The comparison between qudits and qubits depends on the specific requirements and constraints of the quantum computation task at hand. Let's break down the scenario you described:
Option 1: Two qudits with 3513 real and imaginary states each. Option 2: 3513 qubits with 1 real and imaginary state each.
To determine which option is better, we need to consider a few factors:
Computational Power: Qudits, which are quantum systems with more than two orthogonal states, have the potential to offer advantages over qubits in certain scenarios. With two qudits, each having 3513 states, you have a total of 3513^2 = 12,330,369 possible quantum states to encode information. This can enable more complex computations and potentially provide computational advantages in certain algorithms.
Noise and Error: Quantum systems are prone to noise and errors due to environmental interactions. Generally, the more states a quantum system has, the more sensitive it can be to noise. In the case of two qudits with 3513 states each, there may be a higher susceptibility to noise and errors compared to 3513 qubits, each with only one state. However, the specific noise characteristics and error correction techniques can influence the overall performance.
Scalability: The scalability of a quantum system is an important consideration. As the number of qubits or qudits increases, the challenges in maintaining coherence and controlling interactions between them can grow significantly. Scaling up the number of qudits may introduce additional complexities, but it can also provide a higher computational capacity if effectively managed.
In summary, the choice between two qudits with 3513 states each or 3513 qubits with 1 state each depends on various factors, including the computational requirements, noise characteristics, error correction capabilities, and scalability considerations. A detailed analysis of the specific quantum algorithm, error rates, and implementation constraints is necessary to make an informed decision in a practical setting.