Related papers: GALA-n: Generic Architecture of Layout-Aware n-Bit…
A cost-effective n-bit Toffoli gate is proposed to be realized (or transpiled) based on the layouts (linear, T-like, and I-like) and the number of n physical qubits for IBM quantum computers. This proposed gate is termed the "layout-aware…
We introduce a new quantum layout-aware approach to realize cost-effective $n$-bit gates using the Bloch sphere, for $2 \le n \le 5$ qubits. These $n$-bit gates are entirely constructed from the Clifford+T gates, in the approach of…
The conventional design technique of any n-bit quantum gate is mainly achieved using unitary matrices multiplication, where n >= 2 and 1 <= m <= n-1 for m target qubits and n-m control qubits. These matrices represent quantum rotations by…
A proposed method for preparing the superposition states of qubits using different axes of the Bloch sphere. This method utilizes the Y-axis of the Bloch sphere using IBM native (square root of X) gates, instead of utilizing the X-axis of…
We present an implementation of multi-controlled quantum gates which provides significant reductions of cost compared to state-of-the-art methods. The operator applied on the target qubit is a unitary, special unitary, or the Pauli X…
To build a general-purpose quantum computer, it is crucial for the quantum devices to implement classical boolean logic. A straightforward realization of quantum boolean logic is to use auxiliary qubits as intermediate storage. This…
Quantum circuits of a general quantum gate acting on multiple $d$-level quantum systems play a prominent role in multi-valued quantum computation. We first propose a new recursive Cartan decomposition of semi-simple unitary Lie group…
We propose a class of randomized quantum algorithms for the task of sampling from matrix functions, without the use of quantum block encodings or any other coherent oracle access to the matrix elements. As such, our use of qubits is purely…
The three-input TOFFOLI gate is the workhorse of circuit synthesis for classical logic operations on quantum data, e.g., reversible arithmetic circuits. In physical implementations, however, TOFFOLI gates are decomposed into six CNOT gates…
We present a novel architecture-aware transpilation method for exact general unitary gate synthesis on superconducting quantum hardware. Our approach is tightly integrated with the optimized block-ZXZ decomposition, exploiting its recursive…
Here we describe an approach for simulating electronic structure on quantum computers with significantly lower asymptotic complexity than prior work. The approach uses a real-space first-quantised representation of the molecular Hamiltonian…
We show the applicability of the Cartan decomposition of Lie algebras to quantum circuits. This approach can be used to synthesize circuits that can efficiently implement any desired unitary operation. Our method finds explicit 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…
We design quantum circuits by using the standard cell approach borrowed from classical circuit design, which can speed-up the layout of circuits with a regular structure. Our standard cells are general and can be used for all types of…
The optimal implementation of quantum gates for closed $N$-qubit systems is one of the key challenges for practical realization of many quantum information processing tasks. In the present article, based on the generalized Bloch vectors…
We give an explicit construction to perform any $n$-qubit computational basis state transposition using $\Theta(n)$ gates. This nearly coincides with the lower bound $\Omega(n/\log(nd))$ on worst-case and average-case gate complexity to…
Implementing a quantum circuit on specific hardware with a reduced available gate set is often associated with a substantial increase in the length of the equivalent circuit. This process is also known as transpilation and due to…
We consider a generic elementary gate sequence which is needed to implement a general quantum gate acting on n qubits -- a unitary transformation with 4^n degrees of freedom. For synthesizing the gate sequence, a method based on the…
We investigate the utility of geometric (Clifford) algebras (GA) methods in two specific applications to quantum information science. First, using the multiparticle spacetime algebra (MSTA, the geometric algebra of a relativistic…
A Boolean-Phase swapping gate is introduced for quantum generality and cost-effectiveness, which is termed the "p-SWAP gate", where p is a customizable phase difference for a set of swapped qubits and 0 <= p <= ${\pm \pi}$ radians. The…