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Quantum signal processing (QSP) is a powerful quantum algorithm to exactly implement matrix polynomials on quantum computers. Asymptotic analysis of quantum algorithms based on QSP has shown that asymptotically optimal results can in…
Continuous improvements in quantum computing hardware are exposing the need for simultaneous advances in software. Large-scale implementation of quantum algorithms requires rapid and automated compilation routines such as circuit synthesis…
We analyze the performance of a quantum computer architecture combining a small processor and a storage unit. By focusing on integer factorization, we show a reduction by several orders of magnitude of the number of processing qubits…
Simulations of nuclear magnetic resonance (NMR) experiments can be an important tool for extracting information about molecular structure and optimizing experimental protocols but are often intractable on classical computers for large…
Experimentally realizable quantum computers are rapidly approaching the threshold of quantum supremacy. Quantum Hamiltonian simulation promises to be one of the first practical applications for which such a device could demonstrate an…
Fault-tolerant quantum error correction (QEC) is crucial for unlocking the true power of quantum computers. QEC codes use multiple physical qubits to encode a logical qubit, which is protected against errors at the physical qubit level.…
Quantum computing represents a significant advancement in computational capabilities. Of particular concern is its impact on asymmetric cryptography through, notably, Shor's algorithm and the more recently developed Regev's algorithm for…
Quantum Monte Carlo and quantum simulation are both important tools for understanding quantum many-body systems. As a classical algorithm, quantum Monte Carlo suffers from the sign problem, preventing its application to most fermion systems…
We present a distributed implementation of Shor's quantum factoring algorithm on a distributed quantum network model. This model provides a means for small capacity quantum computers to work together in such a way as to simulate a large…
We consider the problem of estimating the expected outcomes of Monte Carlo processes whose outputs are described by multidimensional random variables. We tightly characterize the quantum query complexity of this problem for various choices…
Efficient quantum control is necessary for practical quantum computing implementations with current technologies. Conventional algorithms for determining optimal control parameters are computationally expensive, largely excluding them from…
Randomized algorithms are crucial subroutines in quantum computing, but the requirement to execute many types of circuits on a real quantum device has been challenging to their extensive implementation. In this study, we propose an…
Quantum information science currently poses a troubling contradiction. It can be summarized as: (1) To factor efficiently, quantum computers must perform exponentially precise energy estimation. (2) Exponentially precise energy estimation…
This thesis deals with a series of quantum computer implementation issues from the Kane 31P in 28Si architecture to Shor's integer factoring algorithm and beyond. The discussion begins with simulations of the adiabatic Kane CNOT and readout…
Two models of computer, a quantum and a classical "chemical machine" designed to compute the relevant part of Shor's factoring algorithm are discussed. The comparison shows that the basic quantum features believed to be responsible for the…
A key challenge in realizing fault-tolerant quantum computers is circuit optimization. Focusing on the most expensive gates in fault-tolerant quantum computation (namely, the T gates), we address the problem of T-count optimization, i.e.,…
Quantum computers have a potential for solving quantum chemistry problems with higher accuracy than classical computers. Quantum computing quantum Monte Carlo (QC-QMC) is a QMC with a trial state prepared in quantum circuit, which is…
In this abstract we study the resource consumption of quantum programs. Specifically, we focus on the expected runtime of programs and, inspired by recent methods for probabilistic programs, we develop a calculus \`a la weakest precondition…
We develop Monte Carlo methods for sampling random states and corresponding bit strings in qubit systems. To this end, we derive exact probability density functions that yield the Porter-Thomas distribution in the limit of large systems. We…
We study expected runtimes for quantum programs. Inspired by recent work on probabilistic programs, we first define expected runtime as a generalisation of quantum weakest precondition. Then, we show that the expected runtime of a quantum…