Quantum Circuit Compression using Qubit logic on Qudits

A Quandela researcher has advanced quantum computing, developing a new approach that significantly reduces the number of physical entangling gates required to implement a quantum circuit. This innovation, called Qubit Logic on Qudits (QLOQ), has been successfully tested in two applications: variational quantum algorithms and unitary decomposition.

In the first application, QLOQ was used to run a variational quantum eigensolver for Lithium Hydride on Quandela’s linear optical quantum computer, achieving a more accurate final ground state energy estimate in simulations than traditional qubit-based approaches.

The second application demonstrated that QLOQ can decompose unitary matrices with significantly fewer CNOT gates than traditional methods. This work has significant implications for the development of practical quantum computing architectures, particularly in photonics where qudits are easy to deploy. Companies involved in this research include Quandela, a leader in photonic quantum processing units.

Current methods for converting qubit-based quantum circuits to qudit-based ones don’t work well under realistic assumptions. Qudits are higher-dimensional quantum systems that can process more information than traditional qubits.The authors propose a new approach called QLOQ (Qubit Logic on Qudits), which allows for the implementation of arbitrary qubit-logic unitary operations using fewer physical entangling gates than traditional qubit encoding. This means that QLOQ can be more efficient and scalable than existing methods.The paper highlights two key advantages of QLOQ:

1. Fewer Entangling Gates: By mapping multiple qubits to a single qudit, entangling gates between them become local operations, which require fewer resources on hardware.
2. Efficient Multi-Controlled Unitary Gates: QLOQ allows for the application of multi-controlled unitary gates between all qubits mapped to a pair of qudits using a single physical two-level (qubit) entangling gate.

The author demonstrates the effectiveness of QLOQ in two areas:

1. Variational Quantum Algorithms (VQAs): They show that QLOQ ansatze for VQAs require significantly fewer physical entangling gates than qubit-based ansatze to achieve a given level of expressibility.
2. Unitary Decomposition: QLOQ can decompose unitary matrices more efficiently than traditional methods, with the number of CNOTs required decreasing exponentially as the number of qubits mapped to each qudit increases.

QLOQ is particularly well-suited for photonics-based quantum computing architectures, where qudits are easier to deploy. The authors illustrate this advantage by comparing the actual time required for QLOQ VQE (5 hours) and estimated time for qubit-based VQE (4.39 years) to converge on a photonic quantum processing unit.

In summary, QLOQ offers a promising approach for implementing qubit-logic unitary operations more efficiently on qudit-based quantum computing architectures. Its advantages in reducing entangling gates and enabling efficient multi-controlled unitary gates make it an attractive solution for various applications, particularly in photonics-based systems.