Quantum digital twins based on hardware-tailored tensor networks for computing quantum dynamics

Quantum computing offers a promise to solve problems that cannot be addressed by classical devices, and an early access to quantum computers is vital for UK national security. The ability to solve complex problems with quantum computers relies on optimising both the hardware (quantum devices) and the software (quantum algorithms). In this project, we will design the tools for improving the quantum software, which can largely save required resources for state preparation and simulation of dynamics. We call these tools the quantum digital twins - specific programmable models that help representing quantum devices in the most efficient way, and thus enabling their optimisation.

Quantum computing (QC) offers a distinct paradigm for performing calculations. Unlike classical computers that operate with bits (taking binary values 0 or 1), quantum devices rely on two-level quantum systems - qubits - that are described by states |0> and |1> that can be put in a superposition. The collection of N qubits can be efficiently evolved on specialised hardware - quantum computers - thus processing information encoded in a quantum form. Classical processing of the same amount of information will require manipulating 2^N complex numbers, a task that becomes impossible already at the size of fifty qubits. We know that in the future quantum computing can exponentially speed up factoring (having a huge impact on cryptography) and help with areas such as simulating materials and chemicals at a scale impossible before (promoting substantial steps towards green energy and sustainability).

Quantum hardware is developed by various industrial and academic institutions worldwide. Qubit counts grow every year, and this makes community hopeful for achieving a practical quantum advantage in the near term. Yet, the current level of noise does not allow for running circuits of sufficient depth. Specifically designed quantum software may help to alleviate this problem if tailored algorithms are developed. This challenge calls for imaginative approaches that account for hardware capabilities and limitations.

To harness benefits from near-term quantum computing, UK needs to channel an effort on developing software tools that enable the scalable prototyping of quantum algorithms and allow for benchmarking quantum devices at the increased scale. We propose to do this by designing quantum digital twins as efficient tensor network emulators of quantum devices.

This project is the collaboration between quantum researchers at the University of Exeter and the National Physical Laboratory. It is built on the three pillars, each representing an open challenge for advancing quantum software and applications: 1) developing efficient tools for quantum state preparation and quantum circuit emulation; 2) developing quantum digital twins of the dynamics; 3) benchmarking quantum algorithms for solving computationally-hard problems in material science.

To tackle these challenges we will address three objectives:
1. We will develop compact tensor network representations for low energy states of relevant quantum Hamiltonians, and translate these tensor networks into low-depth quantum circuits for efficient initial quantum state preparation.
2. We will develop scalable tensor network-based emulators of quantum dynamics as quantum digital twins, taking advantage of the knowledge of the hardware-specific Hamiltonians.
3. We will benchmark the scalability of quantum digital twins for emulating quantum devices in materials simulations, and determine the threshold for potential quantum advantage.

As a result of the project, we will have the efficient tools that enable the scalable prototyping and improving of quantum simulation, thus maximizing the performance of quantum computers at increasing scale.