Near-term quantum computers are expected to work in an environment where each
operation is noisy, with no error correction. Therefore, quantum-circuit
optimizers are applied to minimize the number of noisy operations. Today,
physicists are constantly experimenting with novel devices and architectures.
For every new physical substrate and for every modification of a quantum
computer, we need to modify or rewrite major pieces of the optimizer to run
successful experiments. In this paper, we present QUESO, an efficient approach
for automatically synthesizing a quantum-circuit optimizer for a given quantum
device. For instance, in 1.2 minutes, QUESO can synthesize an optimizer with
high-probability correctness guarantees for IBM computers that significantly
outperforms leading compilers, such as IBM's Qiskit and TKET, on the majority
(85%) of the circuits in a diverse benchmark suite.
A number of theoretical and algorithmic insights underlie QUESO: (1) An
algebraic approach for representing rewrite rules and their semantics. This
facilitates reasoning about complex symbolic rewrite rules that are beyond the
scope of existing techniques. (2) A fast approach for probabilistically
verifying equivalence of quantum circuits by reducing the problem to a special
form of polynomial identity testing. (3) A novel probabilistic data structure,
called a polynomial identity filter (PIF), for efficiently synthesizing rewrite
rules. (4) A beam-search-based algorithm that efficiently applies the
synthesized symbolic rewrite rules to optimize quantum circuits.Comment: Full version of PLDI 2023 pape