Quantum Computing: a Treasure Hunt, not a Gold Rush
Quantum computers promise a significant step up in computational power over conventional computers, but also suffer a number of counterintuitive limitations --- both in their computational model and in leading lab implementations. In this talk, we review how quantum computers compete with conventional computers and how conventional computers try to hold their ground. Then we outline what stands in the way of successful quantum ML applications.
3. ERROR-FREE QUANTUM ALGORITHMS
• No new decision powers (proof by simulation)
• No NP-complete problems solved exactly in poly time
• No asymptotic speed-up for sorting, etc
• Hence, no universal speed-up
• No speedup from single gates expected
• Main promise is in accelerators
• Surprisingly few good applications
• Surprisingly difficult to build hardware
4. NOISE AND ERROR CORRECTION
• Entangled states globalize noise & errors:
local faults have global effects
• No error masking by gates
• Errors accumulate multiplicatively:
• 500 gates with 0.995 fidelity
0.995500 ~ 0.082 circuit fidelity
• Error correction by duplication and majority not available
• Quantum error correction has much greater overhead
9. DILEMMA FOR NISQ APPS
1. Known computational problems + inputs relevant to applications
• Asymptotically optimal algorithms
• Good heuristics exploit problem structure
• Big data need big memory and wide I/O
• Ongoing improvements in algorithms and HW
2. Emerging and made-up problems + contrived inputs
• What quantum computers do best, may be useless
• Baseline for conventional computing unknown & likely to improve
• Recent leaps in massively parallel simulation, HW improvements
10.
11.
12. • Input: description of a quantum circuit
• Defines the probability distribution
of measurement outcomes
• Output: samples from the distribution
• Some error allowed (approximation)
• Hardness results for certain circuits
(under mild assumptions)
• Worst-case and average-case results
• Exact sampling on classical computer
• Approximate sampling
• “Imminent availability” on QCs
CIRCUIT SAMPLING PROBLEMS
13. FROM AMPLITUDES TO SAMPLES
• A quantum computer: one amplitude at a time <x | U y>
• How many amplitudes does a simulator need to produce on n qubits?
• One is not enough
• 2n are way too many
• Basic rejection sampling
• Pick M values of y uniformly at random
• r = <x | U y>, then p(y) = r r*
• Discard all y with p(y) > M/2n
• Accept each y with probability p(y) 2n / M
• For n=49 and statistical error 10-4, need M = 41
• Frugal rejection sampling: M’ =10 (arxiv:1807.10749)
• Verification
• Let QC pick y at random
• Compute r=<x | U y>
• Check if p(y) = r r* is heavy
• OR estimate cross-entropy
14. THE NEED FOR FAST CIRCUIT SIMULATION
• To validate QC
• To evaluate architectures and error correction
• To debug and improve QCs
• To set a performance baseline for QC claims
• To price QC
18. 5x9 qubits
642 gates, depth 26
Saving 100000 amplitudes
One Xeon server with 96 threads (2.0GHz)
20 min, 17.4 GiB peak RAM, $0.24
STEP TWO
19. NISQ CIRCUITS
Leaky faucets
• Qubits decay
• Quantum gates err
• Errors accumulate without QECC
Unfair competition for common simulators
• Simulated states are stable
• Simulated gates are exact
20. APPROXIMATE SIMULATION OF NISQ CIRCUITS
• Quantum computers lose
information with every gate
a) verify answer & repeat
b) each answer is a vote
• Simulators can stay just above
that data-loss rate…
while using reasonable
memory and runtime
22. REACTION FROM GOOGLE
Make the benchmarks harder,
but still feasible on Q computers
• Use q.gates that are
harder to simulate : iSWAP vs CZ
• Apply more gates in parallel
• Reorder gates
to complicate simulation
24. QC AND ML?
• Need to reliably show “strong” quantum supremacy
• Processing large amounts of data on a QC
• “Large” – more than a few hundred floats
• Quantum algorithms with scalable advantage
• Many of the candidates have been “dequantized”
• Simulation of QCs:
• Helps in design
• Indispensable in verification
• Also a performance competitor