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Geometry and dimensionality have played crucial roles in our understanding of the fundamental laws of nature, with examples ranging from curved space-time in general relativity to modern theories of quantum gravity. In quantum many-body…
The primary objective of this paper is to present an exact and general procedure for mapping any sequence of quantum gates onto a network of probabilistic p-bits which can take on one of two values 0 and 1. The first $n$ p-bits represent…
Quantum circuits that are classically simulatable tell us when quantum computation becomes less powerful than or equivalent to classical computation. Such classically simulatable circuits are of importance because they illustrate what makes…
This article surveys quantum computational complexity, with a focus on three fundamental notions: polynomial-time quantum computations, the efficient verification of quantum proofs, and quantum interactive proof systems. Properties of…
Instantaneous quantum polynomial quantum circuit Born machines (IQP-QCBMs) have been proposed as quantum generative models with a classically tractable training objective based on the maximum mean discrepancy (MMD) and a potential quantum…
The computational problem of distinguishing two quantum channels is central to quantum computing. It is a generalization of the well-known satisfiability problem from classical to quantum computation. This problem is shown to be…
In the past four decades, the notion of quantum polynomial-time computability has been mathematically modeled by quantum Turing machines as well as quantum circuits. This paper seeks the third model, which is a quantum analogue of the…
We introduce an intermediate quantum computing model built from translation-invariant Ising-interacting spins. Despite being non-universal, the model cannot be classically efficiently simulated unless the polynomial hierarchy collapses.…
Quantum computers promise to outperform their classical counterparts at certain tasks. However, existing quantum devices are error-prone and restricted in size. Thus, effective compilation methods are crucial to exploit limited quantum…
As research on building scalable quantum computers advances, it is important to be able to certify their correctness. Due to the exponential hardness of classically simulating quantum computation, straight-forward verification through…
The use of quantum computing to accelerate complex optimization problems is a burgeoning research field. This paper applies Quantum Linear System Algorithms (QLSAs) to Newton systems within Interior Point Methods (IPMs) to take advantage of…
Quantum linear system algorithms (QLSAs) have the potential to speed up algorithms that rely on solving linear systems. Interior Point Methods (IPMs) yield a fundamental family of polynomial-time algorithms for solving optimization…
We present a Hamiltonian quantum computation scheme universal for quantum computation (BQP). Our Hamiltonian is a sum of a polynomial number (in the number of gates L in the quantum circuit) of time-independent, constant-norm, 2-local…
In order to establish the computational equivalence between quantum Turing machines (QTMs) and quantum circuit families (QCFs) using Yao's quantum circuit simulation of QTMs, we previously introduced the class of uniform QCFs based on an…
We study the classical simulability of a polynomial-size quantum circuit $C_n$ on $n$ qubits followed by sparse classical post-processing (SCP) on $m$ bits, where $m \leq n \leq {\rm poly}(m)$. The SCP is described by a non-zero Boolean…
Quantum computation is frequently mischaracterized as the simultaneous execution of exponentially many classical computations. This article offers a conceptual clarification of why this ``branchwise parallelism'' picture is misleading,…
Approximating the partition function of the ferromagnetic Ising model with general external fields is known to be #BIS-hard in the worst case, even for bounded-degree graphs, and it is widely believed that no polynomial-time approximation…
High-performance computing systems are rapidly evolving into heterogeneous platforms that fuse quantum accelerators with traditional classical processing units (CPUs) and graphical processing units (GPUs). This convergence calls for…
During the last ten years, superconducting circuits have passed from being interesting physical devices to becoming contenders for near-future useful and scalable quantum information processing (QIP). Advanced quantum simulation experiments…
It is known that several sub-universal quantum computing models, such as the IQP model, the Boson sampling model, the one-clean qubit model, and the random circuit model, cannot be classically simulated in polynomial time under certain…