The quantum simulation kernel is an important subroutine appearing as a very long gate sequence in many quantum programs. In this paper, we propose Paulihedral, a block-wise compiler framework that can deeply optimize this subroutine by exploiting hi
gh-level program structure and optimization opportunities. Paulihedral first employs a new Pauli intermediate representation that can maintain the high-level semantics and constraints in quantum simulation kernels. This naturally enables new large-scale optimizations that are hard to implement at the low gate-level. In particular, we propose two technology-independent instruction scheduling passes, and two technology-dependent code optimization passes which reconcile the circuit synthesis, gate cancellation, and qubit mapping stages of the compiler. Experimental results show that Paulihedral can outperform state-of-the-art compiler infrastructures in a wide-range of applications on both near-term superconducting quantum processors and future fault-tolerant quantum computers.
Computational chemistry is the leading application to demonstrate the advantage of quantum computing in the near term. However, large-scale simulation of chemical systems on quantum computers is currently hindered due to a mismatch between the comput
ational resource needs of the program and those available in todays technology. In this paper we argue that significant new optimizations can be discovered by co-designing the application, compiler, and hardware. We show that multiple optimization objectives can be coordinated through the key abstraction layer of Pauli strings, which are the basic building blocks of computational chemistry programs. In particular, we leverage Pauli strings to identify critical program components that can be used to compress program size with minimal loss of accuracy. We also leverage the structure of Pauli string simulation circuits to tailor a novel hardware architecture and compiler, leading to significant execution overhead reduction by up to 99%. While exploiting the high-level domain knowledge reveals significant optimization opportunities, our hardware/software framework is not tied to a particular program instance and can accommodate the full family of computational chemistry problems with such structure. We believe the co-design lessons of this study can be extended to other domains and hardware technologies to hasten the onset of quantum advantage.
Practical error analysis is essential for the design, optimization, and evaluation of Noisy Intermediate-Scale Quantum(NISQ) computing. However, bounding errors in quantum programs is a grand challenge, because the effects of quantum errors depend on
exponentially large quantum states. In this work, we present Gleipnir, a novel methodology toward practically computing verified error bounds in quantum programs. Gleipnir introduces the $(hatrho,delta)$-diamond norm, an error metric constrained by a quantum predicate consisting of the approximate state $hatrho$ and its distance $delta$ to the ideal state $rho$. This predicate $(hatrho,delta)$ can be computed adaptively using tensor networks based on the Matrix Product States. Gleipnir features a lightweight logic for reasoning about error bounds in noisy quantum programs, based on the $(hatrho,delta)$-diamond norm metric. Our experimental results show that Gleipnir is able to efficiently generate tight error bounds for real-world quantum programs with 10 to 100 qubits, and can be used to evaluate the error mitigation performance of quantum compiler transformations.
Building a quantum computer that surpasses the computational power of its classical counterpart is a great engineering challenge. Quantum software optimizations can provide an accelerated pathway to the first generation of quantum computing applicati
ons that might save years of engineering effort. Current quantum software stacks follow a layered approach similar to the stack of classical computers, which was designed to manage the complexity. In this review, we point out that greater efficiency of quantum computing systems can be achieved by breaking the abstractions between these layers. We review several works along this line, including two hardware-aware compilation optimizations that break the quantum Instruction Set Architecture (ISA) abstraction and two error-correction/information-processing schemes that break the qubit abstraction. Last, we discuss several possible future directions.
We present CertiQ, a verification framework for writing and verifying compiler passes of Qiskit, the most widely-used quantum compiler. To our knowledge, CertiQ is the first effort enabling the verification of real-world quantum compiler passes in a
mostly-automated manner. Compiler passes written in the CertiQ interface with annotations can be used to generate verification conditions, as well as the executable code that can be integrated into Qiskit. CertiQ introduces the quantum circuit calculus to enable the efficient checking of equivalence of quantum circuits by encoding such a checking procedure into an SMT problem. CertiQ also provides a verified library of widely-used data structures, transformation functions for circuits, and conversion functions for different quantum data representations. This verified library not only enables modular verification but also sheds light on future quantum compiler design. We have re-implemented and verified 26 (out of 30) Qiskit compiler passes in CertiQ, during which three bugs are detected in the Qiskit implementation. Our verified compiler pass implementations passed all of Qiskits regression tests without showing noticeable performance loss.
Gottesman-Kitaev-Preskill (GKP) states appear to be amongst the leading candidates for correcting errors when encoding qubits into oscillators. However the preparation of GKP states remains a significant theoretical and experimental challenge. Until
now, no clear definitions for fault-tolerantly preparing GKP states have been provided. Without careful consideration, a small number of faults can lead to large uncorrectable shift errors. After proposing a metric to compare approximate GKP states, we provide rigorous definitions of fault-tolerance and introduce a fault-tolerant phase estimation protocol for preparing such states. The fault-tolerant protocol uses one flag qubit and accepts only a subset of states in order to prevent measurement readout errors from causing large shift errors. We then show how the protocol can be implemented using circuit QED. In doing so, we derive analytic expressions which describe the leading order effects of the non-linear dispersive shift and Kerr non-linearity. Using these expressions, we show that to mitigate the non-linear dispersive shift and Kerr terms would require the protocol to be implemented on time scales four orders of magnitude longer than the time scales relevant to the protocol for physically motivated parameters. Despite these restrictions, we numerically show that a subset of the accepted states of the fault-tolerant phase estimation protocol maintain good error correcting capabilities even in the presence of noise.
