Synthesis of and compilation with time-optimal multi-qubit gates

Abstract

We develop a method to synthesize a class of entangling multi-qubit gates for a quantum computing platform with fixed Ising-type interaction with all-to-all connectivity. The only requirement on the flexibility of the interaction is that it can be switched on and off for individual qubits. Our method yields a time-optimal implementation of the multi-qubit gates. We numerically demonstrate that the total multi-qubit gate time scales approximately linear in the number of qubits. Using this gate synthesis as a subroutine, we provide compilation strategies for important use cases: (i) we show that any Clifford circuit on $n$ qubits can be implemented using at most $2n$ multi-qubit gates without requiring ancilla qubits, (ii) we decompose the quantum Fourier transform in a similar fashion, (iii) we compile a simulation of molecular dynamics, and (iv) we propose a method for the compilation of diagonal unitaries with time-optimal multi-qubit gates, as a step towards general unitaries. As motivation, we provide a detailed discussion on a microwave controlled ion trap architecture with magnetic gradient induced coupling (MAGIC) for the generation of the Ising-type interactions.

35 pages, 7 figures, v2: improved section 3.2.3 + new example

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• Constant Depth Code Deformations in the Parity Architecture
• Fault-tolerant quantum computing with the parity code and noise-biased qubits
• General, efficient, and robust Hamiltonian engineering
• Time-optimal multi-qubit gates: Complexity, efficient heuristic and gate-time bounds
• The role of higher-order terms in trapped-ion quantum computing with magnetic gradient induced coupling
• Multi-Mode Global Driving of Trapped Ions for Quantum Circuit Synthesis
• Benchmarking Digital-Analog Quantum Computation
• Hamiltonian simulation with explicit formulas for Digital-Analog Quantum Computing