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If a quantum computer is stabilized by fault-tolerant quantum error correction (QEC), then most of its resources (qubits and operations) are dedicated to the extraction of error information. Analysis of this process leads to a set of…
Experiments with superconducting quantum processors have successfully demonstrated the basic functions needed for quantum computation and evidence of utility, albeit without a sizable array of error-corrected qubits. The realization of the…
We investigate unitary and state $t$-designs from a computational complexity perspective. First, we address the problems of computing frame potentials that characterize (approximate) $t$-designs. We present a quantum algorithm for computing…
Under suitable assumptions, the quantum phase estimation (QPE) algorithm is able to achieve Heisenberg-limited precision scaling in estimating the ground state energy. However, QPE requires a large number of ancilla qubits and large circuit…
Experimental groups are now fabricating quantum processors powerful enough to execute small instances of quantum algorithms and definitively demonstrate quantum error correction that extends the lifetime of quantum data, adding urgency to…
Calculating the molecular ground-state energy is a central challenge in computational chemistry. Conventional methods such as the Complete Active Space Configuration Interaction scale exponentially with molecular size, limiting their…
The Hubbard model is a challenging quantum many-body problem and serves as a benchmark for quantum computing research. Accurate computation of its ground and excited state energies is essential for understanding correlated electron systems.…
Quantum computing is rapidly emerging as a promising technology for solving complex optimization problems that arise in various engineering fields. Therefore, it holds significant promise to transform the computational foundations of power…
This paper reviews various engineering hurdles facing the field of quantum computing. Specifically, problems related to decoherence, state preparation, error correction, and implementability of gates are considered.
The development of a large scale quantum computer is a highly sought after goal of fundamental research and consequently a highly non-trivial problem. Scalability in quantum information processing is not just a problem of qubit…
Quantum computers have been proposed to solve a number of important problems such as discovering new drugs, new catalysts for fertilizer production, breaking encryption protocols, optimizing financial portfolios, or implementing new…
Quantum computers are hypothetical devices, based on quantum physics, that would enable us to perform certain computations hundreds of orders of magnitude faster than digital computers. This feature is coined as "quantum supremacy" and one…
Quantum computers offer an intriguing path for a paradigmatic change of computing in the natural sciences and beyond, with the potential for achieving a so-called quantum advantage, namely a significant (in some cases exponential) speed-up…
We show for the one-dimensional quantum $XY$ model with $s=1/2$ that the energy gap between the ground and first excited states behaves anomalously as a function of the system size at the first-order quantum phase transition. Although it is…
We discuss a model for quantum computing with initially mixed states. Although such a computer is known to be less powerful than a quantum computer operating with pure (entangled) states, it may efficiently solve some problems for which no…
Computing many-body ground state energies and resolving electronic structure calculations are fundamental problems for fields such as quantum chemistry or condensed matter. Several quantum computing algorithms that address these problems…
Fault-tolerant schemes can use error correction to make a quantum computation arbitrarily ac- curate, provided that errors per physical component are smaller than a certain threshold and in- dependent of the computer size. However in…
A fundamental challenge in quantum physics is determining the ground-state properties of many-body systems. Whereas standard approaches, such as variational calculations, consist of writing down a wave function ansatz and minimizing over…
Ground-state properties are central to our understanding of quantum many-body systems. At first glance, it seems natural and essential to obtain the ground state before analyzing its properties; however, its exponentially large Hilbert…
We show that the rate of closing of the energy gap between the ground state and the first excited state, as a function of system size, behaves in many qualitatively different ways at first-order quantum phase transitions of the…