The block-ZXZ synthesis of an arbitrary quantum circuit

Abstract

Given an arbitrary $2^w\times 2^w$ unitary matrix $U$, a powerful matrix decomposition can be applied, leading to four different syntheses of a $w$-qubit quantum circuit performing the unitary transformation. The demonstration is based on a recent theorem by Führ and Rzeszotnik, generalizing the scaling of single-bit unitary gates ($w=1$) to gates with arbitrary value of~$w$. The synthesized circuit consists of controlled 1-qubit gates, such as NEGATOR gates and PHASOR gates. Interestingly, the approach reduces to a known synthesis method for classical logic circuits consisting of controlled NOT gates, in the case that $U$ is a permutation matrix.

Improved (non-sinkhorn) algorithm to obtain the proposed circuit

References in corpus (6)

• Synthesis of Quantum Logic Circuits
• Engineering of arbitrary U(N) transformations by quantum Householder reflections
• A Depth-Optimal Canonical Form for Single-qubit Quantum Circuits
• Sinkhorn normal form for unitary matrices
• Scaling a unitary matrix
• The Canonical Coset Decomposition of Unitary Matrices Through Householder Transformations

Cited by in corpus (10)

• LEAP: Scaling Numerical Optimization Based Synthesis Using an Incremental Approach
• Constant-Depth Circuits for Dynamic Simulations of Materials on Quantum Computers
• QFAST: Quantum Synthesis Using a Hierarchical Continuous Circuit Space
• Heuristics for Quantum Compiling with a Continuous Gate Set
• Quantum circuit synthesis using Householder transformations
• QGo: Scalable Quantum Circuit Optimization Using Automated Synthesis
• Domain-Specific Compilers for Dynamic Simulations of Quantum Materials on Quantum Computers
• Constructive quantum scaling of unitary matrices
• Enhancing quantum models of stochastic processes with error mitigation
• High-Precision Multi-Qubit Clifford+T Synthesis by Unitary Diagonalization