相关论文: Early fault-tolerant simulations of the Hubbard mo…
The most scalable proposed methods of simulating lattice fermions on noisy quantum computers employ encodings that eliminate nonlocal operators using a constant factor more qubits and a nontrivial stabilizer group. In this work, we…
The framework of this thesis is fault-tolerant quantum algorithms. Grover's algorithm and quantum walks are described in Chapter 2. We start by highlighting the central role that rotations play in quantum algorithms, explaining Grover's,…
We consider simulating an $n$-qubit Hamiltonian with nearest-neighbor interactions evolving for time $t$ on a quantum computer. We show that this simulation has gate complexity $(nt)^{1+o(1)}$ using product formulas, a straightforward…
A higher-order Suzuki-Trotter decomposition or Trotterization can be exploited to mitigate the Trotter error in digital quantum simulation. This work revisits the second-order symmetric Trotterization in terms of the Trotter error, where…
We investigate the sampling efficiency for the simulations of quantum many-body systems at finite temperatures when initial sampling states are generated by applying Trotter gates to random phase product states (RPPSs). We restrict the…
The most advanced techniques using fault-tolerant quantum computers to estimate the ground-state energy of a chemical Hamiltonian involve compression of the Coulomb operator through tensor factorizations, enabling efficient block-encodings…
Because of their long coherence time and compatibility with industrial foundry processes, electron spin qubits are a promising platform for scalable quantum processors. A full-fledged quantum computer will need quantum error correction,…
In order to evaluate, validate, and refine the design of new quantum algorithms or quantum computers, researchers and developers need methods to assess their correctness and fidelity. This requires the capabilities of quantum circuit…
Quantum computing holds the promise of solving problems intractable for classical computers, but practical large-scale quantum computation requires error correction to protect against errors. Fault-tolerant quantum computing (FTQC) enables…
Quantum computing promises revolutionary advances in modeling materials and molecules. However, the up-to-date runtime estimates for utility-scale applications on certain quantum hardware systems are in the order of years rendering quantum…
One of the premier utilities of present day noisy quantum computers is simulation of many-body quantum systems. We study how long in time is such a discrete-time simulation representative of a continuous time Hamiltonian evolution, namely,…
As far as we know, a useful quantum computer will require fault-tolerant gates, and existing schemes demand a prohibitively large space and time overhead. We argue that a first generation quantum computer will be very valuable to design,…
Hamiltonian simulation is believed to be one of the first tasks where quantum computers can yield a quantum advantage. One of the most popular methods of Hamiltonian simulation is Trotterization, which makes use of the approximation…
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…
Fault-tolerant quantum computation critically depends on architectures uniting high encoding rates with physical implementability. Quantum low-density parity-check (qLDPC) codes, including bivariate bicycle (BB) codes, achieve dramatic…
In this work we investigate methods to improve the efficiency and scalability of quantum algorithms for quantum chemistry applications. We propose a transformation of the electronic structure Hamiltonian in the second quantization framework…
Classical simulations are essential for the development of quantum computing, and their exponential scaling can easily fill any modern supercomputer. In this paper we consider the performance and energy consumption of large Quantum Fourier…
The Lie-Trotter formula, together with its higher-order generalizations, provides a direct approach to decomposing the exponential of a sum of operators. Despite significant effort, the error scaling of such product formulas remains poorly…
We revisit quantum phase estimation algorithms for the purpose of obtaining the energy levels of many-body Hamiltonians and pay particular attention to the statistical analysis of their outputs. We introduce the mean phase direction of the…
Classical simulation of quantum circuits plays a crucial role in validating quantum hardware and delineating the boundaries of quantum advantage. Among the most effective simulation techniques are those based on the stabilizer extent, which…