Related papers: Second-quantized fermionic operators with polyloga…
We present an algorithm for systematic encoding of Hermitian codes. For a Hermitian code defined over GF(q^2), the proposed algorithm achieves a run time complexity of O(q^2) and is suitable for VLSI implementation. The encoder architecture…
Mapping fermionic operators to qubit operators is an essential step for simulating fermionic systems on a quantum computer. We investigate how the choice of such a mapping interacts with the underlying qubit connectivity of the quantum…
Recent experimental progress in controlling neutral group-II atoms for optical clocks, and in the production of degenerate gases with group-II atoms has given rise to novel opportunities to address challenges in quantum computing and…
Quantum computing is emerging as a promising tool in nuclear physics. However, the cost of encoding fermionic operators hampers the application of algorithms in current noisy quantum devices. In this work, we analyze an encoding scheme…
As physical implementations of quantum architectures emerge, it is increasingly important to consider the cost of algorithms for practical connectivities between qubits. We show that by using an arrangement of gates that we term the…
We present an asymptotically improved algorithm for implementing the Quantum Fourier Transform (QFT) in both the exact and approximate settings. Historically, the approximate QFT has been implemented in $\Theta(n \log n)$ gates, and the…
A compelling application of quantum computers with thousands of qubits is quantum simulation. Simulating fermionic systems is both a problem with clear real-world applications and a computationally challenging task. In order to simulate a…
The structure and dynamics of quantum many-body systems are the result of a delicate interplay between underlying interactions, which leads to intricate entanglement structures. Despite this apparent complexity, symmetries emerge and have…
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…
One of the major promises of quantum computing is the realization of SIMD (single instruction - multiple data) operations using the phenomenon of superposition. Since the dimension of the state space grows exponentially with the number of…
We show how to efficiently simulate continuous-time quantum query algorithms that run in time T in a manner that preserves the query complexity (within a polylogarithmic factor) while also incurring a small overhead cost in the total number…
This article proposes a formalism which unifies Hamiltonian simulation techniques from different fields. This formalism leads to a competitive method to construct the Hamiltonian simulation with a comprehensible, simple-to-implement circuit…
We present a classical algorithm for simulating universal quantum circuits composed of "free" nearest-neighbour matchgates or equivalently fermionic-linear-optical (FLO) gates, and "resourceful" non-Gaussian gates. We achieve the promotion…
We present a classical simulation method for fermionic quantum systems which, without loss of generality, can be represented by parity-preserving circuits made of two-qubit gates in a brick-wall structure. We map such circuits to a…
Among the list of major threats to quantum computation, quantum decoherence poses one of the largest because it generates losses to the environment within a computational system which cannot be recovered via error correction methods. These…
Quantum information theory and strongly correlated electron systems share a common theme of macroscopic quantum entanglement. In both topological error correction codes and theories of quantum materials (spin liquid, heavy fermion and…
The efficient encoding of the fermionic Schr\"odinger equation as a spin system Hamiltonian is a long-term problem. I describe an encoding for the fermionic position space Schr\"odinger equation on a finite-volume periodic lattice with a…
We introduce a framework which allows to systematically and arbitrarily scale the code distance of local fermion-to-qubit encodings in one and two dimensions without growing the weights of stabilizers. This is achieved by embedding…
The paradigm behind digital quantum computing inherits the idea of using binary information processing. Nature in fact gives much more rich structures of physical objects that can be used for encoding information, which is especially…
Mapping fermionic systems to qubits on a quantum computer is often the first step for algorithms in quantum chemistry and condensed matter physics. However, it is difficult to reconcile the many different approaches that have been proposed,…