Research Area

proximate Quantum Compilation and Quantum Simulation

Objective and Background

The idea that quantum dynamics of many-body physics is better simulated by controllable quantum systems was put forward by Richard Feynman 40 years ago. This is known as quantum simulation and is expected to be one of the most promising short term goals of near term quantum computing devices with inevitable applications in diverse areas ranging from quantum chemistry and material science to high energy physics. Quantum simulators currently come in two different flavours: analogue and digital. In an analogue simulator a purpose built controllable quantum many-body system is prepared in the laboratory with the ability to mimic a specific model Hamiltonian of interest. In a digital simulator the quantum dynamics is mapped to a series of discrete time gates that are used to directly manipulate the information encoded in the quantum state. 

While analogue simulators are built with a specific model in mind, digital simulation offers the possibility to program different Hamiltonian models so that a wide range of quantum dynamics is, in principle, accessible on the same device. The possibility of universal simulation of many-body quantum dynamics afforded by digital quantum simulation is a tantalising one. In reality, however, the current devices are still some distance from this goal with noisy gate operations and readout. Ultimately, significant progress in error correcting techniques is needed. In fact it has been on analogue devices where the most significant progress has been made in simulating many-body dynamics. However, recent progress in error mitigation techniques for digital devices has brought us closer to getting quantitative results from noisy simulations. 

One dimensional interacting quantum spin systems are perhaps the simplest non-trivial models used in the field of many-body physics. Despite the obvious shortcomings on noisy near-term quantum devices, there have been several interesting digital simulations which are restricted to either small systems or short times. These simulations can be viewed as important benchmarks of device capability. 

In our first work, we show how noisy near-term quantum devices can be used to shed important light on a research topic which is at the forefront of research in low-dimensional quantum spin dynamics. The issue we address concerns the nature of the emergent high temperature anomalous hydrodynamics of the spin-1/2 XXZ spin chain at the isotropic point. We create and evolve random states on the quantum device in order to perform stochastic trace evaluation, which in turn allows us to calculate infinite temperature correlation functions of the system. We then analyse how these correlations decay in time to extract the conductivity properties of the material being simulated.

Figure caption:

(a) The ibmq montreal qubit connectivity, with a 1-dimensional $XXZ$ model (OBC) mapped onto a 21-qubit chain in the device (we label them $q_{j}$). Site $q_0$ is mapped to the encircled qubit, and is untouched by the randomisation procedure. (b) Red (blue) is CNOT pattern A (B) used in the random state preparation. These are alternated at each layer of the iterated random circuit. (c) The bipartite von Neumann entanglement entropy of the 20 qubit chain as a function of the number of layers in the random circuit. These results are from a clean simulation with connectivity matching that of ibmq montreal. The dashed line represents the maximum Page value. (d) The spin density profile of the final state of one sampling of the random circuit