It has been shown that, for even
n, evolving
n qubits according to a Hamiltonian that is the sum of pairwise interactions between the particles, can be used to exactly implement an
(n+1)-qubit fanout gate using a particular constant-depth circuit~[\href{https://arXiv.org/abs/quant-ph/0309163}{arXiv:quant-ph/0309163}]. However, the coupling coefficients in the Hamiltonian considered in that paper are assumed to be all equal. In this paper, we generalize these results and show that for all
n, including odd
n, one can exactly implement an
(n+1)-qubit parity gate and hence, equivalently in constant depth an
(n+1)-qubit fanout gate, using a similar Hamiltonian but with unequal couplings, and we give an exact characterization of the constraints that the couplings must satisfy in order for them to be adequate to implement fanout via the same circuit.}{In particular, we show the following:Letting
Jij be the coupling strength between the $\ordth{i}$ and $\ordth{j}$ qubits, the set of couplings
{Jij} is adequate to implement fanout via the circuit above if and only if there exists
J>0 such that 1. each
Jij is an odd integer multiple of
J, and 2. for each
i, there are an even number of
j=i such that
Jij/J≡3(mod4).
We present a novel implementation of an n-qubit fanout gate using resonance engineering. Our proposed mechanism uses Jaynes-Cummings interactions between multiple qubits and a common harmonic oscillator to realize a fanout gate at the system-level. Our theoretical analysis establishes upper bounds on the gate error, demonstrating linear infidelity scaling in constant time -- a favorable trade-off compared to a conventional CNOT decomposition. To validate the performance of our scheme at large system sizes, we exploit permutation symmetry to reduce the simulation complexity from exponential to polynomial in the number of qubits, enabling simulation up to 100 qubits. The results of this numerical analysis are consistent with our theoretical findings and allow us to characterize the performance well. Our gate will enable faster stabilizer readouts and could provide polynomial speedups in many quantum algorithms.
Simulating the dynamics of dissipative quantum many-body systems governed by local Lindbladians is a fundamental task in quantum computation. While the near-optimal gate count has been achieved for Hamiltonian simulation, comparable results for Lindbladian simulation remain elusive. In this work, we develop quantum algorithms for lattice Lindbladians by exploiting their locality. First, we consider sparsely dissipative systems, in which the dissipation is sparsely located, including boundary-driven systems. We establish a near-optimal quantum algorithm for their dynamics with gate count
O(Ntpolylog(Nt/ε)), where
N is the system size,
t is the evolution time, and
ε is the allowable error. We then consider generic lattice Lindbladians with finite-range interactions and dissipation, and develop an algorithm for simulating time-evolved observables with gate count
O((Nt)4/3polylog(Nt/ε)) per sample with the sampling complexity
Θ(ε−2). The gate count has the smallest known dependence on the system size among algorithms retaining polylogarithmic dependence on
1/ε. Our algorithms are based on two techniques that exploit locality: patching and merging. Patching decomposes dissipative dynamics into dynamics on subsystems with exponentially small error, generalizing a key idea underlying the Haah-Hastings-Kothari-Low algorithm for near-optimal Hamiltonian simulation. Merging absorbs reversed dissipative dynamics into other parts of the evolution, substantially reducing the overhead associated with quasi-probabilistic sampling. These results demonstrate that locality can be fully exploited to achieve fast quantum simulation of dissipative many-body dynamics, opening the way to applications such as predicting nonequilibrium phenomena and preparing desirable quantum states.
Quantum computers based on crystals of trapped ions are a prominent technology for quantum computation. A unique feature of trapped ions is their long-range Coulomb interactions, which can be exploited to realize large-scale multiqubit entanglement gates. However, scaling up the number of qubits, N , in these systems, while retaining high-fidelity and high-speed operations, is challenging. Specifically, designing multiqubit entanglement gates in long ion crystals of hundreds of ions involves an NP-hard optimization problem, rendering scale-up not only a technological challenge, but also a conceptual challenge. Here we introduce a method that mitigates this challenge, effectively allowing for a polynomial-time design of fast, robust, and programmable entanglement gates, acting on the entire ion-crystal. We show that while the number of simultaneous entanglement operations scales as N 2 , the gate duration scales as N , leading to a scaling advantage. We use our methods to investigate the drive-power requirements and susceptibility to noise and errors of these multiqubit gates. Our method delineates a path toward scaling up quantum computers based on ion-crystals with hundreds of qubits.
Quantum computers based on crystals of trapped ions are a prominent technology for quantum computation. A unique feature of trapped ions is their long-range Coulomb interactions, which can be exploited to realize large-scale multiqubit entanglement gates. However, scaling up the number of qubits,
N, in these systems, while retaining high-fidelity and high-speed operations, is challenging. Specifically, designing multiqubit entanglement gates in long ion crystals of hundreds of ions involves an NP-hard optimization problem, rendering scale-up not only a technological challenge, but also a conceptual challenge. Here we introduce a method that mitigates this challenge, effectively allowing for a polynomial-time design of fast, robust, and programmable entanglement gates, acting on the entire ion-crystal. We show that while the number of simultaneous entanglement operations scales as
N2, the gate duration scales as
N, leading to a scaling advantage. We use our methods to investigate the drive-power requirements and susceptibility to noise and errors of these multiqubit gates. Our method delineates a path towards scaling up quantum computers based on ion-crystals with hundreds of qubits.