arXiv subjects

Kaiwen Gui

Publications and source records attributed to Kaiwen Gui.

4 recordsLinked to original sources

arXiv2024

Spacetime-Efficient Low-Depth Quantum State Preparation with Applications

We propose a novel deterministic method for preparing arbitrary quantum states. When our protocol is compiled into CNOT and arbitrary single-qubit gates, it prepares an $N$-dimensional state in depth $O(\log(N))$ and spacetime allocation (a metric that accounts for the fact that oftentimes some ancilla qubits need not be active for the entire circuit) $O(N)$, which are both optimal. When compiled into the $\{\mathrm{H,S,T,CNOT}\}$ gate set, we show that it requires asymptotically fewer quantum resources than previous methods. Specifically, it prepares an arbitrary state up to error $ε$ with optimal depth of $O(\log(N) + \log (1/ε))$ and spacetime allocation $O(N\log(\log(N)/ε))$, improving over $O(\log(N)\log(\log (N)/ε))$ and $O(N\log(N/ε))$, respectively. We illustrate how the reduced spacetime allocation of our protocol enables rapid preparation of many disjoint states with only constant-factor ancilla overhead -- $O(N)$ ancilla qubits are reused efficiently to prepare a product state of $w$ $N$-dimensional states in depth $O(w + \log(N))$ rather than $O(w\log(N))$, achieving effectively constant depth per state. We highlight several applications where this ability would be useful, including quantum machine learning, Hamiltonian simulation, and solving linear systems of equations. We provide quantum circuit descriptions of our protocol, detailed pseudocode, and gate-level implementation examples using Braket.

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arXiv2022

Optimized Quantum Program Execution Ordering to Mitigate Errors in Simulations of Quantum Systems

Simulating the time evolution of a physical system at quantum mechanical levels of detail -- known as Hamiltonian Simulation (HS) -- is an important and interesting problem across physics and chemistry. For this task, algorithms that run on quantum computers are known to be exponentially faster than classical algorithms; in fact, this application motivated Feynman to propose the construction of quantum computers. Nonetheless, there are challenges in reaching this performance potential. Prior work has focused on compiling circuits (quantum programs) for HS with the goal of maximizing either accuracy or gate cancellation. Our work proposes a compilation strategy that simultaneously advances both goals. At a high level, we use classical optimizations such as graph coloring and travelling salesperson to order the execution of quantum programs. Specifically, we group together mutually commuting terms in the Hamiltonian (a matrix characterizing the quantum mechanical system) to improve the accuracy of the simulation. We then rearrange the terms within each group to maximize gate cancellation in the final quantum circuit. These optimizations work together to improve HS performance and result in an average 40% reduction in circuit depth. This work advances the frontier of HS which in turn can advance physical and chemical modeling in both basic and applied sciences.

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arXiv2021

Term Grouping and Travelling Salesperson for Digital Quantum Simulation

Digital simulation of quantum dynamics by evaluating the time evolution of a Hamiltonian is the initially proposed application of quantum computing. The large number of quantum gates required for emulating the complete second quantization form of the Hamiltonian, however, makes such an approach unsuitable for near-term devices with limited gate fidelities that cause high physical errors. In addition, Trotter error caused by noncommuting terms can accumulate and harm the overall circuit fidelity, thus causing algorithmic errors. In this paper, we propose a new term ordering strategy, max-commute-tsp (MCTSP), that simultaneously mitigates both algorithmic and physical errors. First, we improve the Trotter fidelity compared with previously proposed optimization by reordering Pauli terms and partitioning them into commuting families. We demonstrate the practicality of this method by constructing and evaluating quantum circuits that simulate different molecular Hamiltonians, together with theoretical explanations for the fidelity improvements from our term grouping method. Second, we describe a new gate cancellation technique that reduces the high gate counts by formulating the gate cancellation problem as a travelling salesperson problem, together with benchmarking experiments. Finally, we also provide benchmarking results that demonstrate the combined advantage of max-commute-tsp to mitigate both physical and algorithmic errors via quantum circuit simulation under realistic noise models.

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arXiv2019

Minimizing State Preparations in Variational Quantum Eigensolver by Partitioning into Commuting Families

Variational quantum eigensolver (VQE) is a promising algorithm suitable for near-term quantum machines. VQE aims to approximate the lowest eigenvalue of an exponentially sized matrix in polynomial time. It minimizes quantum resource requirements both by co-processing with a classical processor and by structuring computation into many subproblems. Each quantum subproblem involves a separate state preparation terminated by the measurement of one Pauli string. However, the number of such Pauli strings scales as $N^4$ for typical problems of interest--a daunting growth rate that poses a serious limitation for emerging applications such as quantum computational chemistry. We introduce a systematic technique for minimizing requisite state preparations by exploiting the simultaneous measurability of partitions of commuting Pauli strings. Our work encompasses algorithms for efficiently approximating a MIN-COMMUTING-PARTITION, as well as a synthesis tool for compiling simultaneous measurement circuits. For representative problems, we achieve 8-30x reductions in state preparations, with minimal overhead in measurement circuit cost. We demonstrate experimental validation of our techniques by estimating the ground state energy of deuteron on an IBM Q 20-qubit machine. We also investigate the underlying statistics of simultaneous measurement and devise an adaptive strategy for mitigating harmful covariance terms.

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