Related papers: On connectivity-dependent resource requirements fo…
We consider the problem of selectively controlling couplings in a practical quantum processor with always-on interactions that are diagonal in the computational basis, using sequences of local NOT gates. This methodology is well-known in…
Here we explore which heuristic quantum algorithms for combinatorial optimization might be most practical to try out on a small fault-tolerant quantum computer. We compile circuits for several variants of quantum accelerated simulated…
Quantum simulation uses a well-known quantum system to predict the behavior of another quantum system. Certain limitations in this technique arise, however, when applied to specific problems, as we demonstrate with a theoretical and…
The steady increase in control over individual quantum systems has backed the dream of a quantum technology that provides functionalities beyond any classical device. Two particularly promising applications have been explored during the…
Block-encoding operators are one of the essential components in quantum algorithms based on Quantum Signal Processing. Their gate complexity largely determines the overall gate complexity of the full algorithm. Using variational methods, we…
Quantum dynamics can be simulated on a quantum computer by exponentiating elementary terms from the Hamiltonian in a sequential manner. However, such an implementation of Trotter steps has gate complexity depending on the total Hamiltonian…
This work proposes double-bracket iterations as a framework for obtaining diagonalizing quantum circuits. Their implementation on a quantum computer consists of interlacing evolutions generated by the input Hamiltonian with diagonal…
Quantum circuit complexity-a measure of the minimum number of gates needed to implement a given unitary transformation-is a fundamental concept in quantum computation, with widespread applications ranging from determining the running time…
As quantum computers become available to the general public, the need has arisen to train a cohort of quantum programmers, many of whom have been developing classical computer programs for most of their careers. While currently available…
Quantum simulation of the electronic structure problem is one of the most researched applications of quantum computing. The majority of quantum algorithms for this problem encode the wavefunction using $N$ Gaussian orbitals, leading to…
Designing quantum processors is a complex task that demands advanced verification methods to ensure their correct functionality. However, traditional methods of comprehensively verifying quantum devices, such as quantum process tomography,…
Quantum computing promises breakthroughs in simulating and solving complex, classically intractable problems. However, current noisy intermediate-scale quantum (NISQ) devices are relatively small and error-prone, prohibiting large-scale…
A limited number of qubits, high error rates, and limited qubit connectivity are major challenges for effective near-term quantum computations. Quantum circuit partitioning divides a quantum computation into a set of computations that…
Quantum simulation is a promising way toward practical quantum advantage, but noise in current quantum hardware poses a significant obstacle. We prove that not only the physical error but also the algorithmic error in a single Trotter step…
These notes begin in Chapter 1 with a review of linear algebra and the postulates of quantum mechanics, leading to an explanation of single- and multi-qubit gates. Chapter 2 explores the challenge of constructing arbitrary quantum states…
Quantum computers face inherent scaling challenges, a fact that necessitates investigation of distributed quantum computing systems, whereby scaling is achieved through interconnection of smaller quantum processing units. However,…
We analyze the complexity of synthesizing random states and unitary operators in a multi-qudit system in two paradigms. In one case, we consider the situation in which we manipulate the system by applying a sequence of one- and two-qudit…
Quantum computers can solve certain problems more efficiently than any possible conventional computer. Small quantum algorithms have been demonstrated on multiple quantum computing platforms, many specifically tailored in hardware to…
Climate change is becoming one of the greatest challenges to the sustainable development of modern society. Renewable energies with low density greatly complicate the online optimization and control processes, where modern advanced…
These notes present a review of the status of quantum computing with arrays of neutral atom qubits, an approach which has demonstrated remarkable progress in the last few years. Scaling digital quantum computing to qubit counts and control…