Emulating two qubits with a four-level transmon qudit for variational quantum algorithms

Abstract

Using quantum systems with more than two levels, or qudits, can scale the computation space of quantum processors more efficiently than using qubits, which may offer an easier physical implementation for larger Hilbert spaces. However, individual qudits may exhibit larger noise, and algorithms designed for qubits require to be recompiled to qudit algorithms for execution. In this work, we implemented a two-qubit emulator using a 4-level superconducting transmon qudit for variational quantum algorithm applications and analyzed its noise model. The major source of error for the variational algorithm was readout misclassification error and amplitude damping. To improve the accuracy of the results, we applied error-mitigation techniques to reduce the effects of the misclassification and qudit decay event. The final predicted energy value is within the range of chemical accuracy. Our work demonstrates that qudits are a practical alternative to qubits for variational algorithms.

Qudit machine learning

“…Figure 9 depicts the results for both a qubit and a qutrit as a function of the system's decoherence time, denoted as T 2 , which constitutes the main limitation in practical implementations. We choose parameter values in accordance with typical experimental settings [18,19,[61][62][63]: ω ij /2π ∼ 3 GHz, Ω R /2π = 10 MHz, T 1 = 100 ms, and T 2 ∈ [100 ns, 100 µs]. Furthermore, we explore the impact of adding multiple layers to the model and compare the medians of the resulting test accuracies.…”

Qudit-based quantum computing with SRF cavities at Fermilab

“…Several theoretical studies have highlighted the advantages of directly encoding HEP problems into qudits, requiring fewer operations [33][34][35][36] and potentially better noise tolerance [37,38]. While one could argue for using transmons as qudits [39][40][41], there are two major issues. First, a transmon has only a few bounded energy eigenstates, and charge noise grows exponentially with Fock number, severely impacting dephasing time [23].…”

Complete population transfer between next-adjacent energy levels of a transmon qudit

“…The transmon [16,17] is a promising qudit platform [18][19][20] due to its long coherence time, [21,22] adequate anharmonicity for gates as short as tens of nanoseconds with little leakage, and its compatibility with multi-level readout. [18,23] In this work, we reposition the Pythagorean coupling as a valuable method for qudit operations by combining it with a more appropriate type of qudits. Using the method of Pythagorean coupling and energy level mapping, we experimentally investigate the population transfer process between next-adjacent energy levels in our transmon qudits.…”