The Full Pipeline of a Quantum Solver

qc/algorithms qc/moc

Every quantum algorithm you meet in this vault is really one stage of a five-stage pipeline: target problem → encoding → algorithm → hardware → post-processing. Key insight: most of the “quantum” part (stage 3) is reused across wildly different problems — QAOA, Shor’s, and VQE are all just different choices at stage 3 — while stages 1, 2, 4, and 5 are where a real-world problem actually gets bent into and out of that shared quantum core.

The five stages

1. Target problem — what you actually want to solve: Combinatorial Optimization (MaxCut, MIS, portfolios, scheduling), Cryptography (RSA, elliptic curves), Chemistry/materials (molecular ground states, reactions).
2. Encoding — rewriting the problem as qubits: QUBO → Ising via $x_i=(1-Z_i)/2$ for optimization (see QAOA — Quantum Approximate Optimization Algorithm), binary/decimal → qubit for numeric problems, fermion → qubit (Jordan-Wigner, Bravyi-Kitaev, or a more compact encoding) for chemistry — see Hamiltonians and Encoding for Quantum Circuits for the full mapping toolkit.
3. Algorithm — the quantum core itself: adiabatic/counter-diabatic evolution (e.g. QAOA), QFT-based (e.g. QPE, Shor’s), or variational (e.g. VQE, ADAPT-VQE).
4. Hardware — making the abstract circuit survive real qubits: circuit compilation for a specific connectivity (see Transpilation), gate optimization for the device’s native gate set, and error correction/mitigation — either full error correction (surface codes, LDPC, bicycle-bivariate codes) for the fault-tolerant future, or mitigation techniques (ZNE, PEC, dynamical decoupling) that suffice today.
5. Post-processing — turning raw quantum output back into an answer: computing observables $⟨\psi |H|\psi ⟩$, repairing constraint violations specific to the target problem (e.g. bit-flip correction using problem structure), or decoding (for error-correction-flavored algorithms).

Why this framing matters

The same five slots recur whether the target problem is combinatorial optimization, chemistry, or (eventually) cryptography — only the specific choice made at each stage changes. Seeing SQD and QAOA as two different fillings of the same five slots, rather than as unrelated algorithms, is what makes the “algorithm zoo” navigable — see The Quantum Algorithm Zoo for how the stage-3 choices themselves cluster by mathematical origin (physics-, math-, or CS-inspired).

Related

• Hamiltonians and Encoding for Quantum Circuits — stage 2 in full depth
• QAOA — Quantum Approximate Optimization Algorithm, Variational Quantum Eigensolver (VQE), Quantum Phase Estimation (QPE) — stage 3 choices
• Transpilation — stage 4, hardware compilation
• Transpiling QAOA Circuits — SWAP Strategies and SAT Mapping — a concrete, optimized version of stage 4 for QAOA specifically
• The Quantum Algorithm Zoo — how stage-3 algorithm choices group by inspiration and what hardware pressure (mitigation vs. full error correction) they each need

Self-Check

• Without naming any specific algorithm, what are the five stages every quantum solver pipeline goes through?
• Why does it help to see QAOA and SQD as different fillings of the same five-stage template rather than as unrelated algorithms?
• Which stage does error mitigation belong to, and why does that stage currently have two very different long-term vs. short-term answers?