Related papers: Truncated phase-based quantum arithmetic: error pr…

Quantum computation with Trotter product formulae is straightforward and requires little overhead in terms of logical qubits. The choice of the orbital basis significantly affects circuit depth, with localised orbitals yielding lowest…

Quantum computing roadmaps predict the availability of 10,000 qubit devices within the next 3-5 years. With projected two-qubit error rates of 0.1%, these systems will enable certain operations under quantum error correction (QEC) using…

With gate error rates in multiple technologies now below the threshold required for fault-tolerant quantum computation, the major remaining obstacle to useful quantum computation is scaling, a challenge greatly amplified by the huge…

The practical use of many types of near-term quantum computers requires accounting for their limited connectivity. One way of overcoming limited connectivity is to insert swaps in the circuit so that logical operations can be performed on…

The construction of large, coherent quantum systems necessary for quantum computation remains an entreating but elusive goal, due to the ubiquitous nature of decoherence. Recent progress in quantum error correction schemes have given new…

The progress in building quantum computers to execute quantum algorithms has recently been remarkable. Grover's search algorithm in a binary quantum system provides considerable speed-up over classical paradigm. Further, Grover's algorithm…

Noise and errors are inevitable parts of any practical implementation of a quantum computer. As a result, large-scale quantum computation will require ways to detect and correct errors on quantum information. Here, we present such a quantum…

Windowed arithmetic [Gidney, 2019] is a technique for reducing the cost of quantum arithmetic circuits with space--time tradeoffs using memory queries to precomputed tables. It can reduce the asymptotic cost of modular exponentiation from…

Facing the worldwide steady progress in building quantum computers, it is crucial for cryptographic community to design quantum-safe cryptographic primitives. To achieve this, we need to investigate the capability of cryptographic analysis…

Recent experimental breakthroughs have signalled the imminent arrival of the early fault-tolerant era. However, for a considerable period in the foreseeable future, relying solely on quantum error correction for full error suppression will…

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…

Various quantum applications can be reduced to estimating expectation values, which are inevitably deviated by operational and environmental errors. Although errors can be tackled by quantum error correction, the overheads are far from…

Quantum algorithms typically demand prohibitively complicated circuits to solve practical problems. Previous studies have shown that classical randomness can accelerate some specific quantum algorithms. In this work, we introduce the…

A foundational assumption of quantum error correction theory is that quantum gates can be scaled to large processors without exceeding the error-threshold for fault tolerance. Two major challenges that could become fundamental roadblocks…

Finite local Hilbert-space truncations arise naturally in quantum simulations of lattice field theories and motivate qudit encodings, but their fault-tolerant advantage over qubit encodings remains unclear. We compare the non-Clifford cost…

We give precise quantum resource estimates for Shor's algorithm to compute discrete logarithms on elliptic curves over prime fields. The estimates are derived from a simulation of a Toffoli gate network for controlled elliptic curve point…

Shor's algorithm (SA) is a quantum algorithm for factoring integers. Since SA has polynomial complexity while the best classical factoring algorithms are sub-exponential, SA is cited as evidence that quantum computers are more powerful than…

Quantum Phase Estimation (QPE) routines are known to fail probabilistically even with perfect gates and input states. This effect stems from an incompatibility of finite-sized quantum registers to capture a phase within QPE with phase…

We show a significant reduction of the number of quantum operations and the improvement of the circuit depth for the realization of the Toffoli gate by using qudits. This is done by establishing a general relation between the dimensionality…

Adiabatic Quantum-Flux-Parametron (AQFP) logic is a promising emerging device technology with six orders of magnitude lower power than CMOS. However, AQFP is challenged by the fact that every gate must be clocked, where proper data transfer…