November 27, 2022

Effective compression of quantum circuits

NISQ devices are still prone to lots of errors, therefore the design of a fully operational large-scale quantum computer with high error tolerance is required. Currently, NISQ devices can be engineered with approximately 100 qubits, but fault-tolerant computers would need millions of physical qubits at the very least to encode the logical information with sufficiently low error rates.

Researchers from the National Institute of Informatics (NII) and Nippon Telegraph and Telephone Corporation (NTT) in Japan tackled the problem from the software development side by compressing quantum circuits in large-scale fault-tolerant quantum computers, potentially reducing the need for hardware improvements.

The researchers focused on the circuit compression of one of these variants: the 3-D-topological code. This code behaves particularly well for distributed quantum computer approaches and has wide applicability to different varieties of hardware. In the 3-D-topological code, quantum circuits look like interlacing tubes or pipes, and are commonly called “braided circuits“. The 3-D diagrams of braided circuits can be manipulated to compress and thus reduce the volume they occupy.

The research team proposes the use of ZX-calculus as a language for this intermediate stage of compilation. ZX-calculus is a 2-D diagrammatic language (using diagrams and imagery instead of words) developed in the late 2000s expressly to allow an intuitive representation of qubit processes. More importantly, it comes with a complete set of manipulation rules.

They have harnessed ZX-calculus by discovering the translation relations between ZX-calculus and the components of the braided circuit. The researchers have shown that these two representations of logical gate circuits can be mapped to one another by identifying a new interpretation that had been hidden within ZX-calculus all along.

The ZX-calculus language can apply a set of transformation rules to alter the structure of the circuit without altering its underlying mathematical meaning (and thus its operation) and therefore ensuring its correctness. By altering that conceptual structure carefully, the volume of the circuit can be minimized, achieving considerable compression rates once this new structure is mapped to the actual braided quantum circuit.

Applying this technique, the researchers report compression reductions of up to 77 percent, equivalent to a 40 percent reduction compared to the best previous efforts. (

The paper has been published in Physical Review X.

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