Related papers: Low-depth simulations of fermionic systems on squa…
While all quantum algorithms can be expressed in terms of single-qubit and two-qubit gates, more expressive gate sets can help reduce the algorithmic depth. This is important in the presence of gate errors, especially those due to…
In ab-initio electronic structure simulations, fermion-to-qubit mappings represent the initial encoding step of the fermionic problem into qubits. This work introduces a physically-inspired method for constructing mappings that…
Quantum computers hold great promise for efficiently simulating Fermionic systems, benefiting fields like quantum chemistry and materials science. To achieve this, algorithms typically begin by choosing a Fermion-to-qubit mapping to encode…
Low depth measurement-based quantum computation with qudits ($d$-level systems) is investigated and a precise relationship between this powerful model and qudit quantum circuits is derived in terms of computational depth and size…
We introduce novel algorithms for the quantum simulation of molecular systems which are asymptotically more efficient than those based on the Trotter-Suzuki decomposition. We present the first application of a recently developed technique…
The quantum simulation of fermionic gauge field theories is one of the anticipated uses of quantum computers in the NISQ era. Recently work has been done to simulate properties of the fermionic Z2 gauge field theory in (1+1) D and the pure…
Quantum computation is traditionally expressed in terms of quantum bits, or qubits. In this work, we instead consider three-level qu$trits$. Past work with qutrits has demonstrated only constant factor improvements, owing to the $\log_2(3)$…
This paper introduces the Hamiltonian-Adaptive Ternary Tree (HATT) framework to compile optimized Fermion-to-qubit mapping for specific Fermionic Hamiltonians. In the simulation of Fermionic quantum systems, efficient Fermion-to-qubit…
Compiling shallow and accurate quantum circuits for Hamiltonian simulation remains challenging due to hardware constraints and the combinatorial complexity of minimizing gate count and circuit depth. Existing optimization method pipelines…
Simulating quantum physics with a device which itself is quantum mechanical, a notion Richard Feynman originated, would be an unparallelled computational resource. However, the universal quantum simulation of fermionic systems is daunting…
Recently we developed a local and constructive algorithm based on Lie algebraic methods for compressing Trotterized evolution under Hamiltonians that can be mapped to free fermions. The compression algorithm yields a circuit which scales…
We perform an extended numerical search for practical fermion-to-qubit encodings with error correcting properties. Ideally, encodings should strike a balance between a number of the seemingly incompatible attributes, such as having a high…
Rapid development in quantum computing leads to the appearance of several quantum applications. Quantum Fourier Transformation (QFT) sits at the heart of many of these applications. Existing work leverages SAT solver or heuristics to…
We propose a universal approach based on Hamiltonian inverse engineering to realize a set of parameterized two-qubit gates. This method possesses unique advantages to simultaneous control of transitions among four energy levels, providing a…
Gate-based universal quantum computation is formulated in terms of two types of operations: local single-qubit gates, which are typically easily implementable, and two-qubit entangling gates, whose faithful implementation remains one of the…
Quantum computing is a promising technology that harnesses the peculiarities of quantum mechanics to deliver computational speedups for some problems that are intractable to solve on a classical computer. Current generation noisy…
We derive a rigorous upper bound on the classical computation time of finite-ranged tensor network contractions in $d \geq 2$ dimensions. Consequently, we show that quantum circuits of single-qubit and finite-ranged two-qubit gates can be…
Near term quantum computers with a high quantity (around 50) and quality (around 0.995 fidelity for two-qubit gates) of qubits will approximately sample from certain probability distributions beyond the capabilities of known classical…
We propose several methods for optimizing the number of qubits in a quantum circuit while preserving the number of non-Clifford gates. One of our approaches consists in reversing, as much as possible, the gadgetization of Hadamard gates,…
Compressible models extend the domain of simulable systems in quantum computers, but little is known about their precise limits of applicability. Using the theory of compressible matchgate circuits, we identify a class of quadratic…