Related papers: Optimal constant-cost implementations of Clifford …
While implementing a quantum algorithm it is crucial to reduce the quantum resources, in order to obtain the desired computational advantage. For most fault-tolerant quantum error-correcting codes the cost of implementing the non-Clifford…
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…
In order to demonstrate non-trivial quantum computations experimentally, such as the synthesis of arbitrary entangled states, it will be useful to understand how to decompose a desired quantum computation into the shortest possible sequence…
Fault-tolerant logical entangling gates are essential for scalable quantum computing, but are limited by the error rates and overheads of physical two-qubit gates and measurements. To address this limitation, we introduce phantom…
We perform optimal-control-theory calculations to determine the minimum number of two-qubit CNOT gates needed to perform quantum state preparation and unitary operator synthesis for few-qubit systems. By considering all possible gate…
We show how to construct a multi-qubit control gate on a quantum register of an arbitrary size N. This gate performs a single-qubit operation on a specific qubit conditioned by the state of other N-1 qubits. We provide an algorithm how to…
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:…
While Clifford operations are relatively easy to implement in fault-tolerant quantum computers,continuous rotation gates remain a significant bottleneck in typical quantum algorithms. In this work, we ask the question: "What is the most…
In superconducting architectures, limited connectivity remains a significant challenge for the synthesis and compilation of quantum circuits. We consider models of entanglement-assisted computation where long-range operations are achieved…
We examine the following problem: given a collection of Clifford gates, describe the set of unitaries generated by circuits composed of those gates. Specifically, we allow the standard circuit operations of composition and tensor product,…
In order for quantum computations to be done as efficiently as possible it is important to optimise the number of gates used in the underlying quantum circuits. In this paper we find that many gate optimisation problems for approximately…
The Clifford group is the set of gates generated by the controlled not gates, the Hadamard gate and the P={{1,0},{0,i}} gate. We will say that a n-qubit state is a Clifford state if it can be prepared using Clifford gates. In this paper we…
We present a planar surface-code-based scheme for fault-tolerant quantum computation which eliminates the time overhead of single-qubit Clifford gates, and implements long-range multi-target CNOT gates with a time overhead that scales only…
We show how to perform measurement-based quantum computing on qudits (high-dimensional quantum systems) using alternative resource states beyond the cluster state. Estimating overheads for gate decomposition, we find that generalizing…
Large-scale quantum computers will require quantum gate operations between widely separated qubits. A method for implementing such operations, known as quantum gate teleportation (QGT), requires only local operations, classical…
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…
The circuit model of a quantum computer consists of sequences of gate operations between quantum bits (qubits), drawn from a universal family of discrete operations. The ability to execute parallel entangling quantum gates offers clear…
We experimentally demonstrate an optical controlled-NOT (CNOT) gate with arbitrary single inputs based on a 4-photon 6-qubit cluster state entangled both in polarization and spatial modes. We first generate the 6-qubit state, and then by…
We give a general proof for the existence and realizability of Clifford gates in the Ising topological quantum computer. We show that all quantum gates that can be implemented by braiding of Ising anyons are Clifford gates. We find that the…
The Clifford operators are an important and well-studied subset of quantum operations, in both the qubit and higher-dimensional qudit cases. While there are many ways to characterize this set, this paper aims to provide an ideal…