We investigate the implementation of controlled-phase (CP) gates with quantum walks in a dual-rail encoding through the use of interacting particles. While previous proposals have focused on indistinguishable particles (bosons or fermions) to achieve unitary fidelity for plane-wave scattering, practical implementations require finite-size wavepackets and routing through single-particle gates, both factors that introduce unavoidable fidelity losses. We show that extending the interaction range beyond on-site or first-neighbor terms provides sufficient control over the scattering potential to engineer CP gates with distinguishable particles that match the ideal bosonic/fermionic performance. For finite Gaussian wavepackets, we derive analytical approximations for the gate fidelity in terms of the transmission coefficient's magnitude and phase derivatives. We find that while distinguishable-particle scattering alone exhibits slightly lower fidelity than the indistinguishable case, the overall architecture that we propose avoids the additional single-particle gates required for routing indistinguishable particles. The roundabout gates needed for the latter indeed introduce fidelity losses approximately one order of magnitude larger than the interaction-induced losses, making the distinguishable-particle approach competitive for practical implementations. Our results establish multi-neighbor interactions as a tool for quantum information processing with continuous-time quantum walks and provide quantitative guidelines for optimizing gate fidelities in finite-size systems.
We investigate the implementation of controlled-phase (CP) gates with quantum walks in a dual-rail encoding through the use of interacting particles. While previous proposals have focused on indistinguishable particles (bosons or fermions) to achieve unitary fidelity for plane-wave scattering, practical implementations require finite-size wavepackets and routing through single-particle gates, both factors that introduce unavoidable fidelity losses. We show that extending the interaction range beyond on-site or first-neighbor terms provides sufficient control over the scattering potential to engineer CP gates with distinguishable particles that match the ideal bosonic/fermionic performance. For finite Gaussian wavepackets, we derive analytical approximations for the gate fidelity in terms of the transmission coefficient's magnitude and phase derivatives. We find that while distinguishable-particle scattering alone exhibits slightly lower fidelity than the indistinguishable case, the overall architecture that we propose avoids the additional single-particle gates required for routing indistinguishable particles. The roundabout gates needed for the latter indeed introduce fidelity losses approximately one order of magnitude larger than the interaction-induced losses, making the distinguishable-particle approach competitive for practical implementations. Our results establish multi-neighbor interactions as a tool for quantum information processing with continuous-time quantum walks and provide quantitative guidelines for optimizing gate fidelities in finite-size systems.
In the present paper, the first in a series of two, we propose a model of universal quantum computation using a fermionic or bosonic multiparticle continuous-time quantum walk with two internal states (e.g., the spin-up and -down states of an electron). A dual-rail encoding is adopted to convert information: A single qubit is represented by the presence of a single quantum walker in either of the two parallel paths. We develop a roundabout gate that moves a walker from one path to the next, either clockwise or counterclockwise, depending on its internal state. It can be realized by a single-particle scattering on a directed weighted graph with the edge weights 1 and $\ifmmode\pm\else\textpm\fi{}i$. The roundabout gate also allows the spatial information of the quantum walker to be temporarily encoded in its internal states. The universal gates are constructed by appropriately combining several roundabout gates, some unitary gates that act on the internal states, and two-particle scatterings on straight paths. No ancilla qubits are required in our model. The computation is done by just passing quantum walkers through properly designed paths. Namely, there is no need for any time-dependent control. A physical implementation of quantum random access memory compatible with the present model will be considered in the second paper [R. Asaka et al., following paper, Phys. Rev. A 107, 022416 (2023)].
Controlling the interplay between particle propagation and quantum correlation generation is a central challenge in quantum transport. Here, we investigate two distinguishable continuous-time quantum walkers evolving on parallel one-dimensional lattices, interacting via distance-dependent potentials. While on-site interactions reproduce the typical bosonic behaviour, extending the interaction to a linear potential over multiple neighbors introduces controlled Bloch-like oscillations and shifts the bound-pair regime to stronger couplings. More generally, we explore a Coulomb-like interaction parameterized by strength, spatial scaling, and decay rate. This reveals a rich dynamical diagram including four distinct regimes: (i) a high-entropy, oscillatory regime akin to a linear potential; (ii) a strongly localized, bound-pair regime; (iii) a novel intermediate regime combining near-ballistic spreading with strong correlations; and (iv) a weakly interacting, free-propagation regime. Notably, regime (iii) achieves concurrent optimization of transport efficiency and entanglement, offering a sweet spot for correlated quantum dynamics. Our results provide a tool for designing interaction-engineered quantum walks with potential applications in quantum information processing and simulations.
Abstract Quantum Walks are unitary processes describing the evolution of an initially localized wavefunction on a lattice potential. The complexity of the dynamics increases significantly when several indistinguishable quantum walkers propagate on the same lattice simultaneously, as these develop non-trivial spatial correlations that depend on the particle’s quantum statistics, mutual interactions, initial positions, and the lattice potential. We show that even in the simplest case of a quantum walk on a one dimensional graph, these correlations can be shaped to yield a complete set of compact quantum logic operations. We provide detailed recipes for implementing quantum logic on one-dimensional quantum walks in two general cases. For non-interacting bosons—such as photons in waveguide lattices—we find high-fidelity probabilistic quantum gates that could be integrated into linear optics quantum computation schemes. For interacting quantum-walkers on a one-dimensional lattice—a situation that has recently been demonstrated using ultra-cold atoms—we find deterministic logic operations that are universal for quantum information processing. The suggested implementation requires minimal resources and a level of control that is within reach using recently demonstrated techniques. Further work is required to address error-correction.
We present a scheme for implementing high-fidelity quantum logic gates using the quantum walk of a few interacting bosons on a one-dimensional lattice. The gate operation is carried out by a single compact lattice described by a one-dimensional Bose-Hubbard model with only nearest-neighbor hopping and on-site interactions. We find high-fidelity deterministic logic operations for a gate set (including the CNOT gate) that is universal for quantum information processing. We discuss the applicability of this scheme in light of recent developments in controlling and monitoring cold-atoms in optical lattices, as well as an implementation with realistic nonlinear quantum photonic devices.
To extend the continuous-time quantum walk (CTQW) to simulate P distinguishable particles on a graph G composed of N vertices, the Hamiltonian of the system is expanded to act on an N^{P}-dimensional Hilbert space, in effect, simulating the multiparticle CTQW on graph G via a single-particle CTQW propagating on the Cartesian graph product G^{□P}. The properties of the Cartesian graph product have been well studied, and classical simulation of multiparticle CTQWs are common in the literature. However, the above approach is generally applied as is when simulating indistinguishable particles, with the particle statistics then applied to the propagated N^{P} state vector to determine walker probabilities. We address the following question: How can we modify the underlying graph structure G^{□P} in order to simulate multiple interacting fermionic CTQWs with a reduction in the size of the state space? In this paper, we present an algorithm for systematically removing "redundant" and forbidden quantum states from consideration, which provides a significant reduction in the effective dimension of the Hilbert space of the fermionic CTQW. As a result, as the number of interacting fermions in the system increases, the classical computational resources required no longer increases exponentially for fixed N.
High-fidelity two-logical-qubit gates are essential for realizing fault-tolerant quantum computation with bosonic codes, yet experimentally reported fidelities have rarely exceeded 90\%. Here, we propose a geometric phase engineering approach for implementing controlled-phase gates for binomially encoded logical qubits. This method leverages the structural simplicity of geometric drives to reduce the numerical optimization dimensionality while fully incorporating system nonlinearities, enabling fast and high-fidelity logical operations. As an example, we experimentally demonstrate a process fidelity of 97.4$\pm$0.8\% for a controlled-Z gate between two binomial codes, surpassing all previously reported two-logical-qubit gates in bosonic codes. This work demonstrates that geometric phase engineering provides an effective and experimentally feasible route to fast, high-fidelity logical operations in bosonic quantum processors.