Zaki Leghtas

1. Centre Automatique et Systèmes - Mines ParisTech

2. Laboratoire de Physique - Ecole Normale Supérieure de Paris

3. Quantic team - INRIA Paris

Superconducting circuits and Schrödinger’s cat

Superconducting circuits

1 cm

𝑓 ≈ 5 GHz, 𝑄 ≈ 106−8

= S SINon-linear element

100 nm × 100 nm

High quality cavity

=

Josephson junction

Tfridge= 10 mK

arXiv: 1905.13641

QubitHarmonic oscillator

Superconducting circuitsSuperconductivity Long lifetimeJosephson effect Large nonlinearityTelecom industry Precise qubit control

Semiconductor industry Complex architectures

Devoret and Schoelkopf, Science (2012) Rigetti computing arXiv:1712.05771

m

How to protect quantum information against errors ?

Protected qubitOverhead " × 𝟏𝟎𝟑"

error

Physical qubit

My Goal: Reduce hardware overhead

Environment

quantum error correction

error

| ۧ1

| ۧ0

𝑉

𝐼Q

The Cat-Qubit: a solution to scalability

Overhead: " × 𝟏𝟎"

Gates: rotations in phase-space

| ۧ1| ۧ0

High quality resonators

Nonlinear interactions

Gates

| ۧ1

Cat-Qubit: non local

Standard qubit: local

| ۧ0

exponentialsuppressionof errors

errors

Leghtas et al. Phys Rev Lett (2013), Mirrahimi, Leghtas et al. NJP (2014), Leghtas et al. Science (2015)

𝑉

Preliminary data: exponential suppression of errors

𝟏 m𝒔

× 𝟒𝟎𝟎𝑇 error(𝜇𝑠)

Target: 1 second (× 106)

=

× 8 standard error correction by Google group: Nature (2015)

distance between states

25 μm

standardqubits

102

103

2 6

Roadmap towards a scalable protected qubit

New: Guillaud, Mirrahimi arXiv:1904.09474 (2019)

2 qubit gate

3 qubit gateLinear repetion code

Building block for universal fault-tolerantquantum computation

1 qubit gate

Summary

Build a protected qubit

Overcome hardware overhead for quantum error correction

MazyarMirrahimi

PierreRouchon

AlainSarlette

TakisKontos

MatthieuDelbecq

AudreyCottet

ZakiLeghtas

Quantum circuits: theory and experiments