Related papers: Approaching the theoretical limit in quantum gate …
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…
Decoupling systems into independently evolving components has a long history of simplifying seemingly complex systems. They enable a better understanding of the underlying dynamics and causal structures while providing more efficient means…
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…
We propose a novel physical realization of a quantum computer. The qubits are electric dipole moments of ultracold diatomic molecules, oriented along or against an external electric field. Individual molecules are held in a 1-D trap array,…
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…
Quantum hashing is a useful technique that allows us to construct memory-efficient algorithms and secure quantum protocols. First, we present a circuit that implements the phase form of quantum hashing using $2^{n-1}$ CNOT gates, where n is…
From a geometric approach, we derive the minimum number of applications needed for an arbitrary Controlled-Unitary gate to construct a universal quantum circuit. A new analytic construction procedure is presented and shown to be either…
Quantum computation offers the potential to solve fundamental yet otherwise intractable problems across a range of active fields of research. Recently, universal quantum-logic gate sets - the building blocks for a quantum computer - have…
Fault-tolerant quantum computing typically requires the transpilation of arbitrary quantum circuits into a finite, universal gate set, such as Clifford+T. As a baseline, Diagonal approximation can be used for synthesizing single-qubit Pauli…
A universal quantum computing scheme, with a universal set of logical gates, is proposed based on networks of 1D quantum systems. The encoding of information is in terms of universal features of gapped phases, for which effective field…
We present a deterministic framework for preparing an arbitrary three-qubit pure state. To leverage entanglement structure in the state-preparation task, we classify three-qubit pure states into five types with respect to a $1|2$…
Although only two quantum states of a physical system are often used to encode quantum information in the form of qubits, many levels can in principle be used to obtain qudits and increase the information capacity of the system. To take…
Quantum Compiling Algorithms decompose (exactly, without approximations) an arbitrary $2^\nb$ unitary matrix acting on $\nb$ qubits, into a sequence of elementary operations (SEO). There are many possible ways of decomposing a unitary…
The optimal cost of a three-qubit Fredkin gate is 5 two-qubit entangling gates, and the overhead climbs to 8 when restricted to controlled-not (CNOT) gates. By harnessing higher-dimensional Hilbert spaces, we reduce the cost of a…
We give quantum circuits that simulate an arbitrary two-qubit unitary operator up to global phase. For several quantum gate libraries we prove that gate counts are optimal in worst and average cases. Our lower and upper bounds compare…
Optimizing quantum circuits by reducing circuit depth is essential for improving the efficiency and scalability of quantum algorithms, particularly as quantum hardware continues to evolve. This can be achieved by restructuring quantum…
Quantum computing is a promising technology to address combinatorial optimization problems, for example via the quantum approximate optimization algorithm (QAOA). Its potential, however, hinges on scaling toy problems to sizes relevant for…
Given an arbitrary single-qubit operation, an important task is to efficiently decompose this operation into an (exact or approximate) sequence of fault-tolerant quantum operations. We derive a depth-optimal canonical form for single-qubit…
A quantum computer has the potential to effciently solve problems that are intractable for classical computers. Constructing a large-scale quantum processor, however, is challenging due to errors and noise inherent in real-world quantum…
Unitary quantum gates constitute the building blocks of Quantum Computing in the circuit paradigm. In this work, we engineer a locally driven two-qubit Hamiltonian whose instantaneous ground-state dynamics generates the controlled-NOT…