. Single qubit
gates are performed by applying an ac field on resonance, like in Nuclear Magnetic Resonance. The
two qubit gates are performed using the J gates (labelled J), which control the exchange interaction
between neighboring bound electrons. The exchange interaction mediates an effective interaction
between the qubits. The readout is performed by transfering the information on the qubit state to
the charge of a quantum dot (not shown), which is then read using an rf-Single Electron Transistor
(picture taken from [13].)
Single qubit operations can be performed by applying resonant magnetic fields
(ESR), and two qubit gates can be obtained by controlling the exchange inter-
action between two neighboring electrons in a nanostructure. The device shown
in Fig. 3 is a double dot in which the exchange interaction between the sin-
gle electrons in the dots is controlled by the central gate voltage. The readout
is performed by monitoring the charge of the dot with a quantum point contact
transistor close to it. The measurement proceeds as follows: first, the dot gate
voltage is changed so that an up spin electron stays in the dot, while a down spin
electron leaves it. In that case, another up spin electron from the reservoir can
enter the dot. Thedetection of changesin the dotchargethus provides ameasure-
ment of the qubit state. Note that such a measurement can have a good fidelity as

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D. Esteve and Denis Vion
required, but is not QND because the quantum state is destroyed afterwards.
Fig. 3. Scanning Electron Micrograph of a double dot implementing two qubits . The qubits are
based on the spin of a single electron in the ground state of each dot (disks). The two qubits are
coupled through the exchange energy between electrons, which is controlled by the central gate.
Single qubit gates are obtained by applying local resonant ac magnetic fields. Readout is performed
by monitoring each dot charge with a point contact transistor, after a sudden change of the dot gate
voltage. An electron with the up spin state stays in the dot, whereas a down spin exits, and is replaced
by an up spin electron. A change in the dot charge thus signals a down spin. (Courtesy of Lieven
Vandersypen, T.U. Delft).
2.3. Charge states in quantum dots
The occupation of a quantum dot by a single electron is not expected to pro-
vide an excellent qubit because the electron strongly interacts with the electric
field. Coherent oscillations in a semiconductor qubit circuit [15] were neverthe-
less observed by measuring the transport current in a double dot charge qubit
repeatitively excited by dc pulses, as shown in Fig. 4.
2.4. Flying qubits
Propagating electron states provide an interesting alternative to localised states.
Propagating states in wires with a small number of conduction channels have
been considered, but edge states in Quantum hall Effect structures offer a better
solution [4] . Due to the absence of back-scattering, the phase coherence time
at low temperature is indeed long: electrons propagate coherently over distances
longer than ??? ??. Qubit states are encoded using electrons propagating in
opposite directions, along the opposite sides of the wires. The qubit initialisa-
tion can be performed by injecting a single electron in an edge state. As shown
in Fig. 5, single qubit gates can be obtained with a quantum point contact that
transmits or re?ects incoming electrons, and two qubit gates can be obtained by

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Fig. 4. Coherent oscillations of a single electron inside a double dot structure, as a function of the
duration of a dc pulse applied to the transport voltage. These oscillations are revealed by the average
current when the pulse is repeated at a large rate (picture taken from Hayashi et al. [15] )
coupling edge states over a short length. The readout can be performed by de-
tecting the passage of the electrons along the wire, using a corrugated edge in
order to increase the readout time. This system is not easily scalable because of
its topology, but is well suited for entangling pairs of electrons and measuring
their correlations.
3. Superconducting qubit circuits
The interest of using the quantum states of a whole circuit for implementing
qubits is to benefit from the wide range of Hamiltonians that can be obtained
when inductors and capacitors are combined with Josephson junctions. These
junctions are necessary because a circuit built solely from inductors and ca-
pacitors constitutes a set of harmonic modes. A Josephson junction [16] has a
Hamiltonian which is not quadratic in the electromagnetic variables, and hence
allows to obtain an anharmonic energy spectrum suitable for a qubit. Josephson
qubits can be considered as artificial macroscopic atoms, whose properties can

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D. Esteve and Denis Vion
‘0’ quantum rail
‘1’ quantum rail
‘0’ quantum rail
‘1’ quantum rail
2
π
2
π
QPC
( D=1/2 )
‘0’ quantum rail
e
‘0’ quantum rail
‘1’ quantum rail
‘1’ quantum rail
e
L
w
qubit (a)
qubit (b)
Fig. 5. Single qubit gate (top) and two qubit gate (bottom) for ?ying qubits based on edge states in
QHE nanostructures (Courtesy of C. Glattli).
be tailored. The internal and coupling Hamiltonians can be controlled by apply-
ing electric or magnetic fields, and bias currents. The qubit readout can also be
performed electrically.
3.1. Josephson qubits
Adirectderivation of the Hamiltonian can often be performed for simplecircuits.
There are however systematic rules to derive the Hamiltonian of a Josephson cir-
cuit [17,18], and different forms are possible depending on the choice of vari-
ables. When branch variables are chosen, the contribution to the Hamiltonian of
a Josephson junction in a given branch is:
???? ? ??????????
where ?? ? ????is the Josephson energy, with ??the critical current of the
junction, and ? the superconducting phase difference between the two nodes con-
nected by the branch. The phase ? is the conjugate of the number ? of Cooper
pairs passed across the junction. In each quantum state of the circuit, each junc-
tion is characterised by the?uctuationsof ? and of ?. Often, thecircuit junctions

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Solid State Quantum Bit Circuits
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are either in the phase or number regimes, characterised by small and large ?uc-
tuations of the phase, respectively. Qubit circuits can be classified according to
the regime to which they belong.
3.1.1. Hamiltonian of Josephson qubit circuits
In the case of a single junction, the electromagnetic Hamiltonian of the circuit
in which the junction is embedded adds to the junction Hamiltonian. The phase
biased junction is in the phase regime, whereas the charge biased junction, a cir-
cuit called the Single Cooper Pair Box, can be in a charge regime, phase regime,
or intermediate charge-phase regime, depending on the circuit parameters. The
Cooper-pair box in the charge regime was the first Josephson qubit in which co-
herent behavior was demonstrated [19].
In practice, all Josephson qubits are multi junction circuits in order to tailor
the Hamiltonian, to perform the readout, and to achieve the longest possible co-
herence times. The main types of superconducting qubit circuits can be classified
along a phase to charge axis, as shown in Fig. 6. The phase qubit [20] developed
at NIST (Boulder) consists of a Josephson junction in a ?ux biased loop, with
two potential wells. The qubit states are two quantized levels in the first poten-
tial well, and the readout is performed by resonantly inducing the transfer to the
second well, using a monitoring SQUID to detect it. The ?ux qubit [21,22] de-
veloped at T.U. Delft consists of three junctions in a loop, placed in the phase
regime. Its Hamiltonian is controlled by the ?ux threading the loop. The ?ux
qubit can be coupled in different ways to a readout SQUID. The quantronium
circuit [7,23–25], developed at CEA-Saclay is derived from the Cooper pair box,
butis operated intheintermediatecharge-phaseregime. Adetailed description of
all Josephson qubits, with extensive references to other works, is given in [5–7].
3.1.2. The single Cooper pair box
ThesingleCooperpairbox[7]consistsofasinglejunctionconnectedtoavoltage
source across a small gate capacitor, as shown in Fig. 7. Its Hamiltonian is the
sum of the Josephson Hamiltonian and of an electrostatic term:
? ????? ? ???? ? ? ????? ??????? ,
where ?? ? ?????????is the charging energy, and ?? ? ????????? the re-
duced gate charge with ?? the gate voltage. The operators? ? and?? obey the
alytically determined, or calculated numerically using a restriction of the Hamil-
tonian in a subspace spanned by a small set of ??? states. They are ?? peri-
odic with the gate charge. The two lowest energy levels provide a quantum bit
(3.1)
commutation relation
????? ?
?
? ?. The eigenstates and eigenenergies can be an-

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D. Esteve and Denis Vion
Ψ (N )
N
flux
phase
charge
charge-phase
c
ab
b
Fig. 6. Josephson qubits can be classified along an axis ranging from the phase regime to the charge
regime: the current biased large junction(a), the ?ux qubit (b), the quantronium charge-phase qubit
(c), the Cooper pair box with small Josephson energy (d). In the phase regime, the number of Cooper
pairs transferred across each junction has large ?uctuations, whereas these ?uctuations are small in
the charge regime. (Courtesy of NIST, T.U. Delft, CEA-Saclay, and Chalmers).
because the eigenenergy spectrum is anharmonic for a wide range of parame-
ters. When ??? ??, the qubit states are two successive ??? states away from
??? ?????????, andsymmetricandantisymmetriccombinationsof successive
??? states in the vicinity of ??? ?????????.
3.1.3. Survey of Cooper pair box experiments
The most direct way to probe the Cooper pair box is to measure the island
charge. Following this idea, the island charge was measured in its ground state
in 1996 [26] by capacitively coupling the box island to an electrometer based
on a Single Electron Transistor (SET) [27]. This readout method could not be
used however for time resolved experiments because its measuring time was too
long. The first Josephson qubit experiment was performed in 1999 at NEC [19],
by monitoring the current through an extra junction connected on one side to the
box island and on the other side to a voltage source. When the box gate charge
is suddenly (i.e. non adiabatically) moved from ??? ? to ??? ???, the initial
groundstate???stateisnolongeraneigenstate, andcoherentoscillationsbetween
states take place between ??? and ??? at the qubit transition frequency. When ??
is suddenly moved back to its initial value ? ?, the probability for the qubit to be
in the excited state ??? is conserved. The readout takes advantage of the available

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Fig. 7. Schematic representation and electrical circuit of a Single Cooper pair box: A small super-
conducting island is connected to a voltage source across a capacitor on one side, and a Josephson
junction on the other side. In the schematic circuit, the cross in a box represents a small Josephson
junction.
energy in the upper state to transfer a Cooper pair across the readout junction.
When the experiment is repeated, the average current through the readout junc-
tion provides a measurement of the qubit state at the end of the gate charge pulse.
This method of readout provides a continuous average measurement of the box.
It proved extremely well suited to many experiments. However, it cannot provide
a single shot readout of the qubit. The evolution of qubit design was then driven
by the aim of achieving a better quantumness and a more efficient readout. Bet-
ter quantumness means a longer coherence time, with a controlled in?uence of
the environment to avoid decoherence. More efficient readout means single shot
readout, with a fidelity as high as possible, and ideally quantum non demolition
(QND). The quantronium operated in 2001 at Saclay was the first qubit circuit
combining a single shot readout with a long coherence time [7,23–25]. In 2003,
the charge readout of a Cooper pair box was achieved at Chalmers [29] using an
rf-SET [30], which is a SET probed at high frequency. A sample and hold charge
readout was operated in 2004 at NEC [31], with a fidelity approaching 90%. In
2004, a Cooper pair box embedded in a resonant microwave cavity was operated
at Yale [32] using the modification of the cavity transmission by the Cooper pair
box, similar to the effect of a single atom in cavity-QED experiments [10].
3.2. How to maintain quantum coherence?
When the readout circuit measures the qubit, its backaction results in full qubit
decoherence during the time needed to get the outcome, and even faster if the