A full stack summary of quantum computing
Journey from problem to quantum solutions in NISQ era
Hey there!
Today, we celebrate the Quantum Day. So, it is a good time to know or revisit end-to-end operation of a quantum computer. In this issue of The Quantum Vibe, I present a full stack perspective on quantum computing. The fact that quantum computers have come this far is nothing short of a marvel. But we shouldn’t forget that each step is a big pool of open problems which scientists and engineers are trying to address for achieving utility based fault tolerant quantum computing.
🧩 Step 1: From Problem to Quantum Formulation
Every quantum journey begins with a problem worth solving. Quantum computers aren’t designed to replace classical ones—they’re meant to handle problems where classical methods struggle, like:
Simulating quantum systems (chemistry, materials, nuclear physics)
Solving hard optimization problems
Factoring large numbers for cryptography
Searching unstructured data
But raw problems don’t directly translate into quantum instructions. First, we reframe the problem into a mathematical form amenable to quantum computation—such as an energy minimization task or a linear system. This step often involves encoding the problem into a Hamiltonian — the dynamical configuration of the system.
🧠 Step 2: Designing or Selecting the Right Algorithm
Once the problem is mapped into a quantum-friendly structure, we pick or design a quantum algorithm to work with it. This is where natural sciences meets computer science.
For quantum simulations: Variational Quantum Eigensolver (VQE)
For optimization: Quantum Approximate Optimization Algorithm (QAOA)
For factoring: Shor’s algorithm
For search: Grover’s algorithm
These algorithms define quantum circuits—sequences of logical gate operations acting on qubits. But they’re still abstract: they don’t yet know anything about the hardware that will run them.
⚙️ Step 3: Compiling to Hardware-Specific Instructions
Here’s where the logic meets the machine.
The quantum circuit must now be compiled to match the constraints of the target quantum hardware.
Gate decomposition: Not all gates are natively supported. For instance, theoretically you can define any gate possible. But an actual computer, say IBM’s transmon based system, can only support X, Z, CZ, ID, reset.
Qubit mapping: Logical qubits are formed by a combination of physical qubits on the chip, considering layout constraints and which qubits can interact. Every logical gate is decomposed into a sequence of fault-tolerant operations on many physical qubits, with checks built in for detecting and correcting errors as they occur.
SWAP gate insertion: If two qubits need to interact but aren’t connected on the hardware, SWAP gates are inserted to bring their data together—adding depth and error risk.
Pulse optimization: On superconducting platforms, gate operations are implemented by shaped microwave pulses. Advanced compilers can optimize these pulses for speed, fidelity, and reduced crosstalk.
❄️ Step 4: Initializing the Physical Qubits
Once the hardware-specific instructions are ready, the quantum processor must be prepared to run the circuit—which means initializing all physical qubits into a clean starting state.
Superconducting qubits are housed inside a dilution refrigerator, cooled to ~10 millikelvin—just above absolute zero. This ensures the qubit is naturally prepared in |0⟩ state, and the system is protected against thermal noise. The dilution refrigerator is rarely turned off. Instead, qubits are actively reset using microwave pulses, ensuring rapid reuse during multi-circuit execution. Any imperfections in this process are detected and scrubbed by stabilizer measurements, which are continually monitored during operation.
Additionally, each qubit undergoes detailed calibration routines, which characterize:
Drive frequencies
Coherence times (T₁, T₂)
Crosstalk with neighbors
Gate pulse shapes for accurate π rotations and entangling gates
This ensures high gate fidelity and prepares the system for circuit execution.
🔄 Step 5: Running the Circuit – Quantum Gate Operations
With the qubits prepared, the compiled circuit is executed. Each quantum gate is applied through precisely shaped control pulses. This is where the quantum state evolves into a complex superposition, entangling multiple qubits. Constructive and destructive interference shapes the probability of different outcomes— encoding the solution within the amplitudes of the quantum state. In fault-tolerant systems, each gate isn’t just applied once—it’s encoded as a series of fault-tolerant primitives. The quantum computer is constantly checking for errors in the background and correcting them, like a quantum immune system.
🛡️ Interlude: Quantum Error Correction in Action
You don’t just run a circuit and then “hope for the best”—the entire architecture is actively correcting for errors on the fly. For instance, in surface codes, this is done by continuously measuring “syndromes” (commuting operators that reveal error patterns) without collapsing the logical state. Error correction is built into every step.
📸 Step 6: Measurement – Collapsing the Quantum State
At the end of the computation, each qubit is measured, collapsing its state into a classical bit (0 or 1). Because quantum mechanics is probabilistic, a single run gives only one outcome. To build a meaningful result, the same circuit is repeated thousands of times to gather a distribution of outcomes. That statistical profile encodes the answer—like finding the ground-state energy, optimal configuration, or hidden pattern. When reading out logical qubits, the outcome is determined not from a single qubit’s measurement, but from a consensus across many physical qubits. Post-processing includes decoding the syndrome data to infer the correct logical result.
🧮 Step 7: Post-Processing & Hybrid Feedback
In today’s NISQ (Noisy Intermediate-Scale Quantum) era, many quantum algorithms are hybrid—involving a classical optimizer that steers a quantum subroutine.
For instance, in VQE:
A quantum circuit prepares a trial state.
The energy is measured.
A classical algorithm adjusts the system parameters and re-runs the circuit.
This loop continues until convergence. The interplay between quantum sampling and classical control extends what’s possible with imperfect hardware.
To summarize, each step in this pipeline— from problem framing to qubit calibration— is intimately connected. Good algorithms, smart compilers, robust hardware boosts measurement fidelity all work coherently to ensure correct outputs. The full-stack perspective is essential to designing scalable, reliable quantum solutions.
So, that’s that from this issue. Until next time, stay curious.