Scalable Design and Synthesis of Reversible Circuits

The expectations on circuits are rising with their number of applications, and technologies alternative to CMOS are becoming more important day by day. A promising alternative is reversible computation, a computing paradigm with applications in quantum computation, adiabatic circuits, program inversion, etc. An elaborated design flow is not available to reversible circuit design yet. In this work, two directions are considered: Exploiting the conventional design flow and developing a new flow according to the properties of reversible circuits. Which direction should be taken is not obvious, so we discuss the possible assets and drawbacks of taking either direction. We present ideas which can be exploited and outline open challenges which still have to be addressed. Preliminary results obtained by initial implementations illustrate the way to go. By this we present and discuss two promising and complementary directions for the scalable design and synthesis of reversible circuits

Local Hamiltonians in Quantum Computation

In this thesis, I investigate aspects of local Hamiltonians in quantum computing. First, I focus on the Adiabatic Quantum Computing model, based on evolution with a time dependent Hamiltonian. I show that to succeed using AQC, the Hamiltonian involved must have local structure, which leads to a result about eigenvalue gaps from information theory. I also improve results about simulating quantum circuits with AQC. Second, I look at classically simulating time evolution with local Hamiltonians and finding their ground state properties. I give a numerical method for finding the ground state of translationally invariant Hamiltonians on an infinite tree. This method is based on imaginary time evolution within the Matrix Product State ansatz, and uses a new method for bringing the state back to the ansatz after each imaginary time step. I then use it to investigate the phase transition in the transverse field Ising model on the Bethe lattice. Third, I focus on locally constrained quantum problems Local Hamiltonian and Quantum Satisfiability and prove several new results about their complexity. Finally, I define a Hamiltonian Quantum Cellular Automaton, a continuous-time model of computation which doesn't require control during the computation process, only preparation of product initial states. I construct two of these, showing that time evolution with a simple, local, translationally invariant and time-independent Hamiltonian can be used to simulate quantum circuits.Comment: Ph.D. Thesis, June 2008, MIT, 176 page

Full stack development toward a trapped ion logical qubit

Quantum error correction is a key step toward the construction of a large-scale quantum computer, by preventing small infidelities in quantum gates from accumulating over the course of an algorithm. Detecting and correcting errors is achieved by using multiple physical qubits to form a smaller number of robust logical qubits. The physical implementation of a logical qubit requires multiple qubits, on which high fidelity gates can be performed. The project aims to realize a logical qubit based on ions confined on a microfabricated surface trap. Each physical qubit will be a microwave dressed state qubit based on 171Yb+ ions. Gates are intended to be realized through RF and microwave radiation in combination with magnetic field gradients. The project vertically integrates software down to hardware compilation layers in order to deliver, in the near future, a fully functional small device demonstrator. This thesis presents novel results on multiple layers of a full stack quantum computer model. On the hardware level a robust quantum gate is studied and ion displacement over the X-junction geometry is demonstrated. The experimental organization is optimized through automation and compressed waveform data transmission. A new quantum assembly language purely dedicated to trapped ion quantum computers is introduced. The demonstrator is aimed at testing implementation of quantum error correction codes while preparing for larger scale iterations.Open Acces

QUANTUM SIMULATIONS OF THE ISING MODEL WITH TRAPPED IONS: DEVIL'S STAIRCASE AND ARBITRARY LATTICE PROPOSAL

A collection of trapped atomic ions represents one of the most attractive platforms for the quantum simulation of interacting spin networks and quantum magnetism. Spin-dependent optical dipole forces applied to an ion crystal create long-range eective spin-spin interactions and allow the simulation of spin Hamiltonians that possess nontrivial phases and dynamics. We trap linear chains of 171Yb+ ions in a Paul trap, and constrain the occupation of energy levels to the ground hyperne clock-states, creating a qubit or pseudo-spin 1/2 system. We proceed to implement spin-spin couplings between two ions using the far detuned Mlmer-Srenson scheme and perform adiabatic quantum simulations of Ising Hamiltonians with long-range couplings. We then demonstrate our ability to control the sign and relative strength of the interaction between three ions. Using this control, we simulate a frustrated triangular lattice, and for the first time establish an experimental connection between frustration and quantum entanglement. We then scale up our simulation to show phase transitions from paramagnetism to ferromagnetism for nine ions, and to anti-ferromagnetism for sixteen ions. The experimental work culminates with our most complicated Hamiltonian - a long range anti-ferromagnetic Ising interaction between 10 ions with a biasing axial field. Theoretical work presented in this thesis shows how the approach to quantum simulation utilized in this thesis can be further extended and improved. It is shown how appropriate design of laser elds can provide for arbitrary multidimensional spin-spin interaction graphs even for the case of a linear spatial array of ions. This scheme uses currently existing trap technology and is scalable to levels where classical methods of simulation are intractable

Reversible Computation: Extending Horizons of Computing

This open access State-of-the-Art Survey presents the main recent scientific outcomes in the area of reversible computation, focusing on those that have emerged during COST Action IC1405 "Reversible Computation - Extending Horizons of Computing", a European research network that operated from May 2015 to April 2019. Reversible computation is a new paradigm that extends the traditional forwards-only mode of computation with the ability to execute in reverse, so that computation can run backwards as easily and naturally as forwards. It aims to deliver novel computing devices and software, and to enhance existing systems by equipping them with reversibility. There are many potential applications of reversible computation, including languages and software tools for reliable and recovery-oriented distributed systems and revolutionary reversible logic gates and circuits, but they can only be realized and have lasting effect if conceptual and firm theoretical foundations are established first

Scaling Quantum Computers with Long Chains of Trapped Ions

Quantum computers promise to solve models of important physical processes, optimize complex cost functions, and challenge cryptography in ways that are intractable using current computers. In order to achieve these promises, quantum computers must both increase in size and decrease error rates. To increase the system size, we report on the design, construction, and operation of an integrated trapped ion quantum computer consisting of a chain of 15 171Yb+ ions with all-to-all connectivity and high-fidelity gate operations. In the process, we identify a physical mechanism that adversely affects gate fidelity in long ion chains. Residual heating of the ions from noisy electric fields creates decoherence due to the weak confinement of the ions transverse to a focused addressing laser. We demonstrate this effect in chains of up to 25 ions and present a model that accurately describes the observed decoherence. To mitigate this noise source, we first propose a new sympathetic cooling scheme to periodically re-cool the ions throughout a quantum circuit, and then demonstrate its capability in a proof-of-concept experiment. One path to suppress error rates in quantum computers is through quantum error correction schemes that combine multiple physical qubits into logical qubits that robustly store information within an entangled state. These extra degrees of freedom enable the detection and correction of errors. Fault-tolerant circuits contain the spread of errors while operating the logical qubit and are essential for realizing error suppression in practice. We demonstrate fault-tolerant preparation, measurement, rotation, and stabilizer measurement of a distance-3 Bacon-Shor logical qubit in our quantum computer. The result is an encoded logical qubit with error rates lower than the error of the entangling operations required to operate it