Related papers: Deciding universality of quantum gates
We present an algorithm for compiling arbitrary unitaries into a sequence of gates native to a quantum processor. As accurate CNOT gates are hard for the foreseeable Noisy- Intermediate-Scale Quantum devices era, our A* inspired algorithm…
We study the Universality and Membership Problems for gate sets consisting of a finite number of quantum gates. Our approach relies on the techniques from compact Lie groups theory. We also introduce an auxiliary problem called Subgroup…
A problem of universality in simulation of evolution of quantum system and in theory of quantum computations is related with the possibility of expression or approximation of arbitrary unitary transformation by composition of specific…
We consider quantum circuits composed of Clifford and T gates. In this context the T gate has a special status since it confers universal computation when added to the (classically simulable) Clifford gates. However it can be very expensive…
Implementation of high-dimensional (HD) quantum gates shows very promising perspectives for HD quantum computation. A bipartite quantum system with arbitrary dimensions $n$ and $m$ is termed a quNit-quMit. Here we propose a synthesis scheme…
In this work, we study distributions of unitaries generated by random quantum circuits containing only symmetry-respecting gates. We develop a unified approach applicable to all symmetry groups and obtain an equation that determines the…
We propose an effective set of elementary quantum gates which provide an encoded universality and demonstrate the physical feasibility of these gates for the solid-state quantum computer based on the multi-atomic systems in the QED cavity.…
A single physical interaction might not be universal for quantum computation in general. It has been shown, however, that in some cases it can generate universal quantum computation over a subspace. For example, by encoding logical qubits…
We consider procedures to realize an approximate universal NOT gate in terms of average fidelity and fidelity deviation. The average fidelity indicates the optimality of operation on average, while the fidelity deviation does the…
Computations with a future quantum computer will be implemented through the operations by elementary quantum gates. It is now well known that the collection of 1-bit and 2-bit quantum gates are universal for quantum computation, i.e., any…
We study how much noise can be tolerated by a universal gate set before it loses its quantum-computational power. Specifically we look at circuits with perfect stabilizer operations in addition to imperfect non-stabilizer gates. We prove…
Near-term quantum computers are primarily limited by errors in quantum operations (or gates) between two quantum bits (or qubits). A physical machine typically provides a set of basis gates that include primitive 2-qubit (2Q) and 1-qubit…
We show that any quantum circuit of treewidth $t$, built from $r$-qubit gates, requires at least $\Omega(\frac{n^{2}}{2^{O(r\cdot t)}\cdot \log^4 n})$ gates to compute the element distinctness function. Our result generalizes a…
We provide an analytic way to implement any arbitrary two-qubit unitary operation, given an entangling two-qubit gate together with local gates. This is shown to provide explicit construction of a universal quantum circuit that exactly…
In quantum computation every unitary operation can be decomposed into quantum circuits-a series of single-qubit rotations and a single type entangling two-qubit gates, such as controlled-NOT (CNOT) gates. Two measures are important when…
We find exact solutions for a universal set of quantum gates on a scalable candidate for quantum computers, namely an array of two level systems. The gates are constructed by a combination of dynamical and geometrical (non-Abelian) phases.…
The conventional paradigm of quantum computing is discrete: it utilizes discrete sets of gates to realize bitstring-to-bitstring mappings, some of them arguably intractable for classical computers. In parameterized quantum approaches, the…
The controlled-not gate and the single qubit gates are considered elementary gates in quantum computing. It is natural to ask how many such elementary gates are needed to implement more elaborate gates or circuits. Recall that a…
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…
It is an oft-cited fact that no quantum code can support a set of fault-tolerant logical gates that is both universal and transversal. This no-go theorem is generally responsible for the interest in alternative universality constructions…