Quantum Computing Virtual Machine. Author: Alexandru Gheorghiu Scientific advisor: PhD. Lorina Negreanu

Transcription

1 Quantum Computing Virtual Machine Author: Alexandru Gheorghiu Scientific advisor: PhD. Lorina Negreanu

2 Quantum Computing Virtual Machine

3 Quantum Computing Computer science + quantum mechanics = quantum computing Complexity theory Adiabatic computing Algorithms Non-determinism Computational model Reversibility Superposition Entanglement Quantum parallelism

4 Models of Quantum Computing Circuit or Gate Model Adiabatic Computing Quantum Turing Machine Topological Quantum Computing Quantum Lambda Calculus Measurement-Based Quantum Computing

5 Which model should be used for a simulation?

6 Which model should be used for a simulation? Final answer: Gate Model

7 Why use the gate model? Simple representation Easy to implement Well documented Familiar Universal

8 Quantum information Bit vs Qubit Byte vs Qubyte Vector representation N N qubits -> 2 basis states

9 Quantum operations Quantum gates = unitary matrices

10 Quantum Computing Virtual Machine

11 What is a Virtual Machine? Initially an efficient, isolated duplicate of a real machine Popek and Goldberg Program that simulates a computer architecture Doesn't have to be an existing architecture Instruction interpreter + simulated architecture

12 Relevant example - Java Virtual Machine (JVM) Write once, run anywhere Process virtual machine Bytecode interpreter Simulates a virtual stack machine

13 Putting it all together

14 Quantum Virtual Machine Quantum architecture based on QRAM hybrid model Classical instructions inspired from Intel x86 assembly Quantum instructions based on gate model Quantum programs (implementing algorithms)

15 QRAM model Theorized by E. Knill Similar to RAM model Uses quantum memory Access to memory is address based Memory is contiguous

16 Hybrid QRAM Composed of classical and quantum subsystems Classical subsystem is master Quantum subsystem is slave Similar to GPU computing

17 Quantum architecture

18 Quantum Memory 16 qubit architecture (registers and addresses have 16 qubits) 8 registers Main memory addressable 16 memory and registers = qubytes or 524,416 qubits All memory areas stored as a single quantum state (a single vector) 524,416 qubits -> 2 components (complex numbers)! 524, 416

19 How much is 2 524, 416? Assume an SD card stores 64 GB and we have 8 bytes per component To store all the components we 158,903 would need 10 SD cards An SD card has 1075 cubic milimeters If we would fill the entire observable universe with SD cards we would 60 only have space for 10! GREAT SCOTT!!!

20 Quantum Memory Registers are used for addressing and storing basic results Mapped memory used to simulate additional registers Stack is used for handling function calls Heap used for dynamic memory Memory segments are adjacent They all form one quantum state vector

21 Instruction set Instructions are divided into classical and quantum The distinction is purely semantical (it's all quantum) Most classical instructions perform measurement Quantum instructions are just implemementations of quantum gates Enough instructions for universality

22 Classical instructions RISC instructions Only operate on basis states Must perform measurement Measure last 4 qubits Normalization

23 Classical instructions Logical: NOT, AND, OR, XOR Arithmetic: ADD, SUB, DIV, MUL Comparison: GT, LT, EQ Memory: LOAD, LOADB, STORE, STOREB, NEW, ALLOC, PUT, GET, PUSH, POP Jump: JUMP, JUMPT, JUMPF, CALL, RET Other: MOV, SHL, SHR

24 Example: ADD VR0 VR2 VR5 Step 1: Identify where registers are in memory

25 Example: ADD VR0 VR2 VR5 Step 2: Perform measurement

26 Example: ADD VR0 VR2 VR5 Step 3: Compute result and store

27 Quantum instructions Can operate on pure quantum states Reversible Universal gate set included: H, CNOT, S, T Implemented as matrix operations

28 Quantum instructions Classical control: X, Y, Z, T, S, H, ROT Quantum control: CNOT, CNOT2 Ordering: SWAP, SWAPB, REV Measurement: MEAS, RAND Other: QMOV For each of them (except MEAS and RAND) we also have the inverse (IX, IY, ICNOT, IQMOV, etc)

29 Example: H VR0 VR2 Step 1: Identify where registers are in memory

30 Example: H VR0 VR2 Step 2: Measure VR2 to use as control

31 Example: H VR0 VR2 Step 3: For each 1 qubit in VR2 perform H on the corresponding qubit in VR0

32 Example: H VR0 VR2 Step 3: For each 1 qubit in VR2 perform H on the corresponding qubit in VR0

33 Structure of a program.code segment.data segment Actual code (instructions) for a specific program Constants and object prototypes Contains instructions and labels Contains storage directives and labels Labels are very useful for flow control DW, DL, DB, DS

34 Quantum programs

35 Conclusions Simulator for a universal quantum computer Architecture based on hybrid QRAM model Instruction set based on quantum gate model Memory represented as single quantum state Classical and quantum instructions Quantum instructions are quantum gates

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37 Loose ends... 1) How is the memory issue resolved? 2) If memory operations are classical and they measure their operands how can we have pure quantum states in memory? 3) Doesn't the use of real numbers introduce approximation errors? 4) How are the quantum gates applied on the memory state exactly?

38 1) How is the memory issue resolved? Lazy initialization Only store what we need at a given time Store only non-zero amplitudes Memory state is sparse (mostly zeroes) Store only non-zero indices of memory state components

39 2) How can we have pure states in memory? Memory operations do not measure content Only measure address register Content is teleported to destination (actually a swap operation) Clonning cannot happen

40 3) Do we have approximation errors? Yes! Using real numbers makes it approximate Using pseudo-random numbers makes it approximately approximate True randomness and symbolic calculus would solve this

41 4) How are the gates applied?

42 Other simulators Many other quantum languages (QCL, Quantum pseudocode, QML, Q etc) Operate on different abstraction levels General approaches are either low-level (quantum system simulator) or high-level (quantum programming languages) The QCVM is a mixed approach

43 Applications Understanding how quantum computations work Expressing quantum algorithms easily (as opposed to just using gates) Possibility to investigate more complex systems (lots of qubits and entanglements)

44 Questions