The electronic conduction channel constitutes the elementary building block of quantum conductors. A fascinating many-body quantum physics arises from the interactions between electrons transferred across individual quantum channels, and the circuit macroscopic quantum degrees of freedom, such as the charge in a metallic node.

The quantum electrodynamics at work results in electrical and thermal properties markedly different from those of the constitutive quantum channels. Apprehending these quantum laws has direct implications for the quantum engineering in the future nanoelectronics.

Remarkably, such quantum circuits composed of a few distinct conduction channels also provide powerful test-beds for the strongly-correlated electron physics, including the quantum criticality that develops in the vicinity of quantum phase transitions, the correlated 1D (Luttinger liquid) physics and the Kondo-type physics.

**Figure 1:** The central metallic island (bright) forms a circuit node of a quantum circuit. It is electrically connected through several quantum conductors tuned by field effect using voltage biased gates (blue, green and yellow).

**Figure 2:** Development of a quantum phase transition observed through the temperature evolution of the conductance across three quantum point contacts connected to a small metallic island.

- Non-local electron quantum state transmission with Coulomb interaction (Science, 2019)
- Circuit engineering of a record quantum coherence length of 0.25mm for electrons in conductors (Phys. Rev. X, 2019)
- Analog quantum simulation of 1D electron physics with tunable circuits (Phys. Rev. X, 2018)
- Tunable quantum criticality and super-ballistic transport in a circuit (Science, 2018)
- Controlling charge quantization with quantum fluctuations (Nature, 2016)
- Observation of the 'charge' Kondo effect (Nature, 2015)
- Correlated 1D (Tomonaga-Luttinger) physics in composite quantum circuits (Nature Communications, 2013)
- An important step towards the knowledge of the quantum laws of electricity (Nature Physics, 2011)

**Transmitting the quantum state of electrons across a metallic island with Coulomb interaction**

H. Duprez, E. Sivre, A. Anthore, A. Aassime, A. Cavanna, U. Gennser, F. Pierre

Science 366, 1243 (2019)

**Macroscopic electron quantum coherence in a solid-state circuit**

H. Duprez, E. Sivre, A. Anthore, A. Aassime, A. Cavanna, A. Ouerghi, U. Gennser, F. Pierre

Phys. Rev. X 9, 021030 (2019)

**Circuit Quantum Simulation of a Tomonaga-Luttinger Liquid with an Impurity**

A. Anthore, Z. Iftikhar, E. Boulat, F.D. Parmentier, A. Cavanna, A. Ouerghi, U. Gennser, F. Pierre

Phys. Rev. X 8, 031075 (2018)

*Physics Viewpoint:* Physics 11, 94 (2018)

**Tunable Quantum Criticality and Super-ballistic Transport in a 'Charge' Kondo Circuit**

Z. Iftikhar, A. Anthore, A.K. Mitchell, F.D. Parmentier, U. Gennser, A. Ouerghi, A. Cavanna, C. Mora, P. Simon, F. Pierre

Science 360, 1315 (2018)

**Controlling charge quantization with quantum fluctuations**

S. Jezouin, Z. Iftikhar, A. Anthore, F.D. Parmentier, U. Gennser, A. Cavanna, A. Ouerghi, I.P. Levkivskyi, E. Idrisov, E.V. Sukhorukov, L.I. Glazman, F. Pierre

Nature 536, 58 (2016)

*Nature News & Views:* Nature 536, 38 (2016)

**Two-channel Kondo effect and renormalization flow with macroscopic quantum charge states**

Z. Iftikhar, S. Jezouin, A. Anthore, U. Gennser, F.D. Parmentier, A. Cavanna, F. Pierre

Nature 526, 233 (2015)

*Nature News & Views:* Nature 526, 203 (2015)

**Tomonaga-Luttinger physics in electronic quantum circuits**

S. Jezouin, M. Albert, F.D. Parmentier, A. Anthore, U. Gennser, A. Cavanna, I. Safi, F. Pierre

Nature Commun. 4, 1802 (2013)

**Strong back-action of a linear circuit on a single electronic quantum channel**

F.D. Parmentier, A. Anthore, S. Jezouin, H. le Sueur, U. Gennser, A. Cavanna, D. Mailly and F. Pierre

Nature Physics 7, 935 (2011)

**Experimental Test of the Dynamical Coulomb Blockade Theory for Short Coherent Conductors**

C. Altimiras, U. Gennser, A. Cavanna, D. Mailly, F. Pierre

Phys. Rev. Lett. 99, 256805 (2007)