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Quantum Computing - Coggle Diagram

- - - - Can tell if eavesdropping occured
      - Share symmetric keys
  - - - QAOA Quantum Approximate Optimization Algorithm
        
        Combinatorial optimization
        
        𝑛 bits, 𝑚 clauses
        Each clause specifies a constraint on a subset of bits
        
        QAOA Algorithm
        
        create a parameterized operator based on objective function
        
        create parameterized operator that rotates around the X axis, ß=0..π
        
        Choose a parameter 𝑝 and repeat 𝑈𝐶 and 𝑈𝐵 with different angles:
        
        Iterate p times for different |γ,ß>
        
        Each term commutes (diagonal in computational basis)
        
        C has integer eigenvalues -> can restrict γ to 0.. 2π
        
        Use Control-Rz gates to rotate by angle γ when Ca=1 (true) -> sample circuit for MaxCut:
        
        QAOA for MaxCut
        
        Init ß and γ to suitable real values
        
        Repeat the following until some suitable convergence criteria is met:
        
        Prepare the state | ψ(ß,γ)> using qaoa circuit -> U(B.ß)
        
        Measure the state in standard basis
        
        Compute <ψ(ß,γ)|H_P|ψ(ß,γ)> -> U(B,ß)U(C,γ)
        
        Find new set of parameters (ß_new, γ_new) using a classical optimization algorithm
        
        Ser current parameters (ß,γ) equal to the new parameters (ß_new, γ_new)
      - VQE Variational Quantum Eigensolver
        
        Quantum chemistry, quantum physics, optimization
        
        VQE Algorithm
        
        Choose W_i, W_ij
        
        Choose circuit depth m
        
        Chose set of controls θ, make trail function |ψ(θ)> w/ C-Phase & single qubit Y(θ) rotations
        
        Evaluate C(θ) and sum up results over used θ estimated values
        
        1 more item...
      - VQF Variational Quantum Factoring
        
        Integer factorization
      - VQG Variational Quantum Generation
        
        Generating representative data such as text, audio, video, etc.
    - - Cost Function C(θ)
        
        Try to minimize/maximize
        
        Describes the problem
        
        Interpret results in a way that is relevant to problem
        
        Value must monotonically decrease (or increase) as result gets closer to the desired state/output
        
        Expectation Value of H for state |ψ>: <ψ|H|ψ> = <H>_ψ
      - Anstz Parameterized quantum circuit
        |ψ(θ)>
        
        Shallow depth (NISQ)
        
        Expressivity and Entanglement
        
        Idea: Adjust parameters to produce different states
        Use the parameters to explore the state space.
      - Classical Optimizer (parameter: θ)
        
        Choose a new set of parameters that will get closer to a global minimum
        
        Optimizer's job :
        look for min (max) point in landscape
        
        Barren Plateu
      - Variational Principle
        
        There exists some minimum energy 𝐸0, known as the ground state energy.
        And a state |𝜓𝑖 〉 that is known as the ground state.
        〈𝜓_0 |𝐻|𝜓_0 〉=𝐸_0
        For any arbitrary state |𝜓〉, its energy is greater than or equal to 𝐸_0.
        〈𝜓|𝐻|𝜓〉≥𝐸_0
  - - - +/- basis: (v(b+1)/N)2pi rotations around Z axis, where v=5 (here), b=qubit index, N=2n=16 (here) number qubits
    - - Quantum Phase Estimation
        
        The quantum phase estimation algorithm uses phase kickback to write the phase of U (in the Fourier basis) to the t qubits in the counting register. We then use the inverse QFT to translate this from the Fourier basis into the computational basis, which we can measure.
      - Shor's Algorithm
        
        Shor’s solution was to use quantum phase estimation on the unitary operator:
- - - - ⟦𝑛,𝑘,𝑑⟧
      - n - number of physical qubits
      - k - number of logic qubits
      - d- hamming distance
  - - - BSQkit
      - Need a scalable, open-source compiler infrastructure for quantum
      - Efficiency is crucial
      - Pass-Driven vs Instrumentation-Driven
        
        Pass Driven
        
        loop unrolling
        
        Procedure cloning
        
        inter-procedural constant propagation
        
        Instrumentation-driven
        
        Leveraging the dual nature of quantum programs
        
        Instrument code such as a fast classical processor executes through the classical portion, collecting information regarding the quantum portion
        
        Further speed-up by memorizing same module calls
        
        Scales better
      - Conclusion
        
        =
        
        Extended LLVM’s classical framework for quantum compilation at the logical level
        
        Managed scalability through:
        
        Output format:
        
        200,000X on average + up to 90% for some benchmarks
        
        Code generation approach:
        
        Up to %70 for large problems
        
        CTQG (classical to quantum gate): Automatic generation of efficient quantum programs from classical descriptions
        
        Developed a scalable program analysis toolbox
        
        ScaffCC can be used as a future research tool
        
        -
        
        NISQ Compiler Insights
        
        Compile for optimal success rate, in addition to performance optimization:
        
        Most important for optimization: CNOT and readout errors.
        
        Single qubit operations, coherence time, gate duration etc. are less important.
        
        Current programs are limited by gate errors rather than decoherence errors.
        
        Choose qubit placement using optimization techniques to maximize the chances of correct execution.
        
        Noise is here to stay:
        
        Qubit manufacturing and gate control unlikely to be perfected soon
        
        Access to recent (1-2X daily) noise data matters
        
        SMT optimization scales to 72 qubits, efficient heuristic strategies can scale to large scale systems with 1000s of qubits.
    - - Develop software transformation for NISQ programs to reduce the impact of hardware errors
      - Just-in-Time Transpilation Reduces Noise
        
        Sources of noise: readout, CNOTs, cross-talk, qubits, …
        
        Qiskit transpilation (level 3) -> optimizes for noise
        
        Selects physical qubits based on daily device calibration
        
        Problem: noise changes even within 1 hr periods
        
        Approach: run calibration as part of job (single gate, random circuits)
        
        Use error metrics to drive L3 transpilation for application circuit
        
        Run just-in-time optimized app right away (dedicated mode)
        
        Results: 3-300% improved (correct samples)
        
        Depends on circuits: #qubits, depth, …
        
        Our mapping: outperforms IBM default
        
        Just-in-time reduces noise
        
        Maybe better calibration algorithm than IBM
    - - Parametric Syntheis
      - SupermarQ
      - number of qubits
    - - no breakpoints
      - runtime assertion
        
        QPE
        
        Deutsch-Jozsa Algorithm
      - Conclusion
        
        We proposed two systematic approaches, namely SWAP-based and NDD/Stabilizer-based designs for quantum state runtime assertion.
        
        Our designs can assert a broad range of states.
        
        We also introduce the idea of approximate assertion, which performs membership check on a set of states.
        
        We showcase that both the precise and approximate assertions can help with debugging quantum programs.
    - - NchooseK
        
        Domain: constraint-programming system
        
        NP-hard/NP-complete problem
        
        Given
        
        n Boolean values
        
        k of which constrained to be true
        
        Notation: nck(N, K)
        
        N : multiset of variables
        
        K: set of allowable true counts
        
        Can combine multiple ones
  - - - Quantitative: multi-shot, multi-device, multi-circuit, …
        Qualitative: statistics, ML, …
    - - Loss of unitary evolution due to
        -Coherent errors -> still pure states, just wrong ones, perturbed U’!=U:
        |Ψ> -> U’|Ψ>
        -Incoherent errors -> mixed states