QIndia Qoffee-o-clock

2. {quantum} computation
〈 past | now | future 〉
Aritra Sarkar
19th June, 2021
Qoffee o’clock at QIndia, QWorld

3. What is science?
• Make predictions?
– usefulness of the scientific process
• Make models?
– easier to semantically explain (?)
– ontologically closer (?)

4. How to choose a model?
• Occam’s razor
– less assumptions
– minimal set of axioms

5. Axiomatization of mathematics
• Like Euclid did for geometry
• Find this “set of axioms” for arithmetic
Complete
Consistent
Decidable
all true mathematical statements can be proved
no contradiction can be obtained
existence of an algorithm for deciding the
truth or falsity of any mathematical statement

6. Universal Turing Machine
TSP multiplication
sorting
… …

7. Church-Turing thesis
Universal
TM
λ
Calculus
Post
Machines
Cellular
Automata
Wang
Tiles
…
algorithm a
physical
process
implementation
TM
implementation
LC
implementation
CA
…
TMa*Ca CAa*Ca
LCa*Ca
TMa= LCa*n[LC:TM]
TMa= CAa*n[CA:TM]
CAa= LCa*n[LC:CA]
CAa= TMa*n[TM:CA]
LCa= TMa*n[TM:LC]
LCa= CAa*n[CA:LC]
problem size n

8. The computing revolution

9. The quantum revolution
understand the new rules of QM that govern existing physical reality

10. Postulates of QM

11. Interpretations and testability
• Most successful set of theory so far: QM + GR + SM
• Axioms are adhoc (?)
• What is “real” ?
• Interpretations:
– needs no interpretation
– Copenhagen
– Many-worlds
– Pilot-wave
– Transactional
– Two-state vector
– QBism
– Relational
– QDarwinism
“New interpretations appear every year.
None ever disappear.” - N. David Mermin

12. Learn by doing
ψ𝑆𝑦𝑠 ψ𝑄𝐶
𝑈𝑆𝑦𝑠 𝑡 ψ𝑆𝑦𝑠 𝑈𝑄𝐶 𝑡 ψ𝑄𝐶
𝑒−𝑖𝐻𝑆𝑦𝑠𝑡
ψ𝑆𝑦𝑠 𝑒−𝑖𝐻𝑄𝐶𝑡
ψ𝑄𝐶
Initialize
Evolve
Measure
from Science... to Technology
actively employing QM to alter the quantum face of our physical world
engineer and control quantum states

13. Church-Turing-Deutsch thesis
Gate-based
QC
Universal
TM
Universal
QTM
…
algorithm a
quantum
process
implementation
CC
implementation
QC
CCa*Ca QCa*Ca
CCa= QCa*[QC:CC]n
problem size n
Adiabatic
QC
Cellular
Automata
…
λ
Calculus

14. QC models
• Circuit model (a.k.a. Gate based QC; standard model of QC)
– most researched; similarity with Boolean logic
• Topological QC
– adiabatically braiding with anyons to execute discrete logic gates
• Measurement based QC (a.k.a Cluster state QC; One-way QC)
– prepare entangled resource state, perform single qubit measurements on it
• Adiabatic QC
– adiabatically evolve ground state of easy Hamiltonian to ground state (solution) of hard (problem) Hamiltonian
– Quantum Annealers (e.g. D-Wave) is a heuristic based on AQC and diabatic evolutions
• All these QC models are equivalent (?)
• Each of them can simulate an UQTM and each other, within polynomial factors (?)
– For any arbitrary algorithm A
• if A takes x time/steps/cycles in Model 1
• it would take atmost x.nk in Model 2 (n is the problem size; k is a constant)
– Any exponential speedup (e.g. Shor’s algorithm) w.r.t CC gets preserved in the translation
– Porting to another model might cancel the benefit; if, the speedup w.r.t. classical algorithm is polynomial

15. Room at the bottom of Hilbert space
• The math is rather easy!
– Generalizing probability to complex numbers
– How about 2 qubits?
• 22 = 4 complex numbers = 8 real numbers
– How about 265 qubits?
• 2265 ≈ # atoms in the Universe!
• You cannot classically simulate 265 qubits! (quantum supremacy)
|ψ ⟩ =
𝑖=0
2𝑛−1
𝛼𝑖|𝑖⟩
On measurement
|ψ ⟩ = |𝑖⟩ with 𝑃 |𝑖⟩ = 𝛼𝑖
2
𝛾0
𝛾1
𝛽0
𝛽1
𝛾0𝛽0|00⟩ + 𝛾0𝛽1|01⟩ + 𝛾1𝛽0|10⟩ + 𝛾1𝛽1|11⟩
⊗
|1⟩
|0⟩
p+
𝑖=0
2𝑛−1
𝛼𝑖
𝑟𝑒2
+ 𝛼𝑖
𝑖𝑚2
= 1
𝛼0
𝛼1
𝛼0
𝛼1

16. It from Qubit
lion
wolf
tiger
dog
cat

17. Quantum algorithm
Superpose
Soln. Space
Encode
Function
Clever
Process
Measure
Initialize
|0⟩⊗n
Classical
Output
Classical
Input
C
B
A D
C
B
A D

18. Slowdown of Moore’s law
• # transistors on IC x2 in 18 months
– Core of digital revolution
• New applications
• Economy
– Various enabling factors
• Algorithms
• Deep UV photolithography
• Slowdown?
– Quantum tunneling
– Heat, von Neumann bottleneck
• Alternate technology?
Computers are
not getting
better at
Exponential
rate
Human data
processing
needs are
growing at an
Exponential
rate
Need for
radically
different
computing
technologies

19. Quantum accelerators
Algorithms
Gate-based circuit
eQASM/QISA
Routing and
mapping
Error-correction
Micro-coded
analog pulses
Cryo-electronics
Quantum chip
Simulator

20. NISQ era
• let’s make qubits!
• errr…. errors!
– Environment isolation
• Freeze it down – superconductors
– Quantum Error Correction!
• Shor’s code, Steane code, Surface
code
• Error threshold
• Universal QC to Q Accelerators
• FTQC to NISQ
NISQ
FTQC
QEC
Classical
Simulation
Limit
number of qubits
error
rate

21. Quantum software 2.0
• Software 1.0 - explicit instructions to the computer written by a programmer
• Software 2.0 - specify desirable behavior of a program and search

22. Roads to quantum advantage
PISQ
NISQ
FTQC
Algorithm
Proof
Application
Demonstration
Quantum supremacy
Quantum application
Quantum hybrid use-case
Quantum algorithm
Quantum processor

23. what CC can
compute
what QC can
compute
what QC can
compute efficiently
what CC can
compute efficiently
what CC can
compute now
what QC can
compute now
what CC will handle
in the near-future
what QC will handle
in the near-future
other
accelerators
‘Practical’ limits of quantum computing

24. ‘Theoretical’ limits of quantum computing
• Quantum Computers is as good as computing gets with our current laws of physics
• Quantum Gravity Computers?
– Sure, it’s possible once we have Interstellar tech.
– not without breaking current laws of physics (like non-linearity in QM, Heisenberg uncertainty limit, light-speed limit,
escaping blackholes, etc.)
– Relativistic QC / Closed-Timelike-Curves

25. Really Big Questions
Why the quantum?
How come existence?
It from bit?
A "participatory universe"?
What makes "meaning"?

26. Law without law
• Law without law: from observer states to physics via algorithmic information theory
– Markus P. Müller (https://doi.org/10.22331/q-2020-07-20-301)
• Every testable part of QM can be derived from Solomonoff induction
– given past data, what’s the most probable data you will see next
– the most probable data is the one which has a shorter program
Program p1: print(“010101010101010101010101010101010101010101010101”)
Program p1: for i in range(0,24):
print(“01”,end=“”)
Program p0/2/3: print(“0101010101010101010101010101010101010101010101xy”)
Program p0/2/3: for i in range(0,23):
print(“01”,end=“”)
print(“xy”,end=“”)
010101010101010101010101010101010101010101010100 l(p0)
010101010101010101010101010101010101010101010101 l(p1)
010101010101010101010101010101010101010101010110 l(p2)
010101010101010101010101010101010101010101010111 l(p3)

27. Quantum Knowledge Seeking Agent
• Participatory agent
• Solomonoff Induction to AIXI (GRL-UAGI)
• Resource constrained EAIT using LEAST metric
• GP and Quine to evolve fitness function on ● ● ● ● ● ?
• Apply to experiments (circuit optimization, Wigner’s friend)
Quines & GP
POMDP

28. QG
CM
QM