Related papers: Computational Complexity and Simulability of Non-H…
From the existence of an efficient quantum algorithm for factoring, it is likely that quantum computation is intrinsically more powerful than classical computation. At present, the best upper bound known for the power of quantum computation…
Numerical simulation results are presented which suggest that a class of non-adiabatic rapid passage sweeps first realized experimentally in 1991 should be capable of implementing a universal set of quantum gates G_{u} that operate with…
Clifford circuits -- i.e. circuits composed of only CNOT, Hadamard, and $\pi/4$ phase gates -- play a central role in the study of quantum computation. However, their computational power is limited: a well-known result of Gottesman and…
Quantum computing's potential for exponential speedup is fundamentally limited by decoherence, a phenomenon arising from environmental interactions. Non-Hermitian quantum mechanics, particularly $PT$-symmetric systems, offers a novel…
The presence of symmetries, be they discrete or continuous, in a physical system typically leads to a reduction in the problem to be solved. Here we report that neither translational invariance nor rotational invariance reduce the…
Quantum computation based on nonadiabatic geometric phases has attracted a broad range of interests, due to its fast manipulation and inherent noise resistance. However, it is limited to some special evolution paths, and the gate-times are…
Quantum algorithms profit from the interference of quantum states in an exponentially large Hilbert space and the fact that unitary transformations on that Hilbert space can be broken down to universal gates that act only on one or two…
A practical fault-tolerant quantum computer is worth looking forward to as it provides applications that outperform their known classical counterparts. However, millions of interacting qubits with stringent criteria are required, which is…
We introduce a novel software-oriented model of quantum computation motivated by the practical constraints of near-term quantum hardware. In this model, gates are specified by constraints expressed in terms of Pauli observables, with each…
We propose a scheme for scalable and robust quantum computing on two-dimensional arrays of qubits with fixed longitudinal coupling. This opens the possibility for bypassing the device complexity associated with tunable couplers required in…
Non-Hermitian quantum systems showcase many distinct and intriguing features with no Hermitian counterparts. One of them is the exceptional point which marks the PT (parity and time) symmetry phase transition, where an enhanced spectral…
We consider models of quantum computation that involve operations performed on some fixed resourceful quantum state. Examples that fit this paradigm include magic state injection and measurement-based approaches. We introduce a framework…
An important result in the theory of quantum control is the "universality" of $2$-local unitary gates, i.e. the fact that any global unitary evolution of a system of $L$ qudits can be implemented by composition of $2$-local unitary gates.…
We construct families of cell complexes that generalize expander graphs. These families are called non-$k$-hyperfinite, generalizing the idea of a non-hyperfinite (NH) family of graphs. Roughly speaking, such a complex has the property that…
To overcome the fast oscillatory behavior of correlation functions for extracting scattering phase shift in real-time quantum simulations encountered in Ref.\cite{Guo:2026qkx}, we propose and test two solutions in the present work. One is…
Nonlinear spectroscopy is a cornerstone of quantum science, providing unique access to multi-point correlations, quantum coherence, and couplings that are invisible to linear methods. However, classical simulation of these phenomena is…
In the popular ${\cal PT}-$symmetry-based formulation of quantum mechanics of closed systems one can build unitary models using non-Hermitian Hamiltonians (i.e., $H \neq H^\dagger$) which are Hermitizable (so that one can write,…
We give a careful proof that a parallelized version of adiabatic quantum computation can efficiently simulate universal gate model quantum computation. The proof specifies an explicit parameter-dependent Hamiltonian $H({\lambda})$ that is…
As quantum computing resources remain scarce and error rates high, minimizing the resource consumption of quantum circuits is essential for achieving practical quantum advantage. Here we consider the natural problem of, given a circuit $C$,…
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…