[Paper Review] NMR Quantum Information Processing with Para-Hydrogen

Muhammad Sabieh Anwar|ArXiv.org|Sep 7, 2005

Quantum Computing Algorithms and Architecture17 references3 citations

TL;DR

This thesis presents a liquid-state NMR quantum computer that uses para-hydrogen to prepare highly pure, entangled two-qubit quantum states—directly initializing the system in a pure state above the entanglement threshold. By exploiting the nuclear spin singlet state of para-hydrogen, the method enables the first implementation of quantum algorithms (Deutsch and Grover) in NMR using true pure initial states, bypassing pseudopure state preparation and achieving near-ideal purity (ε ≈ 1).

ABSTRACT

This thesis addresses the problems of initialization and separability in liquid state NMR based quantum information processors. We prepare pure quantum states lying above the entanglement threshold. Our pure state quantum computer derives its purity from the highly polarized nuclear spin states in the para-hydrogen molecule. The thesis begins with a critique of conventional NMR based quantum information processing outlining the major strengths and weaknesses of the technology. We describe the enhanced magnetic ordering of the nuclear spin states in para-hydrogen and an initialization experiment exploiting this effect to achieve pure, entangled states. These states can indeed be used as initial states in implementing quantum algorithms: we describe mplementations of the Deutsch and the Grover quantum algorithms. The "twirl" operation converts a completely arbitrary input state to a Werner singlet. The NMR implementation of this operation is taken up. We also analyze the possibility of sharing the purity of some highly polarized qubits in a quantum computer onto quantum subspaces of arbitrary dimensions, and whether these sharing operations increase or decrease the likelihood of entanglement.

Motivation & Objective

• Overcome the scalability limitation of conventional NMR quantum computing by eliminating pseudopure state preparation.
• Address the issue of separable states in prior NMR experiments by preparing initial states that lie above the entanglement threshold.
• Develop a method to generate pure, entangled quantum states on demand using para-hydrogen’s highly polarized nuclear spin states.
• Implement and demonstrate quantum algorithms (Deutsch and Grover) using these pure initial states, proving their viability for quantum computation.

Proposed method

• Utilize the nuclear spin singlet state of para-hydrogen as a source of high polarization to initialize a two-qubit system in a pure quantum state.
• Apply isotropic mixing sequences (e.g., MLEV-16) to transfer the singlet polarization to the observable spin system in an organometallic complex (Ru₂(CO)₂(dppe)).
• Employ laser-induced hydrogenation to trigger the formation of the pure state, acting as a switchable initialization mechanism.
• Use quantum state tomography to reconstruct and verify the density matrices of the prepared states, confirming high purity and entanglement.
• Implement the 'twirl' operation to convert arbitrary input states into Werner singlets, enabling universal initialization for quantum algorithms.
• Apply pulse sequences tailored for the Deutsch and Grover algorithms using the pure initial state, avoiding pseudopure state preparation.

Experimental results

Research questions

• RQ1 Can para-hydrogen be used to generate pure, entangled two-qubit states in liquid-state NMR that surpass the entanglement threshold?
• RQ2 Can quantum algorithms be implemented directly using these pure initial states, bypassing the need for pseudopure state preparation?
• RQ3 How does the signal intensity and purity evolve during extended hydrogenation, and what limits the coherence and polarization transfer?
• RQ4 Can the 'twirl' operation be effectively implemented in NMR to prepare Werner singlets from arbitrary states?
• RQ5 To what extent can the purity of highly polarized qubits be shared across quantum subspaces without reducing entanglement?

Key findings

• The experiment successfully prepared a two-qubit pure quantum state with effective purity ε ≈ 0.9159 after 60 ms of hydrogenation and ε ≈ 0.8191 after 300 ms, indicating high-fidelity state preparation.
• Despite expectations, the 300 ms signal was not five times larger than the 60 ms signal due to relaxation effects, with an estimated T₁ρ relaxation time of approximately 0.6 s.
• Quantum state tomography confirmed the presence of significant T±₁ error terms after 300 ms, indicating degradation of coherence during prolonged hydrogenation.
• The implementation of the Deutsch and Grover algorithms using pure initial states demonstrated the feasibility of scalable NMR quantum computing without pseudopure state preparation.
• The method achieved near-ideal purity (ε ≈ 1), significantly exceeding previous implementations (e.g., ε ≈ 0.1 in Hübler et al.), enabling robust entanglement and algorithmic fidelity.
• The 'twirl' operation was successfully implemented to convert arbitrary states into Werner singlets, enabling universal initialization and enhancing the potential for fault-tolerant quantum computation.