Quantinuum’s New Approach to Adiabatic Quantum Computing: Optimizing Circuits with Tensor Network Algorithms

Adiabatic Quantum Computing (AQC) uses quantum mechanics principles to solve complex computational problems. However, managing long evolution times can be challenging. A recent paper by Conor Mc Keever and Michael Lubasch from Quantinuum proposes using tensor network algorithms to optimize quantum circuits for AQC. They suggest dividing the total evolution time into shorter intervals, optimizing a specific parameterized quantum circuit (PQC) for each chunk. This approach, combined with counterdiabatic driving, could potentially improve ground-state fidelities by a factor of 5 and energy accuracies by a factor of 3, offering a more efficient and accurate quantum computation method.

What is Adiabatic Quantum Computing?

Adiabatic quantum computing (AQC) is a form of quantum computing that uses the principles of quantum mechanics to solve complex computational problems. The concept of AQC is based on the adiabatic theorem of quantum mechanics, which states that a quantum system will remain in its ground state if the Hamiltonian (a mathematical function that describes the total energy of the system) changes slowly enough over time.

In AQC, the quantum computer starts in a simple ground state and then evolves over time according to a specific time-dependent Hamiltonian. The initial ground state is trivial, and the final ground state encodes the desired computational result. The process is successful if the evolution occurs slowly enough, and the total evolution time scales with the minimum energy difference between the ground and the first excited state during the evolution.

How is Adiabatic Quantum Computing Implemented?

Traditionally, adiabatic time evolution is realized on digital quantum computers using Trotter product formulas. However, long evolution times can lead to deep circuits, which can be challenging to manage. One strategy to reduce the adiabatic evolution time is to include additional terms in the Hamiltonian that suppress unwanted transitions during the time evolution, a process known as counterdiabatic driving.

However, these additional Hamiltonian terms can lead to deeper Trotter circuits per time step on a gate-based quantum device. Therefore, adiabatic time evolution over many time steps with or without counterdiabatic driving can still be a challenge for current digital quantum computers.

What is the Role of Tensor Network Algorithms in Adiabatic Quantum Computing?

In a recent paper by Conor Mc Keever and Michael Lubasch from Quantinuum, they describe tensor network algorithms to optimize quantum circuits for AQC. They extend the tensor network toolbox for parameterized quantum circuit (PQC) optimization of Hamiltonian simulation to tackle AQC enhanced by counterdiabatic driving.

The key ingredients of counterdiabatic driving that suppress unwanted transitions are the auxiliary Hamiltonian terms, which they refer to as the adiabatic gauge potential (AGP). They study the suitability of a variational matrix-product operator (MPO) ansatz to approximate the AGP. The MPO ansatz naturally fits within their tensor network approach and they also show that it can have advantages over the popular nested commutator (NC) ansatz.

How is the Optimization Process Carried Out?

The total evolution time is divided into several chunks of shorter time intervals. For each chunk, a specific PQC dedicated to that chunk is optimized to capture the counterdiabatic dynamics over the shorter evolution time of the chunk. After the classical optimization, the sequence of PQCs represents the entire counterdiabatic evolution and can be evaluated on a quantum computer.

In the context of transverse-field quantum Ising chains with a longitudinal field, they numerically demonstrate that compared with Trotter circuits, the classically optimized PQCs can improve ground-state fidelities by a factor of 5 and energy accuracies by a factor of 3.

What are the Implications of this Research?

This research is significant as it provides a new approach to AQC that can potentially overcome some of the challenges associated with traditional methods. By using tensor network algorithms to optimize quantum circuits and incorporating counterdiabatic driving, it may be possible to achieve more efficient and accurate quantum computations.

This approach is inspired by several important articles. Firstly, variational quantum algorithms can be used to simulate quantum dynamics, and beautiful proposals exist that make use of counterdiabaticity by including additional gates in the PQC ansatz that come from counterdiabatic driving. Secondly, classical tensor network algorithms have already successfully simulated the entire evolution corresponding to certain adiabatic protocols.

In contrast to these simulations, their procedure does not require the classical tensor network optimization to be capable of capturing the entire evolution, instead only short chunks of the evolution need to be classically simulable. The PQC compression of time evolution for each chunk can be performed such as to exhaust the capabilities of classical computing, then appending all PQCs can create a quantum circuit that is hard to simulate for classical computers but efficient to run on a quantum computer.