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Systems of linear equations are used to model a wide array of problems in all fields of science and engineering. Recently, it has been shown that quantum computers could solve linear systems exponentially faster than classical computers,…
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…
Solving differential equations is one of the most promising applications of quantum computing. Recently we proposed an efficient quantum algorithm for solving one-dimensional Poisson equation avoiding the need to perform quantum arithmetic…
A universal quantum computer can simulate diverse quantum systems, with electronic structure for chemistry offering challenging problems for practical use cases around the hundred-qubit mark. While current quantum processors have reached…
Integer programming (IP) is an NP-hard combinatorial optimization problem that is widely used to represent a diverse set of real-world problems spanning multiple fields, such as finance, engineering, logistics, and operations research. It…
Parallel computation enables multiple processors to execute different parts of a task simultaneously, improving processing speed and efficiency. In quantum computing, parallel gate implementation involves executing gates independently in…
Estimating the eigenstate properties of quantum systems is a long-standing, challenging problem for both classical and quantum computing. Existing universal quantum algorithms typically rely on ideal and efficient query models (e.g. time…
We introduce an algorithm to compute Hamiltonian dynamics on digital quantum computers that requires only a finite circuit depth to reach an arbitrary precision, i.e. achieves zero discretization error with finite depth. This finite number…
When a probe qubit is coupled to a quantum register that represents a physical system, the probe qubit will exhibit a dynamical response only when it is resonant with a transition in the system. Using this principle, we propose a quantum…
The mixing of scalar substances in fluid flows by stirring and diffusion is ubiquitous in natural flows, chemical engineering, and microfluidic drug delivery. Here, we present a spectral quantum algorithm for scalar mixing by solving the…
A milestone in the field of quantum computing will be solving problems in quantum chemistry and materials faster than state-of-the-art classical methods. The current understanding is that achieving quantum advantage in this area will…
This work aims to address the bottleneck issues of hardware resource limitation and decoherence error in the Hamiltonian simulation of quantum fluids, which are caused by the standard quantum Fourier transform and the evolution of momentum…
The quantum algorithm with polynomial time for discrete logarithm problem proposed by Shor is one of the most significant quantum algorithms, but a large number of qubits may be required in the Noisy Intermediate-scale Quantum (NISQ) era.…
We show that the Variational Quantum-Classical Simulation algorithm admits a finite circuit depth scaling collapse when targeting the critical point of the transverse field Ising chain. The order parameter only collapses on one side of the…
This work presents an algorithm to generate depth, quantum gate and qubit optimized circuits for $GF(2^m)$ squaring in the polynomial basis. Further, to the best of our knowledge the proposed quantum squaring circuit algorithm is the only…
We present a systematic pathway for solving differential equations within the quantum linear systems framework by combining block encoding with Quantum Singular Value Transformation (QSVT). The approach is demonstrated on a complex…
We establish and analyse the performance and resource requirements of an end-to-end fault-tolerant quantum algorithm for computing the absorption spectrum and population dynamics of photoexcited pyrazine. The quantum circuit construction…
We introduce a simple, widely applicable formalism for designing "error-divisible" two qubit gates: a quantum gate set where fractional rotations have proportionally reduced error compared to the full entangling gate. In current noisy…
An important aspect that strongly impacts the experimental feasibility of quantum circuits is the ratio of gate times and typical error time scales. Algorithms with circuit depths that significantly exceed the error time scales will result…
We demonstrate the applicability of a universal gate set in the parity encoding, which is a dual to the standard gate model, by exploring several quantum gate algorithms such as the quantum Fourier transform and quantum addition. Embedding…