Related papers: T-count Optimized Design of Quantum Integer Multip…
This paper presents a method for constructing quantum circuits for schoolbook multiplication using controlled add-subtract circuits, asymptotically halving the Toffoli count compared to traditional controlled-adder-based constructions.…
Quantum computation is traditionally expressed in terms of quantum bits, or qubits. In this work, we instead consider three-level qu$trits$. Past work with qutrits has demonstrated only constant factor improvements, owing to the $\log_2(3)$…
We provide evidence that commonly held intuitions when designing quantum circuits can be misleading. In particular we show that: a) reducing the T-count can increase the total depth; b) it may be beneficial to trade CNOTs for measurements…
Quantum computing has the potential to solve problems that are intractable for classical computers, with possible applications in areas such as drug discovery and high-energy physics. However, the practical implementation of quantum…
In this paper, we report efficient quantum circuits for integer multiplication using Toom-Cook algorithm. By analysing the recursive tree structure of the algorithm, we obtained a bound on the count of Toffoli gates and qubits. These bounds…
Resource consumption is an important issue in quantum information processing, particularly during the present NISQ era. In this paper, we investigate resource optimization of implementing multiple controlled operations, which are…
How many T gates are needed to approximate an arbitrary $n$-qubit quantum state to within error $\varepsilon$? Improving prior work of Low, Kliuchnikov, and Schaeffer, we show that the optimal asymptotic scaling is…
To approximate arbitrary unitary transformations on one or more qubits, one must perform transformations which are outside of the Clifford group. The gate most commonly considered for this purpose is the T = diag(1, exp(i \pi/4)) gate. As T…
In this research, we create a scalable version of the quantum Fourier transform-based arithmetic circuit to perform addition and subtraction operations on N n-bit unsigned integers encoded in quantum registers, and it is compatible with…
While quantum computing holds great potential in combinatorial optimization, electronic structure calculation, and number theory, the current era of quantum computing is limited by noisy hardware. Many quantum compilation approaches can…
Quantum compilers that reduce the number of T gates are essential for minimizing the overhead of fault-tolerant quantum computation. Achieving further T-count reduction calls for identifying equivalent circuit transformation rules beyond…
Quantum addition based on the quantum Fourier transform can be an integral part of a quantum circuit and proved to be more efficient than the existing classical ripple carry adder. Our study includes identifying the quantum resource…
We give a novel procedure for approximating general single-qubit unitaries from a finite universal gate set by reducing the problem to a novel magnitude approximation problem, achieving an immediate improvement in sequence length by a…
Building a quantum computer is a daunting challenge since it requires good control but also good isolation from the environment to minimize decoherence. It is therefore important to realize quantum gates efficiently, using as few operations…
The AND gate is not reversible$\unicode{x2014}$on qubits. However, it is reversible on qutrits, making it a building block for efficient simulation of qubit computation using qutrits. We first observe that there are multiple two-qutrit…
Fault-tolerant quantum computing typically requires the transpilation of arbitrary quantum circuits into a finite, universal gate set, such as Clifford+T. As a baseline, Diagonal approximation can be used for synthesizing single-qubit Pauli…
Pauli-based computation (PBC) is driven by a sequence of adaptively chosen, non-destructive measurements of Pauli observables. Any quantum circuit written in terms of the Clifford+$T$ gate set and having $t$ $T$ gates can be compiled into a…
Prior work of Beverland et al. has shown that any exact Clifford+$T$ implementation of the $n$-qubit Toffoli gate must use at least $n$ $T$ gates. Here we show how to get away with exponentially fewer $T$ gates, at the cost of incurring a…
Quantum computers promise exponential speedups for problems in cryptography, chemistry, and optimization. Realizing this promise requires fault tolerance: physical qubits are noisy, so logical qubits must be encoded redundantly across many…
Quantum modular adders are one of the most fundamental yet versatile quantum computation operations. They help implement functions of higher complexity, such as subtraction and multiplication, which are used in applications such as quantum…