Formal Constraint-based Compilation for Noisy Intermediate-Scale Quantum
  Systems
Noisy, intermediate-scale quantum (NISQ) systems are expected to have a few
hundred qubits, minimal or no error correction, limited connectivity and limits
on the number of gates that can be performed within the short coherence window
of the machine. The past decade's research on quantum programming languages and
compilers is directed towards large systems with thousands of qubits. For near
term quantum systems, it is crucial to design tool flows which make efficient
use of the hardware resources without sacrificing the ease and portability of a
high-level programming environment. In this paper, we present a compiler for
the Scaffold quantum programming language in which aggressive optimization
specifically targets NISQ machines with hundreds of qubits. Our compiler
extracts gates from a Scaffold program, and formulates a constrained
optimization problem which considers both program characteristics and machine
constraints. Using the Z3 SMT solver, the compiler maps program qubits to
hardware qubits, schedules gates, and inserts CNOT routing operations while
optimizing the overall execution time. The output of the optimization is used
to produce target code in the OpenQASM language, which can be executed on
existing quantum hardware such as the 16-qubit IBM machine. Using real and
synthetic benchmarks, we show that it is feasible to synthesize near-optimal
compiled code for current and small NISQ systems. For large programs and
machine sizes, the SMT optimization approach can be used to synthesize compiled
code that is guaranteed to finish within the coherence window of the machine.
Prakash Murali Ali Javadi-Abhari Frederic T. Chong Margaret Martonosi