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In the present paper methods and algorithms of modeling quantum operations for quantum computer integrated circuits design are developed. We examine different ways of quantum operation descriptions, including operator-sums, unitary…
A number of quantum algorithms have been performed on small quantum computers; these include Shor's prime factorization algorithm, error correction, Grover's search algorithm and a number of analog and digital quantum simulations. Because…
A possibility of performing the C-NOT gate operation at the ground and the first excited states of two harmonic oscillators interacting via a two-level system subject to complete control is demonstrated. The system resembles Turing machine,…
A Toffoli gate ($C^{n}$-NOT gate) is regarded as an important unitary gate in quantum computation, and is simulated by a quantum circuit composed of $C^{2}$-NOT gates. This paper presents a quantum circuit with a new configuration of…
Optimal implementation of quantum gates is crucial for designing a quantum computer. We consider the matrix representation of an arbitrary multiqubit gate. By ordering the basis vectors using the Gray code, we construct the quantum circuit…
Controlled-NOT (CNOT) gates are commonly included in the standard gate set of quantum processors and provide an important way to entangle qubits. For fixed-frequency qubits using the cross-resonance entangling technique, using the…
A system of unitary transformations providing two optimal copies of an arbitrary input cubit is obtained. An algorithm based on classical Boolean algebra and allowing one to find any unitary transformation realized by the quantum CNOT…
We consider the decomposition of arbitrary isometries into a sequence of single-qubit and Controlled-NOT (C-NOT) gates. In many experimental architectures, the C-NOT gate is relatively 'expensive' and hence we aim to keep the number of…
Crosstalk and several sources of operational interference are invisible when qubit or a gate is calibrated or benchmarked in isolation. These are unlocked during the execution of full quantum circuit applying entangling gates to several…
What is the time-optimal way of realizing quantum operations? Here, we show how important instances of this problem can be related to the study of shortest paths on the surface of a sphere under a special metric. Specifically, we provide an…
We present a theoretical result, which is based on the linear algebra theory (similar operators). The obtained theoretical results optimize the experimental technique to construct quantum computer e.g., reduces the number of steps to…
A large-scale quantum circuit can be partitioned into multiple subcircuits through circuit cutting, where each subcircuit is executed multiple times and the expectation value of the original circuit is reconstructed by classical…
As the effort to scale up existing quantum hardware proceeds, it becomes necessary to schedule quantum gates in a way that minimizes the number of operations. There are three constraints that have to be satisfied: the order or dependency of…
We present a scalable set of universal gates and multiply controlled gates in a qudit basis through a bijective mapping from N qubits to qudits with D = 2^N levels via rotations in U(2). For each of the universal gates (H, CNOT, and T), as…
Nonadiabatic holonomic quantum computation has received increasing attention due to its robustness against control errors. However, all the previous schemes have to use at least two sequentially implemented gates to realize a general…
High-fidelity single- and two-qubit gates are essential building blocks for a fault-tolerant quantum computer. While there has been much progress in suppressing single-qubit gate errors in superconducting qubit systems, two-qubit gates…
We propose a scheme for implementing the CNOT gate over qubits encoded in a pair of electron spins in a double quantum dot. The scheme is based on exchange and spin orbit interactions and on local gradients in Zeeman fields. We find that…
Methods and results for numerical simulations of one and two interacting rf-Squid systems suitable for adiabatic quantum gates are presented. These are based on high accuracy numerical solutions to the static and time dependent Schroedinger…
We report coherent operation of a singlet-triplet qubit controlled by the arrangement of two electrons in an adjacent double quantum dot. The system we investigate consists of two pairs of capacitively coupled double quantum dots fabricated…
We consider recent works on the simulation of quantum circuits using the formalism of matrix product states and the formalism of contracting tensor networks. We provide simplified direct proofs of many of these results, extending an…