Enabling accuracy-aware Quantum compilers using symbolic resource estimation

Abstract

Approximation errors must be taken into account when compiling quantum programs into a low-level gate set. We present a methodology that tracks such errors automatically and then optimizes accuracy parameters to guarantee a specified overall accuracy while aiming to minimize the implementation cost in terms of quantum gates. The core idea of our approach is to extract functions that specify the optimization problem directly from the high-level description of the quantum program. Then, custom compiler passes optimize these functions, turning them into (near-)symbolic expressions for (1) the total error and (2) the implementation cost (e.g., total quantum gate count). All unspecified parameters of the quantum program will show up as variables in these expressions, including accuracy parameters. After solving the corresponding optimization problem, a circuit can be instantiated from the found solution. We develop two prototype implementations, one in C++ based on Clang/LLVM, and another using the Q# compiler infrastructure. We benchmark our prototypes on typical quantum computing programs, including the quantum Fourier transform, quantum phase estimation, and Shor's algorithm.

QIRO: A Static Single Assignment-based Quantum Program Representation for Optimization

“…One particularly eicient way to generate resource (or quantum gate) counts, is to strategically lower and replace quantum operations by classical ones in a way that preserves the structure of the quantum program, and increments simple counters for each measured resource [23]. In this process, all adjoint and controlled circuits must irst be lowered using the passes described above.…”

“…Any remaining and unused operations from the quantum dialects must be stripped, and circuit deinitions and calls must be converted to standard MLIR functions. Special care must be taken when removing measurements, so as to provide a conservative estimate for computations that depend on measurement outcomes [23]. Finally, the purely classical IR can be lowered to LLVM IR using standard MLIR infrastructure, and subsequently compiled into an executable outputting the inal resource counts for a given input size.…”

“…A simpliied implementation of this resource estimator was used to compute the rotation gate counts in Section 6.3. We note that the run time for computing resource estimates may be reduced further using custom compiler passes such as the ones employed by Meuli et al [23].…”

“…Extrapolating our measurements to 2000 bits based on a polynomial of degree 4 (as the number of gates scales quartically), we roughly estimate to be able to process Shor's algorithm in QIRO on the order of a week, rather than upwards of 10 4 years in ProjectQ and 10 3 years in Qiskit. To further speed up resource estimation, we plan to implement custom compiler passes such as the ones proposed by Meuli et al [23].…”

An Automated Deductive Verification Framework for Circuit-building Quantum Programs

“…Certifying the complexity of quantum implementations (e.g., polynomial number of gates in the size of the input) is of primary importance as in mid-term, implementations will have to deal with limited hardware capacities, hence the need for tight circuit constructions. We stress that, while raised by several programming [30] or compilation works [48], this aspect of certification is not addressed by existing formal verification approaches [35,45,1].…”