We present a new hardware-efficient paradigm for universal quantum computation which is based on encoding, protecting and manipulating quantum information in a quantum harmonic oscillator.This proposal exploits multi-photon driven dissipative processes to encode quantum information in logical bases composed of Schr\“odinger cat states. More precisely, we consider two schemes. In a first scheme, a two-photon driven dissipative process is used to stabilize a logical qubit basis of two-component Schr\“odinger cat states. While such a scheme ensures a protection of the logical qubit against the photon dephasing errors, the prominent error channel of single-photon loss induces bit-flip type errors that cannot be corrected. Therefore, we consider a second scheme based on a four-photon driven dissipative process which leads to the choice of four-component Schr\“odinger cat states as the logical qubit. Such a logical qubit can be protected against single-photon loss by continuous photon number parity measurements. Next, applying some specific Hamiltonians, we provide a set of universal quantum gates on the encoded qubits of each of the two schemes. In particular, we illustrate how these operations can be rendered fault-tolerant with respect to various decoherence channels of participating quantum systems. Finally, we also propose experimental schemes based on quantum superconducting circuits and inspired by methods used in Josephson parametric amplification, which should allow to achieve these driven dissipative processes along with the Hamiltonians ensuring the universal operations in an efficient manner.
Making a system state follow a prescribed trajectory despite fluctuations and
errors commonly consists in monitoring an observable (temperature,
blood-glucose level…) and reactingon its controllers (heater power, insulin
amount …). In the quantum domain, there is a change of paradigm in feedback
since measurements modify the state of the system, most dramatically when the
trajectory goes through superpositions of measurement eigenstates. Here, we
demonstrate the stabilization of an arbitrary trajectory of a superconducting
qubit by measurement based feedback. The protocol benefits from the long
coherence time ($T_2>10 mu$s) of the 3D transmon qubit, the high efficiency
(82%) of the phase preserving Josephson amplifier, and fast electronics
ensuring less than 500 ns delay. At discrete time intervals, the state of the
qubit is measured and corrected in case an error is detected. For Rabi
oscillations, where the discrete measurements occur when the qubit is supposed
to be in the measurement pointer states, we demonstrate an average fidelity of
85% to the targeted trajectory. For Ramsey oscillations, which does not go
through pointer states, the average fidelity reaches 75%. Incidentally, we
demonstrate a fast reset protocol allowing to cool a 3D transmon qubit down to
0.6% in the excited state.
We demonstrate full frequency conversion in the microwave domain using a
Josephson three-wave mixing device pumped at the difference between the
frequencies of its fundamental eigenmodes.By measuring the signal output as a
function of the intensity and phase of the three input signal, idler and pump
tones, we show that the device functions as a controllable three-wave
beam-splitter/combiner for propagating microwave modes, in accordance with
theory. Losses at the full conversion point are found to be less than 10^-2.
Potential applications of the device include quantum information transduction
and realization of an ultra-sensitive interferometer with controllable
feedback.
The Josephson ring modulator (JRM) is a device, based on Josephson tunnel
junctions, capable of performing non-degenerate mixing in the microwave regime
without losses. The genericscattering matrix of the device is calculated by
solving coupled quantum Langevin equations. Its form shows that the device can
achieve quantum-limited noise performance both as an amplifier and a mixer.
Fundamental limitations on simultaneous optimization of performance metrics
like gain, bandwidth and dynamic range (including the effect of pump depletion)
are discussed. We also present three possible integrations of the JRM as the
active medium in a different electromagnetic environment. The resulting
circuits, named Josephson parametric converters (JPC), are discussed in detail,
and experimental data on their dynamic range are found to be in good agreement
with theoretical predictions. We also discuss future prospects and requisite
optimization of JPC as a preamplifier for qubit readout applications.
Quantum fluctuations in an anharmonic superconducting circuit enable
frequency conversion of individual incoming photons. This effect, linear in the
photon beam intensity, leads toramifications for the standard input-output
circuit theory. We consider an extreme case of anharmonicity in which photons
scatter off a small set of weak links within a Josephson junction array. We
show that this quantum impurity displays Kondo physics and evaluate the elastic
and inelastic photon scattering cross sections. These cross sections reveal
many-body properties of the Kondo problem that are hard to access in its
traditional fermionic version.
The simultaneous suppression of charge fluctuations and offsets is crucial
for preserving quantum coherence in devices exploiting large quantum
fluctuations of the superconducting phase.This requires an environment with
both extremely low DC and high RF impedance. Such an environment is provided by
a superinductance, defined as a zero DC resistance inductance whose impedance
exceeds the resistance quantum $R_Q = h/(2e)^2 simeq 6.5 mathrm{kOmega}$ at
frequencies of interest (1 – 10 GHz). In addition, the superinductance must
have as little dissipation as possible, and possess a self-resonant frequency
well above frequencies of interest. The kinetic inductance of an array of
Josephson junctions is an ideal candidate to implement the superinductance
provided its phase slip rate is sufficiently low. We successfully implemented
such an array using large Josephson junctions ($E_J >> E_C$), and measured
internal losses less than 20 ppm, self-resonant frequencies greater than 10
GHz, and phase slip rates less than 1 mHz.
Using a superconducting circuit, the Josephson mixer, we demonstrate the
first experimental realization of spatially separated two-mode squeezed states
of microwave light. Driven bya pump tone, a first Josephson mixer generates,
out of quantum vacuum, a pair of entangled fields at different frequencies on
separate transmission lines. A second mixer, driven by a $pi$-phase shifted
copy of the first pump tone, recombines and disentangles the two fields. The
resulting output noise level is measured to be lower than for vacuum state at
the input of the second mixer, an unambiguous proof of entanglement. Moreover,
the output noise level provides a direct, quantitative measure of entanglement,
leading here to the demonstration of 6 Mebit.s$^{-1}$ (Mega entangled bits per
second) generated by the first mixer.