Advances in Quantum Simulation Unlock Access to Physics Beyond Two-Body Interactions

Exploring the complex behaviour of quantum systems remains a significant challenge, often hampered by the limitations of current simulation technology, which struggles to replicate interactions beyond simple, two-particle scenarios. Or Katz, Alexander Schuckert from NIST/University of Maryland, and Tianyi Wang from Duke University, together with Eleanor Crane from King’s College London, Alexey V. Gorshkov from NIST/University of Maryland, and Marko Cetina from Duke University, now present a novel approach to overcome these hurdles. Their research introduces a hybrid digital-analog protocol, seamlessly blending the precision of digital computation with the continuous flow of analog simulation, to effectively generate complex quantum interactions. This breakthrough allows scientists to simulate systems governed by simultaneous, multi-body interactions, a crucial step towards understanding phenomena in areas like condensed matter physics, chemistry, and high-energy physics, and importantly, achieves this without the errors that plague existing methods, opening up new possibilities for quantum simulation on near-term hardware.

Gorshkov, and Marko Cetina now present a novel approach to overcome these hurdles. Their research introduces a hybrid digital-analog protocol, seamlessly blending the precision of digital computation with the continuous flow of analog simulation, to effectively generate complex quantum interactions.

This breakthrough allows scientists to simulate systems governed by simultaneous, multi-body interactions, a crucial step towards understanding phenomena in areas like condensed matter physics, chemistry, and high-energy physics, and importantly, achieves this without the errors that plague existing methods, opening up new possibilities for quantum simulation on near-term hardware.

Hybrid Quantum Simulation of Many-Body Interactions

Scientists have achieved a breakthrough in quantum simulation by demonstrating a hybrid digital-analog protocol capable of generating complex many-body interactions, specifically three- and four-body interactions, without the limitations of traditional digital or analog methods. This work overcomes a significant hurdle in simulating systems relevant to condensed matter physics, chemistry, and high-energy physics, which often require these higher-order interactions. The core of the achievement lies in embedding analog evolution between shallow layers of digital entangling gates, creating an effective Hamiltonian that allows for non-perturbative generation of these interactions and eliminates Trotter error.

Experiments were conducted on a trapped-ion processor, utilizing a linear chain of fifteen 171Yb+ ions to encode qubits and control their evolution. The team successfully implemented a field-cluster Hamiltonian, a model featuring three-body interaction terms, and a cluster-Ising Hamiltonian, realizing a topological spin chain with strong zero modes, alongside a Hamiltonian incorporating four-body interactions. Measurements confirm the creation of a symmetry-protected topological phase, evidenced by a non-zero string order parameter, which reached near unity during adiabatic preparation of the ground state of the cluster Hamiltonian.

The researchers demonstrated adiabatic preparation of ground states on a five-qubit subsystem, initializing the system in a product state and then ramping down longitudinal fields while simultaneously activating three-body interactions. Data shows a clear decrease in bulk magnetization as the three-body interactions were increased, while the string order parameter remained consistently high, confirming the emergence of the topological phase. Further experiments involved a dynamical transition from open to periodic boundary conditions, where measurements of edge correlations and boundary stabilizers aligned with theoretical predictions, demonstrating precise control over the system’s Hamiltonian evolution.

Hybrid Control Enables Higher-Order Interactions

This research demonstrates a new method of hybrid digital-analog quantum control, enabling the creation of effective Hamiltonians with complex, multi-body interactions, specifically, three- and four-body terms, that are difficult to achieve using conventional digital or analog approaches. The team successfully implemented this technique on a trapped-ion processor, realizing spin chain models exhibiting unusual properties like persistent strong zero modes even at high temperatures, and showcasing the ability to simulate systems governed by these higher-order interactions.

The significance of this work lies in overcoming limitations inherent in current quantum simulation platforms, which typically support only one- and two-body interactions. By combining the strengths of both digital and analog control, researchers can access a broader range of physical systems relevant to condensed matter physics, chemistry, and high-energy physics, and explore more complex quantum dynamics. The method preserves the non-commutativity of interactions and their energy spectrum, offering a powerful and versatile approach to quantum simulation.

The authors acknowledge that the shallow digital circuits used in their hybrid scheme, while crucial for preventing state entanglement and simplifying measurement, introduce a degree of complexity, and that simulating dynamics with these circuits can be computationally challenging. They also note that implementing certain digital circuits remains a significant hurdle. Future research will likely focus on extending this hybrid approach to larger systems and exploring its application to a wider range of physical models, further expanding the capabilities of quantum simulation.