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Georgetown University-Graduate School of Arts & Sciences

Gaining a Deeper Understanding of Nature with Quantum Simulators and Quantum Computers

Jeffrey Cohn

Published Jan 1, 2019• 0 citations
OpenAlex

Abstract

Exact simulation of quantum systems is intractable on current classical computers due to the time required to calculate the exponential number of amplitudes which represent a quantum state.This thesis explores how highly tuned quantum devices, such as quantum simulators and digital quantum computers, can be utilized to gain a deeper understanding of nature.In Chapter 1 we begin by reviewing some of the basics of quantum information.Chapter 2 highlights the advantages of using entangled states in metrology and how quantum simulators can be realized on a system of trapped ions.Chapter 3 develops the gate model of quantum computing and reviews many of the foundational algorithms needed to simulate many-body systems.Chapter 4 originates from the paper "Verification of a many-ion simulator of the Dicke model through slow quenches across a phase transition."[1].This chapter examines how a system of trapped ions can be engineered to emulate a famous model known as the Dicke model, which involves coupling many spins to a single bosonic mode.After confirming that the Dicke model indeed has been realized, we show in Chapter 5 how simple protocols can be used to prepare highly entangled states.This chapter originates from the paper, "Bang-bang shortcut to adiabaticity in the Dicke model as realized in a Penning trap experiment" [2].These states have the potential to provide giant gains in making precision measurements.Finally, with the use of universal quantum computers on the horizon, we develop a framework, in Chapter 6, for extracting thermal properties of many-body systems on these machines.This chapter eminates Many thanks are in order for the people who helped me get to where I am in my career.First, my parents, Robert and Maureen Cohn, who have always been there to support me.In this respect I am also grateful for the support provided by my grandparents Alien and Joeseph

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Exact simulation of quantum systems is intractable on current classical computers due to the time required to calculate the exponential number of amplitudes which represent a quantum state.This thesis explores how highly tuned quantum devices, such as quantum simulators and digital quantum computers, can be utilized to gain a deeper understanding of nature.In Chapter 1 we begin by reviewing some of the basics of quantum information.Chapter 2 highlights the advantages of using entangled states in metrology and how quantum simulators can be realized on a system of trapped ions.Chapter 3 develops the gate model of quantum computing and reviews many of the foundational algorithms needed to simulate many-body systems.Chapter 4 originates from the paper "Verification of a many-ion simulator of the Dicke model through slow quenches across a phase transition."[1].This chapter examines how a system of trapped ions can be engineered to emulate a famous model known as the Dicke model, which involves coupling many spins to a single bosonic mode.After confirming that the Dicke model indeed has been realized, we show in Chapter 5 how simple protocols can be used to prepare highly entangled states.This chapter originates from the paper, "Bang-bang shortcut to adiabaticity in the Dicke model as realized in a Penning trap experiment" [2].These states have the potential to provide giant gains in making precision measurements.Finally, with the use of universal quantum computers on the horizon, we develop a framework, in Chapter 6, for extracting thermal properties of many-body systems on these machines.This chapter eminates Many thanks are in order for the people who helped me get to where I am in my career.First, my parents, Robert and Maureen Cohn, who have always been there to support me.In this respect I am also grateful for the support provided by my grandparents Alien and Joeseph
Quantum simulation involves using a quantum system to study another quantum system. The proposal to simulate quantum physics using quantum mechanical devices, as outlined by Richard Feynman in 1982, stems from classical computers' challenges in simulating quantum systems. The pursuit of simulating complex quantum systems has led to the intersection of quantum mechanics and quantum computing. This offers new opportunities to understand and manipulate the quantum world. Central to describing quantum dynamics is the Hamiltonian operator H^\hat{H}H^, which governs the time evolution of physical systems and serves as the mathematical foundation for quantum simulations. This thesis explores the methodologies and advancements in simulating Hamiltonian operators on quantum computers, focusing on decomposing these operators into quantum gates and the efficiency gains over classical computational approaches. Initially, the thesis explains the fundamental theory and basics of quantum computing. Further it dives into the foundations of the Hamiltonian operator within quantum mechanics, highlighting its role in describing the dynamics of quantum systems. The complexity and high-dimensional nature of Hamiltonian matrices necessitate using quantum computers to simulate quantum phenomena accurately and efficiently. The process of simulating the Hamiltonian operator on a quantum computer involves a detailed examination of the strategies for decomposing the operator into a sequence of quantum gates. This decomposition is crucial for translating the abstract mathematical description of quantum systems into the physical operations of a quantum computer. By utilizing the principles of quantum mechanics, such as superposition and entanglement, quantum gates manipulate qubits to mimic the evolution of quantum states as the Hamiltonian operator dictates. Latter portions of the thesis are dedicated to comparing the efficiency of quantum simulations against traditional classical simulations and inspecting efficient quantum simulations. Quantum computers offer a polynomial or an exponential speedup for certain classes of problems, such as those involving highly entangled quantum states or requiring the simulation of complex quantum dynamics. This advantage is due to the quantum computer's ability to naturally represent and process quantum information - a task for which classical computers require exponential resources as the system size increases. The efficiency of simulating the Hamiltonian operator on a quantum computer is further enhanced through optimization techniques and algorithmic improvements. These include error mitigation strategies and the development of quantum algorithms tailored to specific types of Hamiltonian operators. The thesis presents a comprehensive analysis of these methods, demonstrating how they make quantum simulations more practical and accessible for scientific research and technological development. In conclusion this thesis is a literature review that examines the transformative potential of quantum simulations. By efficiently simulating the Hamiltonian operator on quantum computers researchers can explore quantum phenomena with precision, paving the way for breakthroughs in quantum physics, materials science, and beyond. The advancements in quantum computing technology and algorithmic approaches discussed here highlight the current capabilities and future explorations in the quantum realm.
The ability to manipulate individual quantum systems in a precise way has led to a new era of quantum technologies, including quantum computation and quantum simulation. In this thesis we present several new implementations of these quantum technologies. We first aim at addressing current experimental challenges for quantum dot based quantum computing. We propose a systematic way to study the dynamics of nuclear spin, which is responsible for the short electron spin coherence time. Our calculation is based on diffusion model and is consistent with experiments. We also invent a novel protocol to realize high-fidelity ultrafast universal quantum gate in recently-developed quantum dot molecule system. Experimental realization of our protocol requires only a simple time engineering of optical pulses. We then propose a new quantum state transfer scheme for Nitrogen-Vacancy center based quantum computer, which is applicable at room temperature. Our method accomplishes high fidelity robust quantum state transfer through uncontrolled thermal nitrogen spin chain between two remote NV registers. Our next study helps building a hybrid quantum computer by entangling disparate systems using photonic links. The photons emitted from two types of system need to be matched in both frequency and pulse shape. We propose a simple method to match the emitted pulse shape from two qubit systems with different transition linewidths. We then focus on quantum simulation with trapped ions. We show the possibility of observing a novel type of temperature driven structural phase transition in trapped ion chain, which originates from anharmonic interaction between different vibrational modes. Afterward, an experimental protocol to simulate a conceptually new state of matter, called time crystal, is proposed based on ions trapped in a ring trap. Finally, we propose two new applications based on the recently developed trapped ion quantum simulator of spin models: (1) simulation of Haldane-Shastry model, which opens the way of experimental study to a remarkable theoretical model involving spin liquid ground state and fractional excitations (2) observation of prethermalization and dynamical phase transition, which are poorly understood non-equilibrium phenomena in closed quantum many-body system.
In this chapter, we examine ion-trap-based quantum simulators. This is the same type of hardware that is employed for ion-trap quantum computers, but we do not describe gated quantum computing in this book. Instead, we focus on examining the complex quantum dynamics in systems where individual ions can be trapped and manipulated. These systems are one of the hallmarks of the second quantum revolution, where we can manipulate quantum systems at the single-quantum level. We describe the phonon modes for ions in a trap, Raman transitions, spin-dependent forces that lead to effective spin models, how to prepare spin ground states, and extensions to the Lipkin-Meshkov-Glick and Dicke models.
We cannot translate quantum behavior arising with superposition states or entanglement efficiently into the classical language of conventional computers (Feynman et al. in Int. J. Theor. Phys. 21:467, 1982 ). A universal quantum computer could describe and help to understand complex quantum systems. But it is envisioned to become functional only within the next decade(s). A shortcut was proposed via simulating the quantum behavior of interest in another quantum system, where all relevant parameters and interactions can be controlled and observables of interest detected sufficiently well. For example simulating quantum spin systems within an architecture of trapped ions (Porras and Cirac in Phys. Rev. Lett. 92:207901, 2004 ). Here we specify how we simulate the spin and all necessary interactions and how we calibrate their amplitudes. For example via a two-ion phase-gate operation on two axial motional modes simultaneously at a fidelity exceeding 95%. We explain the complete mode of operation of a quantum simulator on the basis of our simple model case—the proof of principle experiment of simulating the transition of a quantum magnet from paramagnetic into entangled ferromagnetic order (Friedenauer et al. in Nat. Phys. 4:757, 2008 ) and emphasize some of the similarities and differences with a quantum computer.
In this section we provide a broad overview of the basic principles of quantum mechanics and how they enable modern quantum technologies. The starting point is the concept of superposition, which allows quantum systems to be in multiple states at the same time and forms the basis of quantum computation using qubits and parallel processing of information. The conversation then turns to quantum entanglement, a non-classical effect that creates strong correlations between particles, and has applications in secure communication and quantum teleportation. Also mentioned is the quantum coherence, which preserves phase relations between quantum states and makes it possible for quantum systems to function correctly. But it is also emphasized that quantum coherence is fragile to environmental perturbations. This chapter also covers quantum measurement, taking into account the probabilistic nature of quantum mechanics, and how the act of observation results in the collapse of a quantum state to a definite outcome. These principles together constitute the theoretical basis of quantum computing, where quantum gates and algorithms and qubits take advantage of superposition, entanglement and interference to offer computational benefits over classical systems. The most important algorithms like Shor’s and Grover’s algorithms that demonstrate a considerable speed-up in solving the problem are discussed along with different models of quantum computing, such as gate, adiabatic and measurement-based models. Furthermore, the section reviews some physical realizations of quantum systems, such as superconducting qubits, trapped ions, photonic systems and topological qubits, with their advantages and difficulties. Overall, this discussion shows how the basic principles of quantum mechanics are the foundation for the development of advanced quantum technologies, while also dealing with the practical difficulties that arise in their implementation.
We introduce a bang-bang shortcut to adiabaticity for the Dicke model, which we implement via a two-dimensional array of trapped ions in a Penning trap with a spin-dependent force detuned close to the center-of-mass drumhead mode. Our focus is on employing this shortcut to create highly entangled states that can be used in high-precision metrology. We highlight that the performance of the bang-bang approach is comparable to standard preparation methods, but can be applied over a much shorter time frame. We compare these theoretical ideas with experimental data which serve as a first step towards realizing this theoretical procedure for generating multi-partite entanglement.