[Paper Review] 5-qubit quantum error correction in a charge qubit quantum computer

Dave Touchette, Haleemur Ali+1 more|arXiv (Cornell University)|Oct 15, 2010

Quantum Computing Algorithms and Architecture24 references3 citations

TL;DR

This paper demonstrates the implementation of the DiVincenzo-Shor 5-qubit quantum error correction code in a solid-state charge qubit quantum register subjected to realistic noise from phase decoherence and relaxation. By applying high-frequency quantum error correction, the fidelity of the encoded logical qubit is maintained arbitrarily close to one, enabling fault-tolerant quantum computation despite multi-qubit errors in a noisy environment.

ABSTRACT

We implement the DiVincenzo-Shor 5 qubit quantum error correcting code into a solid-state quantum register. The quantum register is a multi charge-qubit system in a semiconductor environment, where the main sources of noise are phase decoherence and relaxation. We evaluate the decay of the density matrix for this multi-qubit system and perform regular quantum error corrections. The performance of the error correction in this realistic system is found to yield an improvement of the fidelity. The fidelity can be maintained arbitrarily close to one by sufficiently increasing the frequency of error correction. This opens the door for arbitrarily long quantum computations.

Motivation & Objective

• To evaluate the performance of the DiVincenzo-Shor 5-qubit quantum error correcting code (QECC) in a realistic solid-state quantum register.
• To analyze the impact of combined phase decoherence and relaxation on quantum fidelity in a multi-charge-qubit system.
• To determine whether high-frequency quantum error correction can maintain fidelity arbitrarily close to one despite multi-qubit errors.
• To assess the feasibility of fault-tolerant quantum computation in charge qubit systems under realistic noise models.
• To compare the relative difficulty of correcting relaxation versus decoherence in a quantum register.

Proposed method

• The study employs a realistic noise model for N-charge-qubit systems, incorporating both phase decoherence and relaxation processes.
• The 5-qubit DiVincenzo-Shor QECC is applied to encode a single logical qubit across five physical charge qubits.
• Density matrix evolution is simulated to track the decay of quantum state fidelity under noise.
• Quantum error correction is applied at regular intervals using a periodic correction protocol with adjustable time intervals Δt.
• The simulation uses the density operator formalism to describe mixed states and perform partial traces to analyze subsystem dynamics.
• Fidelity is computed as a function of time to evaluate the effectiveness of error correction under different noise conditions.

Experimental results

Research questions

• RQ1 Can the 5-qubit quantum error correcting code effectively suppress multi-qubit errors arising from phase decoherence and relaxation in a solid-state charge qubit register?
• RQ2 How does the required frequency of quantum error correction depend on the dominant noise type—decoherence or relaxation?
• RQ3 To what extent can fidelity be maintained arbitrarily close to one through repeated error correction in a realistic noisy environment?
• RQ4 Is relaxation more detrimental to quantum fidelity than decoherence, and does it require a higher correction frequency?
• RQ5 Can the 5-qubit code, designed for single-qubit errors, still effectively correct multi-qubit errors in a realistic noise model?

Key findings

• The 5-qubit quantum error correction code successfully maintains quantum fidelity arbitrarily close to one when error correction is applied with sufficiently high frequency.
• Relaxation was found to be significantly harder to correct than decoherence, requiring a higher correction frequency to achieve comparable fidelity preservation.
• When both decoherence and relaxation are present, the required correction frequency is dominated by the relaxation rate, as it is the more challenging noise source.
• For a time interval Δt = 0.001ω₀, fidelity remained nearly perfect over extended simulation times, demonstrating effective error suppression.
• The simulation confirms that even with realistic multi-qubit errors, the 5-qubit code can preserve quantum information indefinitely if error correction is applied frequently enough.
• The results validate the theoretical threshold for fault-tolerant quantum computation in a solid-state implementation, provided error correction frequency is sufficiently high.