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Variational quantum algorithms (VQAs) have been proposed as one of the most promising approaches to demonstrate quantum advantage on noisy intermediate-scale quantum (NISQ) devices. However, it has been unclear whether VQAs can maintain…
Fault-tolerant quantum computers compose elements of a discrete gate set in order to approximate a target unitary. The problem of minimising the number of gates is known as gate-synthesis. The approximation error is a form of coherent…
We characterize the variational power of quantum circuit tensor networks in the representation of physical many-body ground-states. Such tensor networks are formed by replacing the dense block unitaries and isometries in standard tensor…
The efficient simulation of complex quantum systems remains a central challenge due to the exponential growth of Hilbert space with system size. Tensor network methods have long been established as powerful approximation schemes, and their…
Gate-level quantum circuits are often derived manually from higher level algorithms. While this suffices for small implementations and demonstrations, ultimately automatic circuit design will be required to realise complex algorithms using…
The efficiency of locally generating unitary designs, which capture statistical notions of quantum pseudorandomness, lies at the heart of wide-ranging areas in physics and quantum information technologies. While there are extensive potent…
Discrete translational symmetry plays a fundamental role in condensed matter physics and lattice gauge theories, enabling the analysis of systems that would otherwise be intractable. Despite this, many open problems remain. Quantum…
Parity-time ($PT$)-symmetric Hamiltonians exhibit non-unitary dynamical evolution while maintaining real spectra, and offer unique approaches to quantum sensing and entanglement generation. Here we present a method for simulating the…
This work introduces and characterizes quantum sequential circuits (QSCs) as a hardware-oriented paradigm for quantum computing, built upon a novel foundational element termed the quantum transistor. Unlike conventional qubit-based…
During the noisy intermediate-scale quantum (NISQ) era, it is important to optimize the quantum circuits in circuit depth and gate count, especially entanglement gates, including the CNOT gate. Among all the unitary operators, diagonal…
Despite using a novel model of computation, quantum computers break down programs into elementary gates. Among such gates, entangling gates are the most expensive. In the context of fermionic simulations, we develop a suite of compilation…
We review two algorithmic advances that bring us closer to reliable quantum simulations of model systems in high energy physics and beyond on noisy intermediate-scale quantum (NISQ) devices. The first method is the dimensional expressivity…
The Hermiticity axiom of quantum mechanics guarantees that the energy spectrum is real and the time evolution is unitary (probability-preserving). Nevertheless, non-Hermitian but $\mathcal{PT}$-symmetric Hamiltonians may also have real…
Variational quantum circuits build the foundation for various classes of quantum algorithms. In a nutshell, the weights of a parametrized quantum circuit are varied until the empirical sampling distribution of the circuit is sufficiently…
The main objective of this paper is to improve the communication costs in distributed quantum circuits. To this end, we present a method for generating distributed quantum circuits from monolithic quantum circuits in such a way that…
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…
Each year, the gap between theoretical proposals and experimental endeavours to create quantum computers gets smaller, driven by the promise of fundamentally faster algorithms and quantum simulations. This occurs by the combination of…
Near-term quantum devices generally suffer from shallow circuit depth and hence limited expressivity due to noise and decoherence. To address this, we propose tensor-network-assisted parametrized quantum circuits, which concatenate a…
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…
The utility of near-term quantum computers and simulators is likely to rely upon software-hardware co-design, with error-aware algorithms and protocols optimized for the platforms they are run on. Here, we show how knowledge of noise in a…