Introduction

Qubits evolve under unitary matrices. Gates compose neatly. Circuits scale visually. In theory, adding another qubit is just a tensor product.
In practice, quantum computing is an engineering war.
This blog documents my attempt to move beyond abstract circuits and design a physical 2-qubit quantum computer using liquid-state Nuclear Magnetic Resonance (NMR). The goal was not scalability or supremacy — it was to understand, at the lowest level, how quantum information behaves when implemented in a real physical system.

This post is intentionally honest. It includes what worked, what broke, and why the project ultimately hit a hard infrastructure ceiling.

Why NMR for Quantum Computing?

NMR is not fashionable in modern quantum computing — and that’s exactly why it’s useful.

Liquid-state NMR offers:

  • Extremely precise control over nuclear spins

  • Long coherence times compared to early solid-state platforms

  • Mature experimental techniques

  • A clean mapping between theory and physical control

But it also comes with a fundamental limitation:

NMR quantum computing is an ensemble system, not a single-system quantum computer.

That single sentence changes everything.

Qubits as Nuclear Spins

In liquid-state NMR:

  • Qubits are nuclear spins (spin-½ nuclei)

  • Common choices: In liquid-state NMR:

    Qubits are nuclear spins (spin-½ nuclei).

    Common choices include:

    • ¹H

    • ¹³C

  • Each nucleus experiences a strong static magnetic field B0B_0B0​

This field causes Zeeman splitting:

  • Spin-up and spin-down correspond to ∣0⟩|0\rangle∣0⟩ and ∣1⟩|1\rangle∣1⟩

  • Energy separation defines the Larmor frequency

ω = γB₀

Different nuclei → different gyromagnetic ratios → distinguishable qubits.

This is how addressability is achieved.

The System Hamiltonian (Where Theory Gets Real)

Unlike circuit models, NMR quantum computation is Hamiltonian-driven.

The system Hamiltonian includes:

  1. Zeeman interaction (individual qubit terms)

  2. Spin–spin coupling (J-coupling) between nuclei

Under the weak-coupling approximation (valid in liquid samples), this interaction enables two-qubit gates.

This is where abstraction disappears.

You are no longer “applying a CNOT gate”.
You are engineering time evolution under a physical Hamiltonian.

Quantum Gates as RF Pulses

In NMR, quantum gates are not discrete operations.

They are implemented using:

  • Radio-frequency (RF) pulses

  • Precisely controlled in amplitude, phase, and duration

Key ideas I worked with:

  • Pulse duration → rotation angle

  • Pulse phase → rotation axis

  • Delays → interaction via J-coupling

For example:

  • A single-qubit rotation becomes a controlled spin precession

  • A two-qubit gate emerges from timed coupling evolution

Every gate is a continuous physical process, not a line in a circuit diagram.

Pulse Programming (PPG): The Real Skill

Pulse Programming (PPG) is the heart of NMR quantum computing.

This includes:

  • Hard vs soft pulses

  • Selective excitation of nuclei

  • Phase cycling

  • Precise timing control

I worked on understanding how pulse sequences are constructed to:

  • Mimic Hadamard gates

  • Generate entanglement

  • Control unwanted interactions

This step alone shattered any illusion that quantum gates are “simple”.

Pseudo-Pure States: The First Reality Check

Unlike ideal quantum computers, NMR systems operate at room temperature.

This means:

  • The system is in a thermal mixed state

  • True pure quantum states do not exist

To make quantum computation appear possible, NMR uses:

  • Pseudo-pure states

These are not pure states.
They are engineered ensemble states that behave as if they were pure for computation.

This was my first major realization:

NMR quantum computing works by clever signal engineering, not by isolating single quantum systems.

It is valid — but fundamentally different from scalable quantum architectures.

Readout: Expectation Values, Not Measurements

In most quantum platforms:

  • Measurement collapses a single quantum system

In NMR:

  • You measure ensemble magnetization

  • The output is an expectation value, not a projective outcome

The signal pipeline:

  1. Nuclear precession generates an RF signal

  2. Free Induction Decay (FID) is recorded

  3. Fourier transform converts time → frequency

  4. Spectral peaks encode quantum information

This readout method is elegant — and also the reason NMR does not scale.

Control Hardware: FPGA and Timing

At the control level, I explored:

  • Why FPGAs are used for pulse control

  • How nanosecond-scale timing matters

  • How synchronization errors propagate into quantum errors

Even with perfect theory, control electronics become the bottleneck.

Quantum computing is not limited by math.
It is limited by clocks, noise, and drift.

What Worked

  • Clear mapping between quantum gates and RF pulses

  • Understanding of Hamiltonian-driven computation

  • Pulse-level view of quantum control

  • End-to-end system architecture design

These skills are rare — and transferable.

Why the Project Stopped

The project did not fail intellectually.

It stopped due to:

  • Limited access to a high-stability NMR spectrometer

  • Insufficient continuous experimental support

  • Hardware precision constraints beyond student-lab capabilities

This was a hard but important lesson:

Quantum computing progress is determined more by infrastructure than intelligence.

Why This Experience Matters

NMR quantum computing is not the future of large-scale quantum computers.

But it is one of the best ways to understand what quantum computation actually demands from the physical world.

After this project, I no longer saw quantum computing as:

  • “Algorithms + qubits”

I saw it as:

  • Control theory

  • Signal processing

  • Materials

  • Noise

  • Engineering discipline

That perspective directly shaped my next pivot: quantum-enhanced neuromorphic sensing, where quantum effects are used realistically — without pretending hardware doesn’t matter.

What Comes Next

In the next blog, I move away from universal quantum computation and toward quantum sensing and hybrid systems — where quantum physics is used not to compute everything, but to sense what classical systems cannot.

👉 Next: Quantum-Enhanced Neuromorphic Sensing: From Biology to Nanoscale Quantum Materials