Constructing quantum circuits with global gates

Abstract

There are various gate sets that can be used to describe a quantum computation. A particularly popular gate set in the literature on quantum computing consists of arbitrary single-qubit gates and 2-qubit CNOT gates. A CNOT gate is however not always the natural multi-qubit interaction that can be implemented on a given physical quantum computer, necessitating a compilation step that transforms these CNOT gates to the native gate set. A particularly interesting case where compilation is necessary is for ion trap quantum computers, where the natural entangling operation can act on more than 2 qubits and can even act globally on all qubits at once. This calls for an entirely different approach to constructing efficient circuits. In this paper we study the problem of converting a given circuit that uses 2-qubit gates to one that uses global gates. Our three main contributions are as follows. First, we find an efficient algorithm for transforming an arbitrary circuit consisting of Clifford gates and arbitrary phase gates into a circuit consisting of single-qubit gates and a number of global interactions proportional to the number of non-Clifford phases present in the original circuit. Second, we find a general strategy to transform a global gate that targets all qubits into one that targets only a subset of the qubits. This approach scales linearly with the number of qubits that are not targeted, in contrast to the exponential scaling reported in (Maslov & Nam, N. J. Phys. 2018). Third, we improve on the number of global gates required to synthesise an arbitrary n-qubit Clifford circuit from the 12n-18 reported in (Maslov & Nam, N. J. Phys. 2018) to 6n-8.

arXiv comment13 pages. v2: added some more figures and fixed a number of (mathematical) typos

References in corpus (23)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Improved Simulation of Stabilizer Circuits
• Trapped-Ion Quantum Computing: Progress and Challenges
• Quantum computation with ions in thermal motion
• Demonstration of a small programmable quantum computer with atomic qubits
• A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery
• Interacting Quantum Observables: Categorical Algebra and Diagrammatics
• Polynomial-time T-depth Optimization of Clifford+T circuits via Matroid Partitioning
• From transistor to trapped-ion computers for quantum chemistry
• Automated optimization of large quantum circuits with continuous parameters
• On the advantages of using relative phase Toffolis with an application to multiple control Toffoli optimization
• Graph-theoretic Simplification of Quantum Circuits with the ZX-calculus
• Parallel Entangling Operations on a Universal Ion Trap Quantum Computer
• Experimental Perfect Quantum State Transfer
• Reducing T-count with the ZX-calculus
• Efficient Arbitrary Simultaneously Entangling Gates on a trapped-ion quantum computer
• Compiling quantum algorithms for architectures with multi-qubit gates
• Use of global interactions in efficient quantum circuit constructions
• T-count optimization and Reed-Muller codes
• Efficient construction of three- and four-qubit quantum gates by global entangling gates
• Universal MBQC with generalised parity-phase interactions and Pauli measurements
• ZX-calculus for the working quantum computer scientist
• Signal processing techniques for efficient compilation of controlled rotations in trapped ions

Cited by in corpus (17)

• Protecting Expressive Circuits with a Quantum Error Detection Code
• Synthesis of and compilation with time-optimal multi-qubit gates
• Constant-cost implementations of Clifford operations and multiply controlled gates using global interactions
• Efficient quantum programming using EASE gates on a trapped-ion quantum computer
• Benchmarking universal quantum gates via channel spectrum
• The Munich Quantum Software Stack: Connecting End Users, Integrating Diverse Quantum Technologies, Accelerating HPC
• The fastest generation of multipartite entanglement with natural interactions
• Constant-depth circuits for Boolean functions and quantum memory devices using multi-qubit gates
• Building Qutrit Diagonal Gates from Phase Gadgets
• Universal graph representation of stabilizer codes
• Minimizing readout-induced noise for early fault-tolerant quantum computers
• Improved Strategies for Fermionic Quantum Simulation with Global Interactions
• Fast Quantum Amplitude Encoding of Typical Classical Data
• A graph-state based synthesis framework for Clifford isometries
• Building globally controlled quantum processors with ZZ interactions
• Transversal AND in Quantum Codes
• A Quantum Genetic Algorithm with application to Cosmological Parameters Estimation