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We study the achievements of quantum circuits comprised of several one- and two-qubit gates. Quantum process matrices are determined for the basic one- and two-qubit gate operations and concatenated to yield the process matrix of the…
The construction of quantum computers is based on the synthesis of low-cost quantum circuits. The quantum circuit of any Boolean function expressed in a Positive Polarity Reed-Muller $PPRM$ expansion can be synthesized using…
Quantum computing promises to revolutionize various fields, yet the execution of quantum programs necessitates an effective compilation process. This involves strategically mapping quantum circuits onto the physical qubits of a quantum…
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…
Full connectivity of qubits is necessary for most quantum algorithms, which is difficult to directly implement on Noisy Intermediate-Scale Quantum processors. However, inserting swap gate to enable the two-qubit gates between uncoupled…
This paper is motivated by two key observations. First, Toffoli ladders can be implemented in three distinct ways: with linear or polylogarithmic depth using no ancilla, or with logarithmic depth using ancilla qubits. Second, two…
In this paper, we investigate how quantum architectures affect the efficiency of the execution of the quantum Fourier transform (QFT) and linear transformations, which are essential parts of the stabilizer/Clifford group circuits. In…
We present an efficient addition circuit, borrowing techniques from the classical carry-lookahead arithmetic circuit. Our quantum carry-lookahead (QCLA) adder accepts two n-bit numbers and adds them in O(log n) depth using O(n) ancillary…
IBM has made several quantum computers available to researchers around the world via cloud services. Two architectures with five qubits, one with 16, and one with 20 qubits are available to run experiments. The IBM architectures implement…
We demonstrate the applicability of a universal gate set in the parity encoding, which is a dual to the standard gate model, by exploring several quantum gate algorithms such as the quantum Fourier transform and quantum addition. Embedding…
Quantum algorithms to solve practical problems in quantum chemistry, materials science, and matrix inversion often involve a significant amount of arithmetic operations which act on a superposition of inputs. These have to be compiled to a…
Arithmetic operations are an important component of many quantum algorithms. As such, coming up with optimized quantum circuits for these operations leads to more efficient implementations of the corresponding algorithms. In this paper, we…
Any unitary operation in quantum information processing can be implemented via a sequence of simpler steps - quantum gates. However, actual implementation of a quantum gate is always imperfect and takes a finite time. Therefore, seeking for…
We present a simple 2d local circuit that implements all-to-all interactions via perturbative gadgets. We find an analytic relation between the values $J_{ij}$ of the desired interaction and the parameters of the 2d circuit, as well as the…
Parallel computation enables multiple processors to execute different parts of a task simultaneously, improving processing speed and efficiency. In quantum computing, parallel gate implementation involves executing gates independently in…
Quantum Computing is making significant advancements toward creating machines capable of implementing quantum algorithms in various fields, such as quantum cryptography, quantum image processing, and optimization. The development of 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…
A common requirement of quantum simulations and algorithms is the preparation of complex states through sequences of 2-qubit gates. For a generic quantum state, the number of gates grows exponentially with the number of qubits, becoming…
Vigorous optimization of quantum gates has led to bipotent quantum architectures, where the optimized gates are available for some qubits but not for others. However, such gate-level improvements limit the application of user-side…
Quantum Approximate Optimization Algorithm (QAOA) and Quantum Annealing are prominent approaches for solving combinatorial optimization problems, such as those formulated as Quadratic Unconstrained Binary Optimization (QUBO). These…