Related papers: Halving the cost of quantum addition
We give a Clifford+T representation of the Toffoli gate of T-depth 1, using four ancillas. More generally, we describe a class of circuits whose T-depth can be reduced to 1 by using sufficiently many ancillas. We show that the cost of…
Reversible logic has attracted much research interest over the last few decades, especially due to its application in quantum computing. In the construction of reversible gates from basic gates, ancilla bits are commonly used to remove…
Before executing a quantum algorithm, one must first decompose the algorithm into machine-level instructions compatible with the architecture of the quantum computer, a process known as quantum compiling. There are many different quantum…
We present quantum circuits for comparison and increment operations that achieve an asymptotically optimal gate count of $\Theta(n)$ and depth of $\Theta(\log n)$ over the Clifford+Toffoli gate set, while using a provably minimal number of…
Efficient constructions for quantum logic are essential since quantum computation is experimentally challenging. This thesis develops quantum logic synthesis as a paradigm for reducing the resource overhead in fault-tolerant quantum…
Implementing quantum algorithms on realistic hardware requires translating high-level global operations into sequences of native elementary gates, a process known as quantum compiling. Physical limitations, such as constraints in…
The quantum Fourier transform (QFT) is a ubiquitous quantum operation that is used in numerous quantum computing applications. The major obstacle to constructing a QFT circuit is that numerous elementary gates are required. Among the…
We present a quantum algorithm for multiplying two $n$-bit integers with overall circuit depth and $T$-depth both bounded by $O(\log^{2} n)$, while using $O(n^{2})$ gates and ancillary qubits. Our construction generates partial products via…
The state of the art of quantum circuits using the ripple-carry strategy for the addition and comparison of two n-bit numbers is presented, as well as optimizations in the Clifford+T gate set, both in terms of CNOT-depth and T-depth, or…
Optimization techniques for decreasing the time and area of adder circuits have been extensively studied for years mostly in binary logic system. In this paper, we provide the necessary equations required to design a full adder in…
Reversible computation has been proposed as a future paradigm for energy efficient computation, but so far few implementations have been realised in practice. Quantum circuits, running on quantum computers, are one construct known to be…
The ability to implement the Quantum Fourier Transform (QFT) efficiently on a quantum computer facilitates the advantages offered by a variety of fundamental quantum algorithms, such as those for integer factoring, computing discrete…
There are two important, and potentially interconnecting, avenues to the realisation of large-scale quantum algorithms: improvement of the hardware, and reduction of resource requirements demanded by algorithm components. In focusing on the…
Reversible logic has applications in low-power computing and quantum computing. However, there are few existing designs for reversible floating-point adders and none suitable for quantum computation. In this paper we propose a…
We improve the Toffoli count of low depth quantum adders, and analyze how their spacetime cost reacts to having a limited number of magic state factories. We present a block lookahead adder that parallelizes across blocks of bits of size…
We simulate the implementation of a T-gate, or $\frac{\pi}{8}$-gate, for a [7,1,3] encoded logical qubit in a non-equiprobable error environment. We demonstrate that the use of certain non-fault tolerant methods in the implementation may…
Efficient arithmetic operations are a prerequisite for practical quantum computing. Optimization efforts focus on two primary metrics: Quantum Cost (QC), determined by the number of non-linear gates, and Logical Depth, which defines the…
This work focuses on reducing the physical cost of implementing quantum algorithms when using the state-of-the-art fault-tolerant quantum error correcting codes, in particular, those for which implementing the T gate consumes vastly more…
We present two new constructions for the Toffoli gate which substantially reduce resource costs in fault-tolerant quantum computing. The first contribution is a Toffoli gate requiring Clifford operations plus only four $T =…
In fault-tolerant quantum circuit synthesis, T gates supplied via magic states dominate space-time cost, while Clifford gates incur negligible overhead. Conventional flows minimize AND count in an {XOR, AND, NOT} basis as a proxy for T,…