Related papers: Efficient Toffoli Gates Using Qudits
Uniformly controlled one-qubit gates are quantum gates which can be represented as direct sums of two-dimensional unitary operators acting on a single qubit. We present a quantum gate array which implements any n-qubit gate of this type…
In quantum control theory, a question of fundamental and practical interest is how an arbitrary unitary transformation can be decomposed into minimum number of elementary rotations for implementation, subject to various physical…
Multiplication over binary fields is a crucial operation in quantum algorithms designed to solve the discrete logarithm problem for elliptic curve defined over $GF(2^n)$. In this paper, we present an algorithm for constructing quantum…
We present some compact quantum circuits for a deterministic quantum computing on electron-spin qubits assisted by quantum dots inside single-side optical microcavities, including the CNOT, Toffoli, and Fredkin gates. They are constructed…
An open quantum walk formalism for dissipative quantum computing is presented. The approach is illustrated with the examples of the Toffoli gate and the Quantum Fourier Transform for 3 and 4 qubits. It is shown that the algorithms based on…
In this paper, we exclusively utilize CNOT gates for implementing permutation groups generated by more than two elements. In Lemma 1, we recall that three CNOT gates are both necessary and sufficient to execute a two-qubit swap gate…
We present a general method to construct fault-tolerant quantum logic gates with a simple primitive, which is an analog of quantum teleportation. The technique extends previous results based on traditional quantum teleportation (Gottesman…
Any single-qubit unitary operation or quantum gate can be considered a rotation. Typical experimental implementations of single-qubit gates involve two or three fixed rotation axes, and up to three rotation steps. Here we show that, if the…
We present an economical dynamical control scheme to perform quantum computation on a one dimensional optical lattice, where each atom encodes one qubit. The model is based on atom tunneling transitions between neighboring sites of the…
Control modular addition is a core arithmetic function, and we must consider the computational cost for actual quantum computers to realize efficient implementation. To achieve a low computational cost in a control modular adder, we focus…
The physical limitations of quantum hardware often require nearest-neighbor qubit structures, in which two-qubit gates are required to construct nearest-neighbor quantum circuits. However, two-qubit gates are considered a major cost of…
Recently, reversible circuit synthesis has been intensively studied. One of the problems that has not been solved for a long time was exact minimization of gate count (GC) in 4-bit circuits. Finally, last year a tool of practical usage for…
Atomic-scale logic and the minimization of heating (dissipation) are both very high on the agenda for future computation hardware. An approach to achieve these would be to replace networks of transistors directly by classical reversible…
Gate-based quantum computation has been extensively investigated using quantum circuits based on qubits. In many cases, such qubits are actually made out of multilevel systems but with only two states being used for computational purpose.…
Gate-based universal quantum computation is formulated in terms of two types of operations: local single-qubit gates, which are typically easily implementable, and two-qubit entangling gates, whose faithful implementation remains one of the…
Qubitization is a modern approach to estimate Hamiltonian eigenvalues without simulating its time evolution. While in this way approximation errors are avoided, its resource and gate requirements are more extensive: qubitization requires…
We analyze the multifractality of the fidelity in an engineered Toffoli gate. Using quantum control methods, we define several optimization problems whose global solutions realize the gate in a chain of three qubits with XY Heisenberg…
How to implement multi-qubit gates is an important problem in quantum information processing. Based on cross phase modulation, we present an approach to realizing a family of multi-qubit gates that deterministically operate on single…
The promise of tremendous computational power, coupled with the development of robust error-correcting schemes, has fuelled extensive efforts to build a quantum computer. The requirements for realizing such a device are confounding:…
We introduce simple qubit-encodings and logic gates which eliminate the need for certain difficult single-qubit operations in superconducting phase-qubits, while preserving universality. The simplest encoding uses two physical qubits per…