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Simulation of quantum systems is expected to be one of the most important applications of quantum computing, with much of the theoretical work so far having focused on fermionic and spin-$\frac{1}{2}$ systems. Here, we instead consider…
Quantum computing hardware is undergoing rapid development from proof-of-principle devices to scalable machines that could eventually challenge classical supercomputers on specific tasks. On platforms with local connectivity, the transition…
We provide practical simulation methods for scalar field theories on a quantum computer that yield improved asymptotics as well as concrete gate estimates for the simulation and physical qubit estimates using the surface code. We achieve…
Protein folding processes are a vital aspect of molecular biology that is hard to simulate with conventional computers. Quantum algorithms have been proven superior for certain problems and may help tackle this complex life science…
Gate-based universal quantum computation is formulated in terms of two types of operations: local single-qubit gates, which are typically easily implementable, and two-qubit entangling gates, whose faithful implementation remains one of the…
Quantum algorithm design usually assumes access to a perfect quantum computer with ideal properties like full connectivity, noise-freedom and arbitrarily long coherence time. In Noisy Intermediate-Scale Quantum (NISQ) devices, however, the…
A common requirement of quantum simulations and algorithms is the preparation of complex states through sequences of 2-qubit gates. For a generic quantum state, the number of gates grows exponentially with the number of qubits, becoming…
Current quantum simulators are primarily qubit-based, making them naturally suitable for simulating 2-level quantum systems. However, many systems in nature are inherently $d$-level, including higher spins, bosons, vibrational modes, and…
Quantum algorithms require accurate representations of electronic states on a quantum device, yet the approximation of electronic wave functions for strongly correlated systems remains a profound theoretical challenge, with existing methods…
We describe methods to construct digital quantum simulation algorithms for quantum spin systems on a regular lattice with local interactions. In addition to tools such as the Trotter-Suzuki expansion and graph coloring, we also discuss the…
A number of quantum algorithms have been performed on small quantum computers; these include Shor's prime factorization algorithm, error correction, Grover's search algorithm and a number of analog and digital quantum simulations. Because…
Since simulating quantum computers requires exponentially more classical resources, efficient algorithms are extremely helpful. We analyze algorithms that create single qubit and specific controlled qubit matrix representations of gates.…
Current and near-term quantum hardware is constrained by limited qubit counts, circuit depth, and the high cost of repeated measurements. We address these challenges for solid state Hamiltonians by introducing a logarithmic-qubit encoding…
Simulation of materials is one of the most promising applications of quantum computers. On near-term hardware the crucial constraint on these simulations is circuit depth. Many quantum simulation algorithms rely on a layer of unitary…
Hamiltonian simulation on quantum computers is strongly constrained by gate counts, motivating techniques to reduce circuit depths. While tensor networks are natural competitors to quantum computers, we instead leverage them to support…
Key to realising quantum computers is minimising the resources required to build logic gates into useful processing circuits. While the salient features of a quantum computer have been shown in proof-of-principle experiments, difficulties…
A universal quantum computing scheme, with a universal set of logical gates, is proposed based on networks of 1D quantum systems. The encoding of information is in terms of universal features of gapped phases, for which effective field…
The practical use of many types of near-term quantum computers requires accounting for their limited connectivity. One way of overcoming limited connectivity is to insert swaps in the circuit so that logical operations can be performed on…
We present a gauge invariant digitization of $(1+1)$d scalar quantum electrodynamics for an arbitrary spin truncation for qudit-based quantum computers. We provide a construction of the Trotter operator in terms of a universal qudit-gate…
As the effort to scale up existing quantum hardware proceeds, it becomes necessary to schedule quantum gates in a way that minimizes the number of operations. There are three constraints that have to be satisfied: the order or dependency of…