[Paper Review] Quantum computation by optically coupled steady atoms/quantum-dots inside a quantum electro-dynamic cavity

Prabhakar Pradhan, M. P. Anantram+1 more|ArXiv.org|Feb 2, 2000

Quantum Information and Cryptography7 citations

TL;DR

This paper proposes a scalable quantum computing architecture using stationary 3-level atoms or quantum dots confined in a high-finesse cavity, leveraging the Stark effect for individual qubit addressing and cavity photons as a common-mode qubit to implement universal quantum gates. The model enables universal quantum computation via one-qubit rotations and controlled-phase operations, with decoherence times exceeding operation cycles by a factor of 10⁶, making it viable for fault-tolerant computation.

ABSTRACT

We present a model for quantum computation using n steady 3-level atoms or 3-level quantum dots, kept inside a quantum electro-dynamics (QED) cavity. Our model allows one-qubit operations and the two-qubit controlled-NOT gate as required for universal quantum computation. The n quantum bits are described by two energy levels of each atom/dot. An external laser and n separate pairs of electrodes are used to address a single atom/dot independent of the others, via Stark effect. The third level of each system and an additional common-mode qubit (a cavity photon) are used for realizing the controlled-NOT operation between any pair of qubits. Laser frequency, cavity frequency, and energy levels are far off-resonance, and they are brought to resonance by modifying the energy-levels of a 3-level system using the Stark effect, only at the time of operation.

Motivation & Objective

• To address the scalability and individual qubit control challenges in existing quantum computing platforms such as ion traps and cavity-QED systems.
• To overcome the limitations of moving atoms in cavity-QED by proposing fixed atoms or quantum dots to enable stable, repeatable operations.
• To enable universal quantum computation using only one-qubit rotations and two-qubit controlled-phase gates via a common-mode cavity photon.
• To ensure long decoherence times relative to gate operation times, achieving a ratio of ~10⁶, which is essential for fault-tolerant quantum computation.
• To provide a solid-state-compatible model that combines advantages of cavity-QED and ion-trap architectures, using external electrodes and lasers for control.

Proposed method

• Qubits are encoded in the two lowest energy levels of each 3-level atom or quantum dot, with the third level used for controlled interactions.
• Individual qubit addressing is achieved via the Stark effect by applying external voltages to localized electrodes, shifting energy levels only for the target qubit.
• The cavity photon serves as a common-mode qubit to mediate entanglement between any two qubits via resonant interaction.
• Controlled-phase operations are implemented by sequentially bringing the target qubit and cavity into resonance, using a Rabi oscillation time of π/Ωc, followed by a π pulse to swap states.
• Off-resonant evolution is minimized by maintaining large detuning (δ ≈ 4×10⁶ Hz), ensuring negligible phase accumulation during non-operational periods.
• Measurement is performed by resonantly coupling the qubit to the cavity to transfer its state to a photon, which is then detected externally.

Experimental results

Research questions

• RQ1 Can individual qubits be addressed without requiring separate lasers per qubit, using only local electric fields?
• RQ2 Can a common-mode cavity photon mediate universal two-qubit entangling gates between any pair of qubits in a scalable architecture?
• RQ3 Is it feasible to maintain long decoherence times relative to gate operation times in a system of fixed atoms or quantum dots in a cavity?
• RQ4 Can the off-resonant phase evolution be suppressed well enough to allow reliable gate operations?
• RQ5 Can this model be extended to solid-state systems using quantum dots with long coherence times?

Key findings

• The model achieves a ratio of decoherence time to gate operation time of approximately 10⁶, indicating that up to 10⁶ operations can be performed within the coherence window.
• For a Rydberg atom with ωge₀ ≈ 5×10¹⁰ Hz, Ωc ≈ 4×10⁵ Hz, and δ ≈ 4×10⁶ Hz, the off-resonant phase evolution is negligible due to large detuning.
• For quantum dots with ωge₀ ≈ 1 THz and Ωc ≈ 10⁸ Hz, the system remains coherent if the phase coherence length exceeds 1/Ωc, which is achievable with isolated, engineered quantum dots.
• The use of Stark shifts allows selective addressing of individual qubits without requiring spatially focused lasers, enabling scalability.
• The controlled-phase gate is implemented via a sequence of resonant Rabi oscillations and π pulses, with the cavity returning to vacuum after each operation.
• Measurement of the final state is feasible by transferring the qubit state to the cavity photon via resonant coupling and detecting the emitted photon.