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Fault-tolerant quantum computing will require error rates far below those achievable with physical qubits. Quantum error correction (QEC) bridges this gap, but depends on decoders being simultaneously fast, accurate, and scalable. This…
A unitary $t$-design is a powerful tool in quantum information science and fundamental physics. Despite its usefulness, only approximate implementations were known for general $t$. In this paper, we provide for the first time quantum…
We explore the use of machine-learning techniques to detect quantum speedup in random walks on graphs. Specifically, we investigate the performance of three different neural-network architectures (variations on fully connected and…
Imperfect measurement can degrade a quantum error correction scheme. A solution that restores fault tolerance is to add redundancy to the process of syndrome extraction. In this work, we show how to optimize this process for an arbitrary…
We initiate the study of diameter computation in geometric intersection graphs from the fine-grained complexity perspective. A geometric intersection graph is a graph whose vertices correspond to some shapes in $d$-dimensional Euclidean…
In order to demonstrate non-trivial quantum computations experimentally, such as the synthesis of arbitrary entangled states, it will be useful to understand how to decompose a desired quantum computation into the shortest possible sequence…
Finding large "cliquish" subgraphs is a central topic in graph mining and community detection. A popular clique relaxation are 2-clubs: instead of asking for subgraphs of diameter one (these are cliques), one asks for subgraphs of diameter…
Compiling a high-level quantum circuit down to a low-level description that can be executed on state-of-the-art quantum computers is a crucial part of the software stack for quantum computing. One step in compiling a quantum circuit to some…
The Quantum Approximate Optimization Algorithm can naturally be applied to combinatorial search problems on graphs. The quantum circuit has p applications of a unitary operator that respects the locality of the graph. On a graph with…
We discuss the realization of a universal set of ultrafast single- and two-qubit operations with superconducting quantum circuits and investigate the most relevant physical and technical limitations that arise when pushing for faster and…
Unitary $T$-designs play an important role in quantum information, with diverse applications in quantum algorithms, benchmarking, tomography, and communication. Until now, the most efficient construction of unitary $T$-designs for $n$-qudit…
We use a random search technique to find quantum gate sequences that implement perfect quantum state preparation or unitary operator synthesis with arbitrary targets. This approach is based on the recent discovery that there is a large…
Due to the scarcity of quantum computing resources, researchers and developers have very limited access to real quantum computers. Therefore, judicious planning and utilization of quantum computer runtime are essential to ensure smooth…
The main aim of this work is to present an explicit construction of a 2-design of ${\rm U}(2)$, relying only on a tool that belongs to every physicists toolbox: the theory of angular momentum. Unitary designs are a rich and fundamental…
Traditional quantum circuit optimization is performed directly at the circuit level. Alternatively, a quantum circuit can be translated to a ZX-diagram which can be simplified using the rules of the ZX-calculus, after which a simplified…
A fundamental question is understanding the rate at which random quantum circuits converge to the Haar measure. One quantity which is important in establishing this rate is the spectral gap of a random quantum ensemble. In this work we…
One of the main milestones in quantum information science is to realise quantum devices that exhibit an exponential computational advantage over classical ones without being universal quantum computers, a state of affairs dubbed quantum…
Dual-unitary brickwork circuits are an exactly-solvable model for many-body chaotic quantum systems, based on 2-site gates which are unitary in both the time and space directions. Prosen has recently described an alternative model called…
Recently, it is shown that quantum computers can be used for obtaining certain information about the solution of a linear system Ax=b exponentially faster than what is possible with classical computation. Here we first review some key…
In the paper, we consider quantum circuits for Quantum fingerprinting (quantum hashing) and quantum Fourier transform (QFT) algorithms. Quantum fingerprinting (quantum hashing) is a well-known technique for comparing large objects using…