Quantum Technologies in the 21 century Eugene Demler Harvard University

Quantum Physics AtomsMoleculesNucleiMaterials Fundamental questions Important applications

3 Moore‘s law From Gordon Moore “No exponential if forever” faster = smaller Every 18 months computer power doubles

Suppress quantum Our alternatives: Exploit quantum H Y = E Y “Quantum Technology is a radical departure in technology, more fundamentally different from current technology than the digital computer is from the abacus”. William D. Phillips,1997 Physics Nobel Laureate

“When we get to the very, very small world – say circuits of seven atoms - we have a lot of new things that would happen that represent completely new opportunities for design. Atoms on a small scale behave like nothing on a large scale, for they satisfy the laws of quantum mechanics…” “There's Plenty of Room at the Bottom” (1959) Richard Feynman

Quantum Computers Exponential speed up of number factoring Shor (1994) Quadratic speed up in database search Grover (1996) Highlights

Bits and Qubits A quantum bit (qubit) is the quantum mechanical generalization of a classical bit, a two-level system such as a spin, the polarization of a photon, or ring currents in a superconductor. Classical bit Physical realization via a charged/uncharged capacitor Quantum objects are waves and can be in states of superposition Qubit spin ring-current photon polarization

Classical & quantum gates The combination of the classical gates allows us to construct all manipulations on classical bits. Is there a set of universal quantum gates ? How does such a set look like ? Manipulation of a quantum bit is much richer than of a classical bit. We can perform rotations around the x -, y -, and z - axis Two-qubit gate gate: XOR (CNOT) Includes entangling gates

Quantum registers  =a 0 [000] + a 1 [001] + a 2 [010] + a 3 [011] a 4 [100] + a 5 [101] + a 6 [110] + a 7 [111] Parallel quantum information processing

Quantum computing = smart computing Example: need to find the tallest wooden block Traditional computing: measure every block and compare them. Smart computing: bring blocks together and check which of them stands out. Requires new types of operations!

Example: Deutsch’s algorithm (1985) We are given a 1-bit function f(x): one bit in, one bit out. → Is f(x) constant or balanced? x f(x) x f(x) x f(x) x f(x) 0 1 f(x) = 0f(x) = x f(x) = 1 constantbalanced classically, require 2 queries to determine whether f(x) is constant or balanced Quantum computers use “massive quantum parallelism” to speed up computations

[0] + [1] x → x y → y  f(x) [0]  [1] [0]  [0][1] +[1][0]  [1][1] [0][f(0)  f(0)] +[1][f(1)  f(1)] single (quantum) query measure [0  1][0  ] if f(x) constant [0  1][0  1] if f(x) balanced [0][0  ] if f(x) constant [1][0  1] if f(x) balanced

Quantum computing = smart computing Quantum Factoring P. Shor (1994) Second example 15= 3  = ?  ?

Quantum Factoring A quantum computer can factor numbers exponentially faster than classical computers Look for a joint property of all 2 N inputs e.g.: the periodicity of a function f(x) = sin(2  x/p)p = period P. Shor (1994) f(x) = a x (Mod N)r = period (a = constant)

Whose phone number is ? Grover’s search algorithm Unsorted database search Grover algorithm sees all entries at once, marks the right answer and amplifies it. Geometrical interpretation: state vector rotates towards the answer every iteration Number of steps O(N 1/2 ) vs O(N)

Quantum Hardware

Candidate Qubits A cross-disciplinary race NMR ions Quantum dots Photons in optical cavities Atoms in cavities Superconducting charge and flux based

Trapped Atomic Ions Yb + crystal ~5  m 8 qubits Record holders in the numbers of q-bits and complexity of operations 8-qbits in 2006

Science 2009 Nature 2009

Elements of a successful quantum computer Existence of coherent qubit system Isolation from environment for sufficient time Universal set of gates. Reproduce all operations Initialization Begin calculations from well defined initial state Readout Ability to access and read qubits Scalability Necessary to increase the number of bits without fundamental change in strategy Your name

Other QC designs: Nitrogen + Vacancy impurity in diamond Fluorescence of an array of single impurities in diamond Most recent QC designs: NV Centers in Diamond Room temperature quantum computing M. Lukin (Harvard)

Other QC designs: Most recent QC designs: Topological QC A. Kitaev (2003) Landau Institute/Caltech n =5/2 state is a quantum topological state which allows topological quantum computations Microsoft Q Station is fully devoted to topological QC Cost: about 20 million in the last 5 years

Quantum Technologies beyond quantum computing Quantum computers with thousands of bits, which can be used to factorize large numbers are still several years away. Already now quantum technology has important applications

World’s most precise clocks The new aluminum clock would neither gain nor lose one second in about 3.7 billion years It employs the logical processing used for atoms storing data in experimental quantum computing Compact versions of super-precise atomic clocks can be the basis for navigational systems of the future. They may eliminate the need for human drivers NIST’s “quantum logic clock” based on Al ions is world’s most precise clock Accuracy of GPS is determined by the precision of clocks. Current accuracy of the order of meters. Needed centimeters.

Quantum sensing and imaging Nitrogen vacancy color Center in diamond combined with quantum information processing can be used for ultra high resolution magnetometry Potential applications for real-time, non-invasive imaging in medecine

Quantum Communications

Needed for the world soccer Cup in Russia in 2018? Critical communication link in the 2010 World Soccer Cup used quantum technology

Solving fundamental problems with quantum technology Open challenges in physical sciences Understand and design quantum materials one of the biggest challenges in Physics in the 21 century High temperature superconductivity ( electricity) Magnetism (d ata storage) 10-20% of electric power is lost in transmission. This problem can be solved by creating lossless transmission lines from high temperature superconductors

Why we can not solve these problems with conventional computers Example: Electrons on a lattice. S System underlying many solid state and materials problems. Magnets, High Temperature Superconductors, Spintronics, …

Each doubling allows for one more spin ½ only

Modeling: from airplanes to wind-tunnels Quantum simulations: understanding high Tc superconductors using artificial quantum systems

Concluding remarks

International Centers for Quantum Sciences and Technology Harvard-MIT Center For Ultracold Atoms, Boston USA Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck, Austria The Institute for Photonic Sciences Barcelona, Spain Max Planck Institute of Quantum Optics Munchen, Germany

Needed: Quantum Center in Russia International, interdisciplinary Center of excellence focused on exploring a new area of quantum science & technology Key component: a new model of research institute based in Russian Federation (RF) Goals: obtain fundamental understanding of complex quantum systems & their control, train new generation of scientists & engineers, develop quantum processing technologies, including Ultra-fast information processors Absolutely secure communication systems High precision navigational and time-keeping systems All-optical energy efficient communication/processing Novel quantum materials with properties designed on demand Novel energy harvesting technologies Ultra-sensitive quantum biomedical diagnostic technologies 34

The first solid-state transistor (Bardeen, Brattain & Shockley, 1947) The first solid state transistor Bardeen, Brattain & Shockley, 1947

Albert Einstein ( ) Erwin Schrödinger ( )Werner Heisenberg ( ) Quantum Mechanics: A 20 th century revolution in physics Quantum objects are waves and can be in states of superposition.

…BAD NEWS! decoherence Decoherence: A peculiarly quantum form of noise that has no classical analog. Decoherence destroys quantum superpositions and is the most important and ubiquitous form of noise in quantum computers 2. Rule #1 holds as long as you don’t look! [1] [0] [0] & [1] or 1.Quantum objects are waves and can be in states of superposition. “qubit”: [0] & [1]

1. Individual atoms and photons ion traps atoms in optical lattices cavity-QED 2. Superconductors Cooper-pair boxes (charge qubits) rf-SQUIDS (flux qubits) 3. Semiconductors quantum dots 4. Other condensed-matter electrons floating on liquid helium single phosphorus atoms in silicon scales works Quantum Computer Physical Implementations

1981. First idea: Feynman q. simulator Shor’s algorithm; Cirac-Zoller gate Diverse approaches qubit gates Quantum byte (trapped ions) Error correction threshold reached Start of q. comp (Trapped ions, neutral atoms, cavity QED, semiconductor, superconducting, linear optics, impurity spins, single molecular cluster, NMR,...) 2015 (?). Few qubit quantum processors Q. simulators timeline for quantum computation timeline for quantum computation

Current status Small-scale (<100 km) quantum networks realized, early commercialization efforts Challenges: speed, distances

Albert Chang (Duke Univ.) Other QC designs: Single electron quantum dots

Albert Einstein ( ) Erwin Schrödinger ( )Werner Heisenberg ( ) Quantum Mechanics: A 20 th century revolution in physics Quantum objects are waves and can be in states of superposition.

44 Quantum Key Distribution via photon qubits through air or optical fibers

45 Nuclear magnetic resonance First realization of Quantum Computer: NMR

1. Individual atoms and photons ion traps atoms in optical lattices cavity-QED 2. Superconductors Cooper-pair boxes (charge qubits) rf-SQUIDS (flux qubits) 3. Semiconductors quantum dots 4. Other condensed-matter electrons floating on liquid helium single phosphorus atoms in silicon scales works Quantum Computer Physical Implementations

Quantum communications Quantum teleportation for information transmission Small-scale (<100 km) quantum networks realized Memory elements connected by quantum channels Quantum conversion between light and matter