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TRANSCRIPT
Farzan Jazaeri and Jean-Michel Sallese
Quantum computers
June, 2019
Ecole Polytechnique Fédérale de Lausanne
Table of Contents
o Timeline of quantum computers. o Why we need a quantum computer? o Qubits and how a qubit works? o How to build a quantum computer. o Cryogenic solid state physics and electronics.
I. Classical computers have enabled amazing things.
II. There are still problems we just can’t solve!
Two obvious facts
Where to use a quantum computer?
4
o Quantum circuits can solve some important problems with exponentially fewer operations than classical algorithmes.
o To simulate nature, we should build a quantum computer.
o There is a very big debate about the “actual quantumness” of the D-wave.
o Non-universal quantum gate computer.
Where did this idea come from?
Quantum bit (qubit)
A qubit can be zero and one at the same time!
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|0> (grounded state) |1> (exited state)
α02 and α1
2 give the probability of finding 0 or 1 after the measurement.
|> =
Why is a quantum computer different?
A quantum state is a superposition of classical states
Most mysterious aspects of qubit => quantum teleportation
o Quantum physics: instantaneous action at distance! o Contrary between quantum Physics and relativity.
Excited
State
Ground
State
Nucleus
Light pulse of
frequency
Electron
State |0> State |1>
How a qubit works?
How a qubit works?
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Excited
State
Ground
State
Nucleus
Light pulse of
frequency
Electron
State |0> State |1> State |0> + |1>
How to build a quantum computer?
DiVincenzo criteria for quantum computers: o A scalable physical system o Ability to initialize the state of the qubits o Long relevant decoherence longer than the gate operation time; o A universal set of quantum gates o A qubit-specific measurement capability
How to build a quantum computer?
• Superconducting qubits are the building block of D-wave machines and key focus of qubit activities at IBM and Google.
Google with the first quantum correction algorithm with a superconducting quantum
circuit with nine qubits [Kelly et al., Nature 519, 66 (2015)]
Nuclear Magnetic Resonance
o A nuclei in a strong static magnetic field are perturbed by a weak oscillating magnetic field.
o The oscillation frequency matches the intrinsic frequency of the nuclei.
o Static magnetic fields up to 20 tesla o The frequency is similar to VHF and UHF television broadcasts (60–
1000 MHz)
Implementation of quantum computers
o At very low temperature in
strong static magnetic field we
have qubits.
o Qubits are carbon nuclei.
o Tiny magnets.
o Electromagnetic radiation to
manipulate the qubits.
28 nm split-gate FDSOI technology
CMOS-compatible Qubit & Read-Write Tools
Silicon-based spin qubits
http://www.mos-quito.eu
Scalable qubit-control architecture?
• silicon qubits are far more compact
Analog-RF Cryo-CMOS
for Qubit control
CMOS-compatible Qubit & Read-Write Tools
http://www.mos-quito.eu
Silicon-based spin qubits
Scalable qubit-control architecture?
28 nm split-gate FDSOI technology
• silicon qubits are far more compact
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Silicon-based spin qubits Now the question, how to manipulate spin state of the electron in such qubits?
Electric spin resonance (EDSR): to control the magnetic moments inside a
material. We can flip the orientation of the magnetic moments through the use
of electromagnetic radiation at resonant frequencies.
CMOS-compatible Qubit & Read-Write Tools
Scalable qubit-control architecture?
28 nm split-gate FDSOI technology
• silicon qubits are far more compact
http://www.mos-quito.eu
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Double Quantum-dot System
[Electrically driven electron spin resonance mediated by spin-valley-orbit
coupling in a silicon quantum dot. npj Quantum Information, 4 6, 2018.]
Edge Quantum dots can provide a practical solution to fabricate spin quibits with minimum complexity.
o Electrons can be transferred from one quantum dot to the other
o Using a RF reflectometry technique with resonant frequency of few hundred MHz.
o Variations in the charge of the edge dots, (tunneling transitions) cause a small shift in the resonance frequency which can be detected in the amplitude and phase of the reflected signal.
RF reflectometry technique
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Double Quantum-dot System
[Electrically driven electron spin resonance mediated by spin-valley-orbit
coupling in a silicon quantum dot. npj Quantum Information, 4 6, 2018.]
Edge Quantum dots can provide a practical solution to fabricate spin quibits with minimum complexity.
DC transport spectroscopy of edge-state quantum dots
[From Voisin et al, Nano Lett. 14, 2094 (2014)]
RF reflectometry technique
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Silicon-based spin qubit [Electrically driven electron spin resonance mediated by spin-valley-
orbit coupling in a silicon quantum dot. npj Quantum Information,
4 6, 2018.]
• The valley eigenstates (v1 and v2 ) are separated by a magnetic field.
• Pauli blockade regime can be achieved: QD1 acts as an effective “spin filter” regulating the current flow induced by EDSR in QD2.
Pauli Spin Blockade: A Map of the current Ids.
Measured drain current Ids as function of the
magnetic field B and microwave frequency ν. The
gates are biased in the spin-blockade regime. Spin–orbit coupling (SOC)
Electric-dipole spin resonance (EDSR)
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Important phenomena at cryogenic
● Incomplete ionization, 𝑁𝐴− 𝑇
100 mK − 77 K
● Decreased phonon scattering
● Hot-carrier effects
● Fermi–Dirac and Boltzmann statistics 𝑇
● Intrinsic carrier concentration 𝑛𝑖 𝑇
● Band gap widening, 𝐸𝑔 𝑇
● Velocity saturation, φms, Thermal voltage 𝑇
Important phenomena
● Quantum confinement
● Dominant impurity / surface
roughness scattering
● Interface charge trapping, 𝐷𝑖𝑡
A.Beckers, F. Jazaeri and C. Enz, "Cryogenic MOS Transistor Model," in IEEE Transactions on Electron Devices, 2018.
Farzan Jazaeri and Jean-Michel Sallese, “Modeling Nanowire and Double-Gate Junctionless Field-Effect Transistors,” Cambridge University Press, 2018
Summary: State of the Art • When can we expect the first quantum computer? • Quantum circuits can solve some important problems
with exponentially fewer operations than classical algorithmes.
• Two important properties: superposition and entanglement => They are just different!
• Quantum states are very fragile. • Extremely hard to build. The field is still in its infancy path. • Several fields have contributed to quantum computation:
• Quantum mechanics, Computer science, Information theory, Cryptography
• Quantum cryptography is nowadays commercially available.
Thank you for your attention!
Classical vs. Quantum Circuits
Toffoli gate (CCNOT gate): If the first two bits are both set to 1, it inverts the third bit.