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The evolution of a driven quantum system is said to be adiabatic whenever the state of the system stays close to an instantaneous eigenstate of its time-dependent Hamiltonian. The celebrated quantum adiabatic theorem ensures that such pure…
Adiabatic quantum computing (AQC) is a promising approach for discrete and often NP-hard optimization problems. Current AQCs allow to implement problems of research interest, which has sparked the development of quantum representations for…
The goal of adiabatic ground-state preparation is to start a simple quantum system in its ground state and adiabatically evolve the Hamiltonian to a complex one, maintaining the ground state throughout the evolution. In ion-trap-based…
Continuous-time quantum error correction (CTQEC) is an approach to protecting quantum information from noise in which both the noise and the error correcting operations are treated as processes that are continuous in time. This chapter…
Matrix product states provide a natural entanglement basis to represent a quantum register and operate quantum gates on it. This scheme can be materialized to simulate a quantum adiabatic algorithm solving hard instances of a NP-Complete…
Crossing a quantum critical point in finite time challenges the adiabatic condition due to the closing of the energy gap, which ultimately results in the formation of excitations. Such non-adiabatic excitations are typically deemed…
Despite its simplicity and strong theoretical guarantees, adiabatic state preparation has received considerably less interest than variational approaches for the preparation of low-energy electronic structure states. Two major reasons for…
Adiabatic elimination is a perturbative model reduction technique based on timescale separation and often used to simplify the description of composite quantum systems. We here analyze a quantum experiment where the perturbative expansion…
A physical realization of self correcting quantum code would be profoundly useful for constructing a quantum computer. In this theoretical work, we provide a partial solution to major challenges preventing self correcting quantum code from…
Blind Quantum Computation (BQC) is a delegation computing protocol that allows a client to utilize a remote quantum server to implement desired quantum computations while keeping her inputs, outputs, and algorithms private. However, qubit…
Construction of a fault-tolerant quantum computer remains a challenging problem due to unavoidable noise in quantum states and the fragility of quantum entanglement. However, most of the error-correcting codes increases the complexity of…
In the circuit model of quantum computing, amplitude amplification techniques can be used to find solutions to NP-hard problems defined on $n$-bits in time $\text{poly}(n) 2^{n/2}$. In this work, we investigate whether such general…
The accelerated progress in manufacturing noisy intermediate-scale quantum (NISQ) computing hardware has opened the possibility of exploring its application in transforming approaches to solving computationally challenging problems. The…
The accurate computation of Hamiltonian ground, excited, and thermal states on quantum computers stands to impact many problems in the physical and computer sciences, from quantum simulation to machine learning. Given the challenges posed…
One of the promising applications of digital quantum processors is the simulation of many-body quantum systems. They have been already used to investigate several ergodicity violating mechanisms, which were initially discovered in synthetic…
The construction of a quantum computer remains a fundamental scientific and technological challenge, in particular due to unavoidable noise. Quantum states and operations can be protected from errors using protocols for fault-tolerant…
Standard quantum error correction (QEC) models typically assume discrete, Markovian noise, obscuring the continuous quantum nature of physical environments. In this manuscript, we investigate the fundamental limits of an actively corrected…
High-rate and large-distance quantum codes are expected to make fault-tolerant quantum computing more efficient, but most of them lack efficient fault-tolerant encoded-state preparation methods. We propose such a fault-tolerant encoder for…
We provide rigorous bounds for the error of the adiabatic approximation of quantum mechanics under four sources of experimental error: perturbations in the initial condition, systematic time-dependent perturbations in the Hamiltonian,…
Fault-tolerant quantum computation (FTQC) schemes that use multi-qubit large block codes can potentially reduce the resource overhead to a great extent. A major obstacle is the requirement of a large number of clean ancilla states of…