The design and implementation of quantum circuits is becoming increasingly challenging due to the technological limitations of quantum computers. To overcome these hurdles, distributed quantum computation has proved useful, making quantum processors cooperate. However, currently available circuit distribution methods focus on unitary operations, while a quantum computer, in order to be capable of performing any general task, must be able to perform a larger class of operations, described by completely positive maps. This work proposes a novel workflow for circuit distribution algorithms addressing this gap, contributing to progress toward fully capable quantum computation.
The design and implementation of quantum circuits is becoming increasingly challenging due to the technological limitations of quantum computers. To overcome these hurdles, distributed quantum computation has proved useful, making quantum processors cooperate. However, currently available circuit distribution methods focus on unitary operations, while a quantum computer, in order to be capable of performing any general task, must be able to perform a larger class of operations, described by completely positive maps. This work proposes a novel workflow for circuit distribution algorithms addressing this gap, contributing to progress toward fully capable quantum computation.
Quantum computing promises to solve some problems that are intractable by classical computers. Several quantum processors based on different technologies and consisting of a few tens of noisy qubits have already been developed. However, qubits are fragile as they tend to decohere extremely quickly and quantum operations are faulty, making reliable computation very difficult. Moreover, quantum processors have hardware constraints such as limited qubit connectivity and shared classical control, making quantum algorithms not directly executable. This thesis focuses on some of the challenges of the implementation of quantum algorithms on near-termintermediate-scale and future large-scale quantum processors. More precisely, it investigates how to perform reliable quantum computation using fault-tolerant protocols and how to execute quantum algorithms on hardware-constrained processors using circuit-mapping techniques.
Distributed quantum computing (DQC) is a rapidly evolving field with its own unique challenges. Distributing a quantum algorithm involves several key steps and considerations. The steps involve decomposition at various levels of abstraction, given the underlying quantum stack and quantum network capabilities. In our DQC design explorations, we focus on the distribution at the algorithm and circuit levels. Algorithmic distribution involves distributing tasks before compilation, allowing different quantum processing units (QPUs) to receive distinct parts of an algorithm. Circuit distribution involves executing a quantum algorithm in a distributed manner at the circuit execution level using circuit and adaptive quantum technologies. If entanglement across QPUs is supported, then quantum states can be shared between qubits on remote quantum processors. This requires a specialized architecture with data and communication qubits with non-local gates such as telegates and teledata gates. This paper presents our progress towards a framework for exploring quantum distribution at the algorithm and circuit levels. Our implementation and case studies demonstrate the feasibility of our approach and show effective pathways for distributed quantum algorithm experiments.
Although the concept of quantum computing has existed for decades, the technology needed to successfully implement a quantum computing system has not yet reached the level of sophistication, reliability, and scalability necessary for commercial viability until very recently. Significant progress on this front was made in the past few years, with IBM planning to create a 1000-qubit chip by the end of 2023, and Google already claiming to have achieved quantum supremacy. Other major industry players such as Intel and Microsoft have also invested significant amounts of resources into quantum computing research. Any viable computing system requires both hardware and software to work together harmoniously in order to perform useful computations. While the achievements of IBM and other companies represent a large step forward for quantum hardware, many gaps remain to be filled with respect to the corresponding software. Specifically, there is currently no clear path towards a complete process for translating quantum algorithms into physical operations that are directly executable on quantum hardware. Such a process is analogous to a compiler that translates programs written in a high-level language into executable machine instructions on a conventional digital computer, and it is necessary if quantum computers are to be harnessed to perform practically useful computations. Existing work has addressed individual components of this process, but so far no unified method for translating the whole of a quantum algorithm into executable operations has been described. I make substantial progress towards filling this gap by describing a set of high-level and low-level quantum circuit design techniques, which when taken together reduce the need of a circuit designer to be concerned with low-level details. On the high-level side, I describe an approach or strategy to designing quantum oracles for Grover's algorithm that allows it to be applied to several types of problems. This approach involves designing oracles in terms of high-level blocks such as counters, multiplexers, comparators, and arbitrary Boolean functions. The implementations of these blocks in terms of lower-level quantum gates are demonstrated in a way that makes it clear that scaled-up versions of them can be generated in a completely automated fashion. For a specific class of problems, which I call state-space path planning problems, I also introduce a paradigm for quantum oracle design that involves representing the problem in terms of individual states and moves. Problems of this sort have applications in robotics and games. Low-level techniques that I introduce
Nowadays, quantum computing has reached the engineering phase, with fully-functional quantum processors integrating hundreds of noisy qubits. Yet – to fully unveil the potential of quantum computing out of the labs into the business reality – the challenge ahead is to substantially scale the qubit number, reaching orders of magnitude exceeding thousands of fault-tolerant qubits. To this aim, the distributed quantum computing paradigm is recognized as the key solution for scaling the number of qubits. Indeed, accordingly to such a paradigm, multiple small-to-moderate-scale quantum processors communicate and cooperate for executing computational tasks exceeding the computational power of single processing devices. The aim of this survey is to provide the reader with an overview about the main challenges and open problems arising with distributed quantum computing from a computer and communications engineering perspective. Furthermore, this survey provides an easy access and guide towards the relevant literature and the prominent results in the field.
Quantum fingerprinting is a technique that maps classical input word to a quantum state.The obtained quantum state is much shorter than the original word, and its processing uses less resources, making it useful in quantum algorithms, communication, and cryptography.One of the examples of quantum fingerprinting is quantum automata algorithms for MOD p = {a i•p | i ≥ 0} languages, where p is a prime number.However, implementing such an automaton on the current quantum hardware is not efficient.Quantum fingerprinting maps a word x ∈ {0, 1} n of length n to a state |ψ(x) of O(log n) qubits, and uses O(n) unitary operations.Computing quantum fingerprint using all available qubits of the current quantum computers is infeasible due to a large number of quantum operations.To make quantum fingerprinting practical, we should optimize the circuit for depth instead of width in contrast to the previous works.We propose explicit methods of quantum fingerprinting based on tools from additive combinatorics, such as generalized arithmetic progressions (GAPs), and prove that these methods provide circuit depth comparable to a probabilistic method.We also compare our method to prior work on explicit quantum fingerprinting methods.
Codesign, an integral part of computer architecture referring to the information interaction in hardware-software stack, is able to boost the algorithm mapping and execution in the computer hardware. This well applies to the noisy intermediate-scale quantum era, where quantum algorithms and quantum processors both need to be shaped to allow for advantages in experimental implementations. The state-of-the-art quantum adiabatic optimization algorithm faces challenges for scaling up, where the deteriorating optimization performance is not necessarily alleviated by increasing the circuit depth given the noise in the hardware. The counterdiabatic term can be introduced to accelerate the convergence, but decomposing the unitary operator corresponding to the counterdiabatic terms into one and two-qubit gates may add additional burden to the digital circuit depth. In this work, we focus on the counterdiabatic protocol with a codesigned approach to implement this algorithm on a photonic quantum processor. The tunable Mach-Zehnder interferometer mesh provides rich programmable parameters for local and global manipulation, making it able to perform arbitrary unitary evolutions. Accordingly, we directly implement the unitary operation associated to the counterdiabatic quantum optimization on our processor without prior digitization. Furthermore, we develop and implement an optimized counterdiabatic method by tackling the higher-order many-body interaction terms. Moreover, we benchmark the performance in the case of factorization, by comparing the final success probability and the convergence speed. In conclusion, we experimentally demonstrate the advantages of a codesigned mapping of counterdiabatic quantum dynamics for quantum computing on photonic platforms.