Prisoners’ Dilemma in a Spatially Separated System Based on Spin–Photon Interactions

At a Glance

Metadata	Details
Publication Date	2022-08-30
Journal	Photonics
Authors	Azmi Ali Altıntaṣ, Fatih Özaydin, Cihan Bayındır, Veysel Bayrakci
Institutions	Istanbul University, Işık University
Citations	13
Analysis	Full AI Review Included

Executive Summary

This analysis details a proposed distributed quantum circuit architecture designed to allow spatially separated players to execute the quantum Prisoners’ Dilemma (PD) game using spin-photon interactions.

Distributed Architecture: The proposal overcomes the classical requirement of co-located qubits by employing stationary matter qubits (spins) and a flying ancillary photonic qubit for inter-site logic operations.
Physical Realization: Logical qubits are realized using electronic spins (e.g., Nitrogen Vacancy (NV) centers in diamond or quantum dots) coupled to optical cavities, enabling interaction with the flying photon.
Core Gate Implementation: The fundamental two-qubit operation is the Controlled-Z (CZ) gate, implemented via the reflection phase shift induced by the spin-photon interaction within the cavity.
Circuit Decomposition: Complex entangling and SWAP operations required for the game (J, J⁺, SWAP) are decomposed entirely into sequences of CZ and single-qubit gates, making the scheme experimentally feasible.
Imperfection Analysis: Modeling experimental nonideality via a Controlled-Phase (CP(alpha)) gate shows that the quantum advantage ceases when the imperfection parameter (alpha) exceeds approximately pi/12, leading to the revival of the classical dilemma and new Nash equilibria.
Feasibility: The proposed setup is within the reach of current technology, leveraging high-fidelity NV center spin control (up to 0.999 fidelity) and demonstrated spin-photon entangling gates (> 96% fidelity).

Technical Specifications

Parameter	Value	Unit	Context
Logical Qubit Type	Electronic Spin	N/A	NV centers in diamond or quantum dots
Ancillary Qubit Type	Photon Polarization	N/A	Flying qubit for inter-site communication
High-Fidelity Condition (g)	> 5 * sqrt(kappa * gamma)	Frequency	Required coupling strength for near-unity reflection
CZ Gate Imperfection (alpha)	≈ pi/12	Radians	Critical threshold for loss of quantum advantage
NV Single-Qubit Gate Fidelity	0.999	Unitless	Reported experimental fidelity (Room Temperature)
NV Two-Qubit Gate Fidelity	0.992	Unitless	Reported experimental fidelity (Room Temperature)
Spin-Photon Entangling Gate Fidelity	> 0.96	Unitless	Experimentally demonstrated on-chip
Payoff: Temptation (t)	5	Arbitrary	Highest classical payoff value
Payoff: Punishment (p)	1	Arbitrary	Lowest classical payoff value
Required Temperature	Ultra-low	Kelvin	Necessary for quantum dot/cavity systems
Entanglement Parameter (gamma)	pi/2	Radians	Maximally entangled game setting

Key Methodologies

The distributed quantum circuit relies on the sequential application of SWAP, J, and J⁺ operators, all built from CZ gates realized via spin-photon interaction.

Qubit Preparation: Alice’s spin, Bob’s spin, and the ancillary photon are initialized in the |C) state (Cooperate).
First SWAP (Alice’s Site): The ancillary photon interacts with Alice’s cavity three times to swap the state between the photon and Alice’s spin qubit. The photon is then transmitted to Bob’s site.
Entangling Operator (Bob’s Site): The photon interacts with Bob’s cavity four times to implement the J operator, entangling the photon (now carrying Alice’s initial state) and Bob’s spin qubit. The photon is returned to Alice’s site.
Second SWAP (Alice’s Site): The photon interacts with Alice’s cavity three times, completing the second SWAP. This leaves the spatially separated spin qubits in the desired entangled state |psi₀).
Player Choices (U_A, U_B): A time delay is introduced, allowing Alice and Bob to apply their chosen single-qubit strategy operators (U_A, U_B) directly to their stationary spin qubits.
Third SWAP (Alice’s Site): The photon is used to implement the third SWAP operation, then transmitted to Bob.
Inverse Entangling Operator (Bob’s Site): The photon interacts with Bob’s cavity to implement the J⁺ operator.
Final SWAP (Alice’s Site): The last SWAP operation is implemented, preparing the spin qubits for measurement.
Measurement: Final state measurement of the spin qubits determines the payoffs based on the resulting state (CC, DD, DC, or CD).

Commercial Applications

The technology and methodology described, focusing on high-fidelity spin-photon interfaces and distributed quantum logic, are critical for several emerging quantum technology sectors.

Quantum Computing Hardware: Provides a viable architecture for modular, distributed quantum processors, allowing for the scaling of qubit counts beyond the limitations of single-chip systems.
Quantum Networking and Communication: The use of flying photonic qubits to mediate entanglement between distant stationary spin qubits is the core mechanism for building quantum repeaters and long-haul quantum internet infrastructure.
Solid-State Quantum Memory: NV centers and quantum dots serve as robust, long-coherence solid-state quantum memory elements, essential for buffering and storing quantum information in network nodes.
High-Fidelity Quantum Gates: The detailed analysis of CZ gate implementation via cavity QED is directly relevant to improving the fidelity and robustness of two-qubit gates in solid-state quantum systems.
Quantum Sensing: NV centers, the preferred spin qubit candidate, are commercially utilized for high-sensitivity magnetometry, electric field sensing, and thermometry at the nanoscale.
Quantum Algorithm Validation: The ability to simulate and execute complex quantum games under realistic noise models provides a platform for validating quantum algorithms and studying decoherence effects in practical applications.

View Original Abstract

Having access to ideal quantum mechanical resources, the prisoners’ dilemma can be ceased. Here, we propose a distributed quantum circuit to allow spatially separated prisoners to play the prisoners’ dilemma game. Decomposing the circuit into controlled-Z and single-qubit gates only, we design a corresponding spin-photon-interaction-based physical setup within the reach of current technology. In our setup, spins are considered to be the players’ logical qubits, which can be realized via nitrogen-vacancy centers in diamond or quantum dots coupled to optical cavities, and the game is played via a flying photon realizing logic operations by interacting with the spatially separated optical cavities to which the spin qubits are coupled. We also analyze the effect of the imperfect realization of two-qubit gates on the game, and discuss the revival of the dilemma and the emergence of new Nash equilibria.

Tech Support

Original Source

DOI: https://doi.org/10.3390/photonics9090617

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