Related papers: Second-quantized fermionic operators with polyloga…
We introduce a framework for simulating hybrid oscillator-qubit quantum processors on qubit-only systems through position encoding. By encoding continuous-variable position and momentum wave functions into qubit amplitudes, our method…
The Fermi-Hubbard model, a fundamental framework for studying strongly correlated phenomena could significantly benefit from quantum simulations when exploring non-trivial settings. However, simulating this problem requires twice as many…
The Quantum Fourier Transformation (QFT) is a well-known subroutine for algorithms on qubit-based universal quantum computers. In this work, the known QFT circuit is used to derive an efficient circuit for the multidimensional QFT. The…
The Quantum Fourier transform (QFT) is a key ingredient in most quantum algorithms. We have compared various spin-based quantum computing schemes to implement the QFT from the point of view of their actual time-costs and the accuracy of the…
We introduce simple qubit-encodings and logic gates which eliminate the need for certain difficult single-qubit operations in superconducting phase-qubits, while preserving universality. The simplest encoding uses two physical qubits per…
Multiplication over binary fields is a crucial operation in quantum algorithms designed to solve the discrete logarithm problem for elliptic curve defined over $GF(2^n)$. In this paper, we present an algorithm for constructing quantum…
Variational quantum algorithms (VQAs) have been proposed as one of the most promising approaches to demonstrate quantum advantage on noisy intermediate-scale quantum (NISQ) devices. However, it has been unclear whether VQAs can maintain…
Modeling low energy eigenstates of fermionic systems can provide insight into chemical reactions and material properties and is one of the most anticipated applications of quantum computing. We present three techniques for reducing the cost…
Quantum simulations of chemistry in first quantization offer important advantages over approaches in second quantization including faster convergence to the continuum limit and the opportunity for practical simulations outside the…
Fermions are the building blocks of matter, forming atoms and nuclei, complex materials and neutron stars. Our understanding of many-fermion systems is however limited, as classical computers are often insufficient to handle the intricate…
We propose a method of encoding a topologically-protected qubit using Majorana fermions in a trapped-ion chain. This qubit is protected against major sources of decoherence, while local operations and measurements can be realized.…
Quantum symmetrization is the task of transforming a non-strictly increasing list of $n$ integers into an equal superposition of all permutations of the list (or more generally, performing this operation coherently on a superposition of…
For quantum algorithms for problems in which the task is to compute an entire field of values, like e.g. computational fluid dynamics (CFD), it is often proposed amplitude encoding w.r.t. multiple qubits; however, the efforts implied by it…
Many quantum algorithms, including recently proposed hybrid classical/quantum algorithms, make use of restricted tomography of the quantum state that measures the reduced density matrices, or marginals, of the full state. The most…
Linear optical quantum computation (LOQC) offers a promising platform for scalable quantum information processing, but its scalability is fundamentally constrained by the probabilistic nature of non-local entangling gates. Qudit circuit…
We introduce a new scheme for quantum circuit design called controlled gate networks. Rather than trying to reduce the complexity of individual unitary operations, the new strategy is to toggle between all of the unitary operations needed…
Executing a logical quantum circuit fault-tolerantly incurs a large spacetime overhead. Recent work has proposed and investigated phantom codes, defined by the property that every in-block logical $\mathrm{CNOT}$ circuit can be implemented…
Quantum algorithms on near-term quantum processors are typically executed using shallow quantum circuits composed of one- and two-qubit gates. However, as circuit depth and gate number increase, gate imperfections and qubit decoherence…
Quantum computers provide a fundamentally new computing paradigm that promises to revolutionize our ability to solve broad classes of problems. Surprisingly, the basic mathematical structures of gate-based quantum computing, such as unitary…
We present a novel input scheme for general second-quantized Hamiltonians of relativistic or non-relativistic many-fermion systems. This input scheme incorporates the fermionic anticommutation relations, particle number variations, and…