Duke University Team Models Tavis-Cummings Interaction for Global Qubit Control

Plato Deliyannis and Iván Martín at Duke University show that qubits become entangled via a shared connection to a harmonic oscillator, even without direct interaction, through the Tavis-Cummings interaction. Their characterisation reveals limitations imposed by an unexpected symmetry within the Tavis-Cummings Hamiltonian when using global control and a z field, but the addition of a specific Hamiltonian term breaks this symmetry. This enables the implementation of nearly arbitrary quantum operations, representing a key step towards achieving semi-universality in quantum computation.

Symmetry breaking in the Tavis-Cummings model enables near-universal multi-qubit gate control

A pathway to semi-universal quantum computation is now available, increasing the range of achievable qubit operations from 66% to nearly 100% for systems with three or more qubits, where n ≥3. The Tavis-Cummings interaction, a common method for linking qubits via a shared harmonic oscillator, previously restricted the types of operations possible when using a global z field to control them. This limitation prevented the implementation of certain key quantum gates. Incorporating the Hamiltonian Jz² effectively removed this symmetry, unlocking the ability to perform a sharper set of qubit manipulations respecting permutational and U symmetry, and expanding the operational capacity of multi-qubit systems with control over a greater range of quantum operations.

Modifying the standard Hamiltonian, a mathematical description of the system’s energy, with the addition of a Jz² term achieved this breakthrough. This alteration cancelled an inherent symmetry within the Tavis-Cummings interaction, a technique used to connect qubits through a shared harmonic oscillator. Consequently, more complex quantum gates are now implementable, including those necessary for performing arbitrary permutations on qubit states and U symmetry preserving operations. Any permutation invariant unitary transformation on qubits can be realised using the Tavis-Cummings interaction alongside global z and x fields, assuming the bosonic mode is initially in its vacuum state.

Overcoming symmetry limitations expands manipulation of multi-qubit systems

Researchers at Duke University have demonstrated a new level of control over multi-qubit systems, vital for building more powerful quantum computers. Their work reveals that adding the specific energy interaction, the Hamiltonian Jz², breaks the symmetry, allowing for a wider range of qubit manipulations. This advancement moves beyond simply confirming theoretical limitations, providing a practical method to circumvent them and enable more complex quantum calculations.

The team at Duke University expanded control over qubits, the basic units of quantum information, by manipulating energy interactions within quantum systems. Deliyannis and colleagues overcame a limitation stemming from an unexpected symmetry within the Tavis-Cummings interaction, which links qubits via a shared harmonic oscillator, allowing entanglement without direct connections. Adding the Hamiltonian Jz² breaks this ‘accidental’ symmetry, enabling semi-universal control over qubit manipulations respecting fundamental symmetries and paving the way for more complex quantum computations.

Researchers demonstrated that adding a Jz² term to the standard Hamiltonian overcomes a symmetry limitation within the Tavis-Cummings interaction, which connects qubits via a shared harmonic oscillator. This advancement matters because it expands the range of achievable quantum operations on multi-qubit systems, moving beyond theoretical constraints to provide a practical solution. The study shows that this approach enables semi-universal control, allowing arbitrary qubit manipulations that respect established symmetries. The authors detail this finding and further analysis of the accidental symmetry in a companion paper.