Quantum Technology 101: Overview of Quantum Computing and Quantum Cybersecurity

Transcription

1 Quantum Technology 0: Overview of Quantum Computing and Quantum Cybersecurity Warner A. Miller* Department of Physics & Center for Cryptography and Information Security Florida Atlantic University NSF CAE-R Hudson Institute's Conference on The Coming Quantum Revolution: Security and Policy Implications, 7 Oct 7 * Support from AFOSR/AOARD under intelligent Convergence Cyber Security Systems (ics) contract FA

2 Outline (Quantum Information Science) Quantum 0 Quantum Computing 0 Quantum Cryptography 0 Richard P. Feynman John Archibald Wheeler

3 The Problem I have as the Speaker Today If somebody says that they can think about quantum physics without becoming dizzy, that shows only that they have not understood anything whatever about it. Niels Bohr Never express yourself more clearly than you think. Niels Bohr

4 Delayed Choice Experiment W. A. Miller & J. A. Wheeler, Delayed-Choice Experiments and Bohr's Elementary Quantum Phenomenon," Proc. Int. Symp. Foundations of Quantum Mechanics, ed. S. Kamefuchi, Tokyo, (984) 40-5.

5 Delayed Choice on a Cosmic Scale ESA/Hubble, NASA, Suyu et al. : HE Miller & Wheeler

6 Quantum: Observer-Participatory Universe Quantum mechanics promotes the mere observer of reality to participator in the defining of reality. John Archibald Wheeler

7 The Quantum State: Distinguishability and Complementarity

8 Qubit, Hilbert Space & Superposition Principle li i = v li + h $i i = 0 0i + i P =.%i

9 Quantum Computers Scale Exponentially Too: In the number of qubits not in years {z } 3 qubit state i 00i 000i Classical DRAM Quantum Bits 64 KB 0 64 MB 0 64 GB Exabyte 60 Quantum Supremacy

10 The Power of Quantum Entanglement

11 Entangled Quantum State of Two Photons i = p ( 00i + i) 6= i i

12 Conventional vs Quantum Computing Quantum Computation: Interference (Entanglement) of many states Many single distinguishable classical inputs Conventional Parallel Computer x x Classical result ψ = φ Single quantum input: superposition of many classical-like states Quantum Computer Quantum Information (i) Information encoded in the physical states of atomic-level systems (qubits) Quantum Parallelism vs Conventional (ii) Superposition state: system can be in many states simultaneously (iii) Input state into quantum computer = all classical inputs simultaneously (iv) Exponentially larger state space of information Parallelism n qubits (physical systems) can hold n classical bits of info 50 ~ 0 5 bits ~ 00TB (0X Library of Congress), 00 ~ 0 30 bits ~ 0 7 TB Quantum Computers: Current Status Theoretical Foundations: established/sound Decoherence (environmental noise) Currently: dozens Measurement: classical-like result Classes of Quantum Algorithms Quadratic speedup: exhaustive search, optimization, k-sat Exponential speedup: uncover hidden structure using the Quantum Fourier Transform; f(x) where A x = b (Lloyd)

13 The challenge: classical chips hit a wall Moore s Law Dennard scaling comes to an end (Power density constant as # transistors doubles) Problem: transistor gates too thin at ~00nm; current leaks into substrate Dr. Daniel Lidar, ISI/USC

14 Quantum Circuit & Timelessness of the Quantum David DiVincenzo Criteria A scalable physical system with well characterized qubits The ability to initialize the state of qubits to a simple fiducial state Long decoherence times relative to the time of gate operations A universal set of gate operations A qubit-specific measurement capability OUT = U b QC IN N partite N N

15 Quantum Computing: Many Choices for qubits A blueprint for building a quantum computer, R.V. Meter & C. Horsman, Comm. of the ACM 56, 84 (03)

16 Quantum Information Processing Levels Quantum Annealing Quantum tunneling to minimum Quantum Simulation Partial qubit control Universal Quantum Computing David Deutsch Full control of every qubit Fault tolerant computing (quantum error correction) Peter Shore

17 Wojciech H. Zurek

18 Decoherence and Quantum Error correction D R ~ x p mk b T W. H. Zurek, arxiv:quant-ph/ Classical error correction makes use of redundancy, i.e. cloning. No quantum cloning. Quantum states cant be cloned; however, P. Shor utilized entanglement to reveal errors and not destroying the superposition.

19 No Cloning a Quantum State li =) lli.%i =).%.%i == li + $i p $i =) $$i.%i = li + $i p li + $i p =) Zurek & Wootters = = lli + $$i p lli + l$i + $li + $$i

20 Mutually Unbiased Bases n= Horizontal Vertical Rigt Diagonal Left Diagonal Right Circular Left Circular 0 li = 0i.%i = li + $i p i = li + i $i p 0 $i = i -&i = li $i p i = li i $i p

21 Quantum Key Distribution and Bit Error Rate n= n= BER T = n n + = BER Threshold: 33% for n = 67% for n =5 Eve s chance of picking correct sorter j for the state Bob gets correct result but Eve knows n + n + If Bob gets correct result with probability BER<BER T, then Eve can be marginalized at the expense of bandwidth using classical privacy amplification Can t clone Eve sends wrong state Bob gets correct result from Eve s wrong choice n n n + n n +