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Wilmott

Perspectives of Quantum Computing

Alexei Kondratyev

Published Apr 16, 2024• 0 citations
Publisher

Abstract

Here, we are facing two fundamental questions.First, can we run quantum computing protocol on classical hardware? That is, can we simulate a quantum computer on the classical one?Second, can we find the way of controlling an actual quantum mechanical system, such that it executes intended computational instructions? That is, can we build the quantum processing unit (QPU)?

DOI
10.54946/wilm.12040

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Here, we are facing two fundamental questions.First, can we run quantum computing protocol on classical hardware? That is, can we simulate a quantum computer on the classical one?Second, can we find the way of controlling an actual quantum mechanical system, such that it executes intended computational instructions? That is, can we build the quantum processing unit (QPU)?
Quantum computing is a revolutionary approach to computation that leverages the principles of quantum mechanics, enabling computers to process information in fundamentally different ways than classical computers. Unlike traditional bits, which represent data as either 0s or 1s, quantum bits, or qubits, can exist in multiple states simultaneously due to superposition. Additionally, qubits can be entangled, allowing them to be interconnected in ways that enhance computational power and efficiency. This unique behavior has the potential to run certain types of computation tasks much faster than classical computers can, marking a significant leap forward in technology. When building actual quantum computers to run practical quantum algorithms, one needs efficient ways to map the algorithms to the hardware components, similar to compiling classical algorithms onto CPU/GPU hardware. This thesis aims to tackle some of the important problems in the mapping process. First, can we address hardware errors and algorithm errors at the same time? Second, can we build a better circuit complexity metric to inspire better quantum architecture design, and can we design better quantum algorithms and compilation techniques using this improved metric? Lastly, can we use physics-level simulation results to inspire better circuit-level optimization techniques? We hope to provide positive answers to all three questions above through three separate architectural innovations.
The topic of this dissertation stands at the crossroads of two emerging technologies: highly-parallel computing and quantum computing. Both seek to go beyond the limits of current computing practice: in the absence of further miniaturization, highly-parallel computing seeks to increase the available computer power substantially. Quantum Computing looks beyond the classical approach to computation, leveraging quantum-mechanical effects to increase computing power in a fundamental way. In the absence and also in the presence of actual quantum computers it is crucial to support the development of quantum computer applications by creating an appropriate software framework. Creating such a framework currently faces two major research challenges. First, one needs to separate the realization of the quantum computer from the software running on it, whether it is an actual physical or a simulated realization. Our first contribution lies with defining a layered software architecture, ranging from a design tool at the higher abstraction levels to a simulated execution layer underneath. At its core sits a ‘Quantum Virtual Machine’ using the Measurement Calculus as the underlying quantum computational model. Such a virtual machine layer makes the application developed on top of it oblivious to how it is executed. The simulated execution of this quantum virtual machine is fundamentally a computationally intensive task. Parallel computing offers a way to throw more computational resources at the problem, in the light of the saturation of sequential performance of current computers. Simulation is the domain of the second challenge, as it has very high performance requirements. The simulation problem thus becomes: how does one expose the inherent parallelism of quantum computing simulation in a fundamental way, so as to be usable for the highly-parallel computers to come? Our second contribution is to provide a formal translation of quantum programs to highly-parallel dataflow computations, and to develop a virtual environment that compiles and executes such programs. This work demonstrates several properties of both the formal as well as the virtual level of computation that validate our approach.
Distributed quantum protocols require measurement outcomes produced at one node to control operations at another. We present QQLink, a programming and orchestration layer that expresses these dependencies in a single program, using workflow nodes, deferred measurement references, and declared entanglement, and derives the cross-node coordination automatically. Its planner constructs a provably acyclic dependency graph in time linear in the total size of the instructions' qubit footprints. The same programs execute through simulator backends or are lowered to dynamic circuits on partitioned quantum hardware. We evaluate seven protocol workflows. Exhaustive feedforward-branch tests on the simulator runtime path, over tomographically complete input sets, yield output-state infidelities of at most 5×10−125\times10^{-12}5×10−12 and no incorrect classical outputs, and replaying every plan in random topological orders leaves each final state unchanged. Separate executor processes run the plans with delayed messages, with the joint quantum state held by a centralized simulation service. Every run with the full plan is correct, and removing required cross-node dependencies causes protocol failures. The lowered circuits match hand-written implementations of the same construction in two-qubit gate and conditional-block counts. Runs on two IBM Heron processors, each partitioned into virtual QPUs, demonstrate same-chip execution in two sessions a week apart. The runs also show large variation between sessions and losses beyond what calibration-derived noise models predict. Coherence-sensitive checks do not establish coherent Toffoli operation or preservation of the intended repetition-code superposition. These results support QQLink's workflow semantics on the tested execution paths and identify limits of the current hardware realization; execution across physically networked QPUs remains future work.