Related papers: Qubit encodings for lattices of dipolar planar rot…
We describe methods for simulating general second-quantized Hamiltonians using the compact encoding, in which qubit states encode only the occupied modes in physical occupation number basis states. These methods apply to second-quantized…
Current quantum simulators are primarily qubit-based, making them naturally suitable for simulating 2-level quantum systems. However, many systems in nature are inherently $d$-level, including higher spins, bosons, vibrational modes, and…
We propose a scheme for encoding many qubits in a single rotor, that is, a continuous and periodic degree of freedom. A key feature of this scheme is its ability to manipulate and entangle the encoded qubits with a single operation on the…
The advent of quantum computing necessitates the transition of worldwide cryptosystems to post-quantum cryptography (PQC), which is founded upon the problem of finding short vectors in high-dimensional structured lattices. It is assumed…
We formally define homological quantum rotor codes which use multiple quantum rotors to encode logical information. These codes generalize homological or CSS quantum codes for qubits or qudits, as well as linear oscillator codes which…
A logical qubit is a two-dimensional subspace of a higher dimensional system, chosen such that it is possible to detect and correct the occurrence of certain errors. Manipulation of the encoded information generally requires arbitrary and…
Rotation symmetric bosonic codes are an attractive encoding for qubits into oscillator degrees of freedom, particularly in superconducting qubit experiments. While these codes can tolerate considerable loss and dephasing, they will need to…
We show that higher-dimensional versions of qubits, or qudits, can be encoded into spin systems and into harmonic oscillators, yielding important advantages for quantum computation. Whereas qubit-based quantum computation is adequate for…
We discuss encodings of fermionic many-body systems by qubits in the presence of symmetries. Such encodings eliminate redundant degrees of freedom in a way that preserves a simple structure of the system Hamiltonian enabling quantum…
Variational quantum algorithms are promising applications of noisy intermediate-scale quantum (NISQ) computers. These algorithms consist of a number of separate prepare-and-measure experiments that estimate terms in a Hamiltonian. The…
A primary objective of quantum computation is to efficiently simulate quantum physics. Scientifically and technologically important quantum Hamiltonians include those with spin-$s$, vibrational, photonic, and other bosonic degrees of…
Simulation of quantum systems is expected to be one of the most important applications of quantum computing, with much of the theoretical work so far having focused on fermionic and spin-$\frac{1}{2}$ systems. Here, we instead consider…
Quantum Fourier transform (QFT) is a widely used building block for quantum algorithms, whose scalable implementation is challenging in experiments. Here, we propose a protocol of quadratic quantum Fourier transform (QQFT), considering cold…
We construct quantum circuits which exactly encode the spectra of correlated electron models up to errors from rotation synthesis. By invoking these circuits as oracles within the recently introduced "qubitization" framework, one can use…
We present a general procedure for constructing lattices of qubits with a Hamiltonian composed of nearest-neighbour two-body interactions such that the ground state encodes a cluster state. We give specific details for lattices in one-,…
Qutrits, the triple level quantum systems in various forms, have been proposed for quantum information processing recently. By the methods presented in this paper a bi-photonic qutrit, which is encoded with the polarizations of two photons…
Quantum computation of vibrational properties of molecules is a promising platform to obtain computational advantages for computational chemistry. However, fault-tolerant quantum computations of vibrational properties remain a relatively…
Correlated quantum many-body phenomena in lattice models have been identified as a set of physically interesting problems that cannot be solved classically. Analog quantum simulators, in photonics and microwave superconducting circuits,…
We propose a scheme for quantum computation in optical lattices. The qubits are encoded in the spacial wavefunction of the atoms such that spin decoherence does not influence the computation. Quantum operations are steered by shaking the…
In an attempt to better leverage superconducting quantum computers, scaling efforts have become the central concern. These efforts have been further exacerbated by the increased complexity of these circuits. The added complexity can…