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Compilation optimizes quantum algorithms performances on real-world quantum computers. To date, it is performed via classical optimization strategies. We introduce a class of quantum algorithms to perform compilation via quantum computers,…
The time evolution of quantum many-body systems is one of the most promising applications for near-term quantum computers. However, the utility of current quantum devices is strongly hampered by the proliferation of hardware errors. The…
We propose an algorithm for simulating the dynamics of a geometrically local Hamiltonian $A$ under a small geometrically local perturbation $\alpha B$. In certain regimes, the algorithm achieves the optimal scaling and outperforms the…
We employ quantum circuit learning to simulate quantum field theories (QFTs). Typically, when simulating QFTs with quantum computers, we encounter significant challenges due to the technical limitations of quantum devices when implementing…
Principal component analysis is an important dimension reduction technique in machine learning. In [S. Lloyd, M. Mohseni and P. Rebentrost, Nature Physics 10, 631-633, (2014)], a quantum algorithm to implement principal component analysis…
Unlike most classical algorithms that take an input and give the solution directly as an output, quantum algorithms produce a quantum circuit that works as an indirect solution to computationally hard problems. In the full quantum computing…
A quantum algorithm for solving the advection equation by embedding the discrete time-marching operator into Hamiltonian simulations is presented. One-dimensional advection can be simulated directly since the central finite difference…
We demonstrate the feasibility of quantum computing for large-scale, realistic chemical systems through the development of a new interface using a quantum circuit simulator and CP2K, a highly efficient first-principles calculation software.…
Time-dependent Hamiltonian simulation (TDHS) is a critical task in quantum computing. Existing algorithms are generally biased with a small algorithmic error $\varepsilon$, and the gate complexity scales as $O(\text{poly}(1/\varepsilon))$…
Can near-term gate model based quantum processors offer quantum advantage for practical applications in the pre-fault tolerance noise regime? A class of algorithms which have shown some promise in this regard are the so-called…
In quantum computing the decoherence time of the qubits determines the computation time available and this time is very limited when using current hardware. In this paper we minimize the execution time (the depth) for a class of circuits…
We introduce a general framework for constructing compact quantum circuits that implement the real-time evolution of Hamiltonians of the form $H = \sigma P_B$, where $\sigma$ is a Pauli string commuting with a projection operator $P_B$ onto…
We present elementary mappings between classical lattice models and quantum circuits. These mappings provide a general framework to obtain efficiently simulable quantum gate sets from exactly solvable classical models. For example, we…
Many claims of computational advantages have been made for quantum computing over classical, but they have not been demonstrated for practical problems. Here, we present algorithms for solving time-dependent PDEs, with particular reference…
Simulating large-scale coupled-oscillator systems presents substantial computational challenges for classical algorithms, particularly when pursuing first-principles analyses in the thermodynamic limit. Motivated by the quantum algorithm…
Until high-fidelity quantum computers with a large number of qubits become widely available, classical simulation remains a vital tool for algorithm design, tuning, and validation. We present a simulator for the Quantum Approximate…
The local Hamiltonian (LH) problem, the quantum analog of the classical constraint satisfaction problem, is a cornerstone of quantum computation and complexity theory. It is known to be QMA-complete, indicating that it is challenging even…
The simulation of large-scale classical systems in exponentially small space on quantum computers has gained attention. The prior work demonstrated that a quantum algorithm offers an exponential speedup over any classical algorithm in…
We investigate the boundary between classical and quantum computational power. This work consists of two parts. First we develop new classical simulation algorithms that are centered on sampling methods. Using these techniques we generate…
Path integral-based simulation methodologies play a crucial role for the investigation of nuclear quantum effects by means of computer simulations. However, these techniques are significantly more demanding than corresponding classical…