Related papers: Constant-cost implementations of Clifford operatio…
Simulating large-scale coupled-oscillator systems presents substantial computational challenges for classical algorithms, particularly when pursuing first-principles analyses in the thermodynamic limit. Motivated by the quantum algorithm…
In this paper we continue to explore "hybrid" quantum circuit models in one-dimension with both unitary and measurement gates, focussing on the entanglement properties of wavefunction trajectories at long times, in the steady state. We…
Resource-efficient and high-precision approximate synthesis of quantum circuits expressed in the Clifford+T gate set is vital for Fault-Tolerant quantum computing. Efficient optimal methods are known for single-qubit RZ unitaries, otherwise…
Unitary operations are the building blocks of quantum programs. Our task is to design effcient or optimal implementations of these unitary operations by employing the intrinsic physical resources of a given n-qubit system. The most common…
We present protocols for implementation of universal quantum gates on an arbitrary superposition of quantum states in a scalable solid-state Ising spin quantum computer. The spin chain is composed of identical spins 1/2 with the Ising…
The quantum circuit model allows gates between any pair of qubits yet physical instantiations allow only limited interactions. We address this problem by providing an interaction graph together with an efficient method for compiling quantum…
In an ordinary quantum algorithm the gates are applied in a fixed order on the systems. The introduction of indefinite causal structures allows to relax this constraint and control the order of the gates with an additional quantum state. It…
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…
Implementing a qubit quantum computer in continuous-variable systems conventionally requires the engineering of specific interactions according to the encoding basis states. In this work, we present a unified formalism to conduct universal…
We study the computational power of unitary Clifford circuits with solely magic state inputs (CM circuits), supplemented by classical efficient computation. We show that CM circuits are hard to classically simulate up to multiplicative…
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 derive an encoded universality representation for a generalized anisotropic exchange Hamiltonian that contains cross-product terms in addition to the usual two-particle exchange terms. The recently developed algebraic approach is used to…
In a previous publication [1] we showed that it is possible to implement universal quantum computation with the anisotropic XY-Heisenberg exchange acting as a single interaction. To achieve this we used encodings of the states of the…
The hybrid approach to quantum computation simultaneously utilizes both discrete and continuous variables which offers the advantage of higher density encoding and processing powers for the same physical resources. Trapped ions, with…
We study the quantum computational power of a generic class of anisotropic solid state Hamiltonians. A universal set of encoded logic operations are found which do away with difficult-to-implement single-qubit gates in a number of quantum…
Let $n\geq 8$ be divisible by 4. The Clifford-cyclotomic gate set $\mathcal{G}_n$ is the universal gate set obtained by extending the Clifford gates with the $z$-rotation $T_n = \mathrm{diag}(1,\zeta_n)$, where $\zeta_n$ is a primitive…
We study the low energy states of finite spin chains with isotropic (Heisenberg) and anisotropic (XY and Ising-like) exchange interaction with uniform and non-uniform coupling constants. We show that for an odd number of sites a spin…
Scalable quantum computation in realistic devices requires that precise control can be implemented efficiently in the presence of decoherence and operational errors. We propose a general constructive procedure for designing robust unitary…
Universal quantum computing relies on high-fidelity entangling operations. Here we demonstrate that four coupled qubits can operate as a quantum gate, where two qubits control the operation on two target qubits (a four-qubit gate). This…
Fault-tolerant quantum computation allows quantum computations to be carried out while resisting unwanted noise. Several error-correcting codes have been developed to achieve this task, but none alone are capable of universal quantum…