Heralded gate search with genetic algorithms for quantum computation

In this paper we present genetic algorithms based search technique for the linear optics schemes, performing two-qubit quantum gates. We successfully applied this technique for finding heralded two-qubit gates and obtained the new schemes with performance parameters equal to the best currently known. The new simple metrics is introduced which enables comparison of schemes with different heralding mechanisms. The scheme performance degradation is discussed for the cases when detectors in the heralding part of the scheme are not photon-number-resolving. We propose a procedure for overcoming this drawback which allows us to restore the reliable heralding signal even with not-photon-number-resolving detectors

Learning, Verifying, and Erasing Errors on a Chaotic and Highly Entangled Programmable Quantum Simulator

Controlled quantum systems have the potential to make major advancements in tasks ranging from computing to metrology. In recent years, quantum devices have experienced tremendous progress, reaching meaningful, intermediate-scale sizes and demonstrating advantage over their classical counterparts. Still, sensing, learning, verifying, and hopefully mitigating errors in these systems is an outstanding and ubiquitous challenge facing all modern quantum platforms. Here we review and expound upon one such platform: arrays of Rydberg atoms trapped in optical tweezers. We demonstrate several key advancements, including the first experimental realization of erasure conversion to prepare two-qubit Bell states with a fidelity in excess of 0.999, and to cool atoms to their motional ground state. We further showcase the tools of universal quantum processing via arbitrary single-qubit gates, fixed two-qubit gates, and mid-circuit measurement, and discuss applications of these techniques for metrology and computing. Then, we turn to the many-body regime, generating highly entangled states with up to 60 atoms through analog quench dynamics. We reveal the emergence of random behavior from unitary quantum evolution, and uncover a universal form of quantum ergodicity linking quantum and statistical mechanics. We exploit these discoveries to verify the global many-body fidelity and then realize practical applications like parameter estimation and noise learning. Finally, we compare against both state-of-the-art quantum and classical processors: we introduce a new proxy for the experimental mixed state entanglement which is comparable amongst all quantum platforms, and that reflects the classical complexity of quantum simulation.</p

Loss-tolerant architecture for quantum computing with quantum emitters

We develop an architecture for measurement-based quantum computing using photonic quantum emitters. The architecture exploits spin-photon entanglement as resource states and standard Bell measurements of photons for fusing them into a large spin-qubit cluster state. The scheme is tailored to emitters with limited memory capabilities since it only uses an initial non-adaptive (ballistic) fusion process to construct a fully percolated graph state of multiple emitters. By exploring various geometrical constructions for fusing entangled photons from deterministic emitters, we improve the photon loss tolerance significantly compared to similar all-photonic schemes

Quantum Search Algorithm for Binary Constant Weight Codes

A binary constant weight code is a type of error-correcting code with a wide range of applications. The problem of finding a binary constant weight code has long been studied as a combinatorial optimization problem in coding theory. In this paper, we propose a quantum search algorithm for binary constant weight codes. Specifically, the search problem is newly formulated as a quadratic unconstrained binary optimization (QUBO) and Grover adaptive search (GAS) is used for providing the quadratic speedup. Focusing on the inherent structure of the problem, we derive an upper bound on the minimum of the objective function value and a lower bound on the exact number of solutions. In our algebraic analysis, it was found that this proposed algorithm is capable of reducing the number of required qubits, thus enhancing the feasibility. Additionally, our simulations demonstrated that it reduces the query complexities by 63% in the classical domain and 31% in the quantum domain. The proposed approach may be useful for other quantum search algorithms and optimization problems.Comment: 11 pages, 4 figure

Quantum computing on cloud-based processors

Thesis (MSc)--Stellenbosch University, 2022.ENGLISH ABSTRACT: The noisy intermediate-scale quantum (NISQ) era refers to the current technological epoch permeated with quantum processors that are big enough (50-100 qubits) to be no longer trivially simulatable with digital computers but not yet capable of full fault-tolerant computation. Such processors provide great testbeds to understand the practical issues and resources needed to realize quantum tasks in these processors, such as quantum algorithms. Many pressing issues arise in this context that are a direct consequence of the limitations of these processors (limited number of qubits, low qubit connectivity, and limited coherence times). Hence, for near-term quantum algorithms, there is an overriding imperative to adopt an approach that takes into account, and attempts to mitigate or circumvent some of these limitations. In this thesis, we examine realizing Grover’s quantum search algorithm for four qubits on IBM Q superconducting quantum processors, and potentially scaling up to more qubits. We also investigate non-canonical forms of the quantum search algorithm that trade accuracy for speed in a way that is more suitable for near-term processors. Our contribution to this topic of research is a slight improvement in the accuracy of the solution to a graph problem, solved with a quantum search algorithm implemented on IBM Q quantum processors by Satoh et .al in IEEE Transactions on Quantum Engineering (2020). We also explore the realization of a measurement-based quantum search algorithm for three qubits. Unfortunately, the number of qubits and two-qubit gates required by such an algorithm puts it beyond the reach of current quantum processors. Based on a recently published work with Professor Mark Tame, we also report a proof-of-concept demonstration of a quantum order-finding algorithm for factor- ing the integer 21. Our demonstration builds upon a previous demonstration by Martín-López et al. in Nature Photonics 6, 773 (2012). We go beyond this work by implementing the algorithm on IBM Q quantum processors using a configuration of approximate Toffoli gates with residual phase shifts, which preserves its functional correctness and allows us to achieve a complete factoring of N D 21 using a quantum circuit with relatively fewer two-qubit gates. Lastly, we realize a small-scale three-qubit quantum processor based on a spontaneous parametric down-conversion source built to generate a polarization-entangled Bell state. The state is enlarged by using the path degree of freedom of one of the photons to make a 3-qubit GHZ state. The generated state is versatile enough to carry out quantum correlation measurements such as Bell’s inequalities and entanglement witnesses. The entire experimental setup is motorized and made automatic allowing remote control of the measurements of each of the qubits, and we design and build a mobile graphical user interface to an provide intuitive and visual way to interact with the experiment.AFRIKAANSE OPSOMMING: Die ruiesende intermediêre skaal kwantum (NISQ) era verwys na die huidige tegnolo- giese epog deurdring met kwantumverwerkers wat groot genoeg is (50-100 qubits) om nie meer doeltreffend gesimuleer te kan word op digitale rekenaars nie, maar nog nie in staat is om volle foutverdraagsame berekening uit te voer nie. Sulke verwerkers bied baie goeie toetsplatforms om die probleme en hulpbronne mee te verstaan wat nodig is om kwantumtake soos kwantumalgoritmes in hierdie verwerkers te verwesenlik. Baie dringende kwessies ontstaan in hierdie konteks wat ’n direkte gevolg is van die beperkings van hierdie verwerkeers (beperkte aantal qubits, lae qubit konnektiwiteit en beperkte samehang tye). Daarom is daar vir naby-termyn kwantum algoritmes ’n oorheersende noodsaaklikheid om ’n benadering aan te neem wat hierdie beperkings in ag neem en pogings aanwend om sommige daarvan te versag of te omseil. In hierdie handeling het ons ondersoek ingestel na Grover se kwantumsoekalgoritmes vir vier qubits op IBM Q supergeleier kwantumverwerkers en die moontlike opskaal na ’n groter aantal qubits. Ons ondersoek ook nie-kanonieke vorms van die kwantum- soekalgoritmes wat akkuraatheid vir spoed verhandel op ’n manier wat meer geskik is vir naby-termyn verwerkers. Ons bydra tot hierdie navorsingsonderwerp is ’n effense verbetering aan die akkuraatheid van die oplossing vir ’n grafiekprobleem opgelos met ’n soekalgoritme wat op IBM Q kwantumverwerkers geïmplimenteer is deur Satoh et al. In IEEE Transactions on Quantum Engineering (2020). Ons ondersoek ook die verwesenliking van ’n waarneming-gebaseerde kwantumsoekalgoritme vir drie qubits. Die aantal qubits en twee-qubit logikahekke wat deur so ’n algoritme vereis word plaas dit buite die bereik van huidige kwantumverwerkers. Gebaseer op ’n onlangs-gepubliseerde navorsingsstuk saam met professor Mark Tame rapporteer ons ook ’n bewys-van-konsep demonstrasie van ’n kwantum volgordebepal- ing algoritme vir die faktorisering van die heelgetal 21. Ons demonstrasie bou voort op ’n vorige demonstrasie deur Martín López et al. In Nature Photonics 6,773 (2012). Ons brei uit op hierdie navorsing deur die die algoritme op IBM Q kwantumverwerk- ers te implimenteer met gebruik van benaderde Toffoli logikahekke met oorblywende faseverskuiwings – wat sy funksionele integriteit behou en ons instaat stel om ’n volledige faktoriseering van N = 21 te bereik met behulp van ’n kwantumstroombaan met ’n kleiner aantal twee-qubit logikahekke. Laastens bewerkstellig ons ’n kleinskaalse drie-qubit kwantumverwerker gebaseer op ’n spontane parametriese fluoressensie (“spontaneous parametric down-conversion”) bron wat gebou is om ’n polarisasie-verstrengelde Bell staat te genereer. Hierdie staat word vergroot deur die baanvryheidsgraad van een van die fotone te gebruik om kwantumkorrelasie metings soos Bell se ongelykhede en verstrengelingsgetuies uit te voer. Die hele eksperimentele opstelling word gemotoriseer en geautomatiseer sodat waarnemings van elk van die qubits deur middel van afstandbeheer gemaak kan word, en ons ontwerp en ontwikkel ’n mobile grafiese gebruikerskoppelvlak om ’n intuïtiewe en visuele manier te bied om met die eksperiment te kommunikeer.Master

Robust and Efficient Hamiltonian Learning

With the fast development of quantum technology, the sizes of both digital and analog quantum systems increase drastically. In order to have better control and understanding of the quantum hardware, an important task is to characterize the interaction, i.e., to learn the Hamiltonian, which determines both static and dynamic properties of the system. Conventional Hamiltonian learning methods either require costly process tomography or adopt impractical assumptions, such as prior information on the Hamiltonian structure and the ground or thermal states of the system. In this work, we present a robust and efficient Hamiltonian learning method that circumvents these limitations based only on mild assumptions. The proposed method can efficiently learn any Hamiltonian that is sparse on the Pauli basis using only short-time dynamics and local operations without any information on the Hamiltonian or preparing any eigenstates or thermal states. The method has a scalable complexity and a vanishing failure probability regarding the qubit number. Meanwhile, it performs robustly given the presence of state preparation and measurement errors and resiliently against a certain amount of circuit and shot noise. We numerically test the scaling and the estimation accuracy of the method for transverse field Ising Hamiltonian with random interaction strengths and molecular Hamiltonians, both with varying sizes and manually added noise. All these results verify the robustness and efficacy of the method, paving the way for a systematic understanding of the dynamics of large quantum systems.Comment: 41 pages, 6 figures, Open source implementation available at https://github.com/zyHan2077/HamiltonianLearnin