QX Simulator and quantum programming - 2020-04-28
0 likes687 views
This document discusses quantum computing simulation and quantum programming. It notes that directly simulating large quantum systems requires exponential resources, but that smart simulation techniques can reduce these requirements. It introduces the QX quantum computing simulator, including its syntax, functionality for noisy circuits, classical control, and parallelism. The document provides examples of simulating simple circuits and algorithms to demonstrate the QX simulator's capabilities.
![26
Reading the output
--------------[quantum state]--------------
(+0.707107,+0.000000) |00> +
(+0.707107,+0.000000) |11> +
----------------------------------------------------
[>>] measurement prediction: | X | X |
-------------------------------------------
[>>] measurement register : | 0 | 0 |
-------------------------------------------
q0q1
The measurement prediction can be 0, 1 or X
The simulator keeps track of the qubit state and can predict perfect measurement outcome.
When a qubit is in superposition, the measurement outcome becomes unknown: X
The measurement register contains the last measurement outcome (0 or 1)
Remark: updated only after measurement!
(0.707107 + i*0.000000) |00> +
(0.000000 + i*0.000000) |01> +
(0.000000 + i*0.000000) |10> +
(0.707107 + i*0.000000) |11> +](https://image.slidesharecdn.com/2020-04-28-qxsimulator-eqcw2-200511114951/85/QX-Simulator-and-quantum-programming-2020-04-28-26-320.jpg)
QX Simulator and quantum programming - 2020-04-28
- 1. QX Simulator and quantum programming EE4575: Electronics for Quantum Computation Week 2 Ir. Aritra Sarkar Dr. Carmen G. Almudever {A.Sarkar-3/C.GraciaAlmudever-1}@tudelft.nl Quantum Computer Architecture Lab Delft University of Technology
- 2. 2 Knowing our limits • 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 level technology • 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 https://www.scientificamerican.com/article/the-limits-of-quantum-computers/
- 3. 3 QC vs. CC • Given the same size QC and CC – QC (QTM) can always simulate CC (UTM) • Universal Gate Sets for QC: (H, Toffoli), (CX, Rx, Rz), (CX, H, T) • Universal Gate Sets for CC: (Toffoli/CCX), (Fredkin/CSWAP), (NAND, Fanout) – NAND: 𝐶𝐶𝑋 𝑎𝑏1 → 𝑎𝑏 𝑎. 𝑏 , FanOut: 𝐶𝐶𝑋 1𝑎0 → 1𝑎𝑎 – CC can always simulate QC (but with worst-case exponential overhead) • QC cannot do super-Turing computation • QC cannot solve NP-Complete problems in P time – Factorial is in BQP (believed to not be NP-C) – If there are no classical divide-and-conquer approach, QC can give a polynomial speedup by Grover search • Why not do everything in QC (since CC is proper sub-set of QC)? – because we don’t have same size QC as CC (HPC, number of GPU cores, etc) – because QC are still too noisy and costly
- 4. 4 Parallelism vs. Superposition • Multiple solutions evaluated in superposition, but cannot access results for every state – Superposition is doesn’t have a classical logic equivalent (e.g. AND/OR) • Useful when used to explore large solution space but requires only the min/max/mean answer Initial Data Parallel Transform Superposition All States embarrassingly parallel no interaction need all answers Not suitable for Q-Acceleration Initial Data Parallel Transform Superposition Central Tendency parallel evolution global/local interactions statistical answer
- 5. 5 BPP vs. BQP • Destructive interference of amplitudes (non-solutions can be made to cancel out) – Generalization of probability theory for complex amplitudes • Not possible in classical probabilistic computing A B C D Initial Data Parallel Transform Superposition of Probabilities Central Tendency parallel evolution global/local interactions statistical answer + +++ ++ ++ CBA D A B C D Initial Data Parallel Transform Superposition of Amplitudes Central Tendency parallel evolution global/local interactions statistical answer - ++ + + CBA D
- 6. 6 Quantum App. Dev. Oracle-based algorithms Full circuit descriptions Functional simulation NISQ implementation FTQC simulation FTQC implementation Physical simulations
- 7. 7 Supremacy – Advantage – Value • Weak Quantum Value • improving solution of any problem, using a QC (possibly in combination with classical methods) so that the results are better than any available purely classical solution • Quantum Value • improving solution of a valuable problem, using a QC (possibly in combination with classical methods) so that the results are better than any available purely classical solution • Weak Quantum Supremacy • solution of any problem using a QC, faster or better than any available classical solution • Quantum Advantage • solution of a valuable problem using a QC, faster or better than any available classical solution • Quantum Supremacy • mathematical proof that any problem has a super-polynomial separation w.r.t. assumptions (e.g. P ≠ NP) between any possible quantum algorithm and any possible classical algorithm • the exhibition of the solution of this problem by a QC at a performance (size, speed, or efficiency) that is infeasible with any available classical computer • Strong Quantum Advantage • Q supremacy + Q advantage (e.g. breaking 2048 RSA with Shor’s algorithm)
- 8. 8 QC simulator – why?
- 10. 10 Quantum simulation 2-qubit system y = a0 a1 a2 a3 æ è ç ç ç ç ç ö ø ÷ ÷ ÷ ÷ ÷ y =a0 00 +a1 01 +a2 10 +a3 11 2N : (N = 2) 50-qubit system? 2N : (N = 50) = 1125899906842624 4N : (N = 50) = 1267650600228229401496703205376
- 11. 11 The cost of simulation • Naive simulation of quantum circuits requires significant resources! • Memory/space: – 2N complex matrix to store the quantum state of N qubits – 2N x 2N complex matrix to store the circuit operations – Total: 2N(1+2N) complex numbers of 16 bytes • Operations/time: – 22N complex multiplications (4 Mul., 1 Add and 1 Sub. each) – 2N(2N-1) ~ 22N complex additions (1 Add.) – Total: 6*22N + 2*22N = 8*22N = 22N+3 FLOPs • For a 25-qubit system: – Memory: 16 777 216.50 GB – Circuit execution time: 3.47 days on an Intel Xeon Processorwith 30GFLOPs/s (double precision) • For a 30-qubit system: – Memory: 17 179 869 200 GB – Circuit execution time: 9.75 years on an Intel Xeon Processorwith 30GFLOPs/s (double precision)
- 12. 12 Feasible? • Exponential simulation complexity • Feasible? Of course not! Not for large number of qubits – Else why build a QC after all? • But how many qubits can we go up to? – About 50-100 in HPC clusters, about 25 on laptops • Why simulate when there are QC with ~100 qubits? • Will the requirement of QC simulators end with better QC?
- 13. 13 Smart simulation N. Khammassi, I. Ashraf, X. Fu, C.G. Almudéver, and K. Bertels, "QX: A high-performance quantum computer simulation platform," in Proc. Designs, Automation and Test in Europe (DATE), Lausanne, Switzerland, March 2017. • How to reduce simulation resource? – Spare Matrix representation – Dynamic state vector representation – Gate operation reduction: substituting permutation matrix operations by swaps, track 0/1 elements – Parallel computation on multicore and multiprocessor platform • Use the structure of the data/operations to our advantage • Worst-case is still exponential – average case is much better
- 14. 14 Conventions cheat sheet Circuits – LSQ on top String representation of state – LSQ on right Vector representation of state – LSQ increments before MSQ Multi-qubit operators |𝑞0 |𝑞1 ... H | … 𝑞1 𝑞0 𝑎|00 𝑎|01 𝑎|10 𝑎|11 𝐼 𝑞1 ⊗ 𝐻 𝑞0 = 1 2 1 1 0 0 1 −1 0 0 0 0 1 1 0 0 1 −1 𝐶𝑁𝑂𝑇𝑐𝑡 = 𝐶𝑁𝑂𝑇𝑞0 𝑞1 = 1 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 𝐶𝑁𝑂𝑇𝑐𝑡 = 𝐶𝑁𝑂𝑇𝑞1 𝑞0 = 1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0
- 15. 15 QX simulator # circuit file qubits 2 h q0 cnot q0,q1 display measure q0 measure q1 display … Input Code cQASM circuit.qc Output Quantum State : (+0.707107,+0.000000) |00> + (+0.707107,+0.000000) |11> + Measurement prediction: | X | X | Measurement register : | 0 | 0 | Quantum State : (+1.000000,+0.000000) |11> + Measurement prediction: | 1 | 1 | Measurement register : | 1 | 1 | Circuit View
- 16. 16 QASM syntax • Program header • Prepare • Gates • Measure • Display • Sub-circuits loops • Measurement based control • Classical operations • Parallelism • Noise model # define qubits qubits 2 .entangle h q0 cnot q0, q1 display .measurement measure q0 measure q1 display_binary 1 2 3 4 5 6 7 8 9 10 11 12 Comment Define number of qubits Sub-circuit definition Hadamard gate CNOT gate • Control q0 • Target q1 Measure in Z-basis Displaycurrent quantum state Displayonly the measurement register
- 17. 17 Disclaimer: “display” • Why is it fake? – Can you really ‘read’ the amplitudes of the wave-function? • What is it fast? – The actual way: Measure multiple times and get the probabilities
- 18. 18 QX syntax
- 19. 19 QX syntax
- 20. 20 Classical controlled gates h q0 measure q0 # measurement outcome in b0 c-x b0, q1 # apply pauli-x to q1 if b0=1 measure q0 measure q1 measure q2 c-x b0, b1, b2, q4 # apply pauli-x to q4 if (b0=1 and b1=1 and b2=1) measure q0 measure q1 # we want to apply a pauli-x to q4 if b0=0 and b1=1 not b0 # invert measurement outcome c-x b0, b1, q4 not b0 # restore measurement outcome • Binary-controlled Gate • Multi-Binary-Controlled Gate • Arbitrary Binary Mask as Gate Control {NOT, AND} is a universalgate-set for Boolean Logic
- 21. 21 Parallelism and Loops qubits 7 .init x q3 h q0 … # iterating 2 times .grover(2) # oracle_1 x q1 x q2 toffoli q0,q1,q4 toffoli q1,q4,q5 toffoli q2,q5,q6 cnot q6,q3 … # inversion x q0 x q1 x q2 h q2 toffoli q0,q1,q2 h q2 … .measure h q3 measure q3 display
- 22. 22 Noisy circuits | |0 |0 H M M M H # simple circuit qubits 3 .circuit h q0 cnot q0,q2 cnot q0,q1 h q0 .measurement measure q0 measure q1 measure q2 # simulator configuration error_model depolarizing_channel,0.01 • Depolarizing channel E Y Z I X Error Probability Circuit under noise
- 23. 23 QX terminal
- 24. 24 QX terminal Executing a circuit: Simulator output :
- 26. 26 Reading the output --------------[quantum state]-------------- (+0.707107,+0.000000) |00> + (+0.707107,+0.000000) |11> + ---------------------------------------------------- [>>] measurement prediction: | X | X | ------------------------------------------- [>>] measurement register : | 0 | 0 | ------------------------------------------- q0q1 The measurement prediction can be 0, 1 or X The simulator keeps track of the qubit state and can predict perfect measurement outcome. When a qubit is in superposition, the measurement outcome becomes unknown: X The measurement register contains the last measurement outcome (0 or 1) Remark: updated only after measurement! (0.707107 + i*0.000000) |00> + (0.000000 + i*0.000000) |01> + (0.000000 + i*0.000000) |10> + (0.707107 + i*0.000000) |11> +
- 27. 27 Demo QX Simulator Exercise 1 Exercise 2 Exercise 3
- 28. 28 Solutions # bitflip qubits 1 x q0 display # hzh qubits 1 .hzh h q0 z q0 h q0 display measure q0 display # h qubits 1 h q0 display measure q0 display Exercise 1 Exercise 2 Exercise 3
- 29. 29 Warmup exercise Exercise 4 Exercise 6 Exercise 5 Exercise 7
- 30. 30 Solutions # cnot qubits 2 .cn x q0 cnot q0,q1 display # cnot qubits 2 .cn cnot q0,q1 cnot q1,q0 cnot q0,q1 display # swap qubits 2 .sw swap q0,q1 display # toffoli qubits 3 .toff x q0 x q1 toffoli q0,q1,q2 measure q0 display Exercise 4 Exercise 5 Exercise 6 Exercise 7
- 31. 31 Teleportation • Transmit 1 qubit – 1 previously shared Bell pair – 2 cbits (nope!! not faster than light) 𝐻 y =a0 0 +a1 1 𝐻 𝑋 𝑍 y =a0 0 +a1 1 Share Bell pair Bell pair measurement Send Decode Received C. H. Bennett, G. Brassard,C. Crépeau, R. Jozsa,A. Peres, and W. K. Wootters in 1993
- 32. 32 Bell test for spooky action https://www.youtube.com/watch?v=AE8MaQJkRcg
- 33. 33 Exercise • Teleportation – 𝛼0 = 0 – 𝛼1 = 1 – What happens when you replace x q0 with h q0? qubits 3 .data x q0 # create |psi> .bell_pair h q1 cnot q1,q2 .encode cnot q0,q1 h q0 measure q0 measure q1 .decode cx b1,q2 cz b0,q2 display
- 34. 34 Superdense coding • Transmit 2 classical bits (opposite of Teleportation) – 1 previously shared Bell pair – 1 qubit • If no shared entanglement, it is impossible to send two classical bits using 1 qubit, as this would violate Holevo's theorem • Necessity of having both qubits to decode the information eliminates the risk of eavesdroppers intercepting messages C. H. Bennett and S. J. Weisner in 1992 H Prepare & Share Bell pair Encode Data Receive & Decode ZX b2 b1 H b2 b1
- 35. 35 Useful resources The QX simulator • N. Khammassi, I. Ashraf, X. Fu, C.G. Almudéver, and K. Bertels, "QX: A high-performance quantum computer simulationplatform," in Proc. Designs, Automationand Test in Europe (DATE), Lausanne, Switzerland, March 2017. • T. Haner and D.S. Steiger, 0.5 Petabyte Simulationof 45-Qubit Quantum Circuit, arXiv prepint1704.01127, 2017. • D. S. Steiger, T. Haner and M. Troyer, ProjectQ: An Open Source Software Framework for Quantum Computing arXiv prepint 1612.08091, 2016. • D. Wecker and K.M. Svore, Liquid:A software design architecture and domain-specific languagefor quantumcomputing, , arXiv prepint 1402.4467, 2014. Papers http://www.quantum-studio.net/
- 37. 37 Take home messages • Q Application dev can continue parallel to QC dev • Worst-case simulation is exponential • Worst-case is rare • Simulators are a good way to understand/develop intuition • Time to start Quantum Hacking! – Contact us if you are interested in M.Sc. thesis on Quantum Algorithms