Related papers: Bootstrapping shallow circuits
Most work in quantum circuit optimization has been performed in isolation from the results of quantum fault-tolerance. Here we present a polynomial-time algorithm for optimizing quantum circuits that takes the actual implementation of…
Quantum Compiling Algorithms decompose (exactly, without approximations) an arbitrary $2^\nb$ unitary matrix acting on $\nb$ qubits, into a sequence of elementary operations (SEO). There are many possible ways of decomposing a unitary…
Solving the electronic Schrodinger equation for strongly correlated ground states is a long-standing challenge. We present quantum algorithms for the variational optimization of wavefunctions correlated by products of unitary operators,…
Quantum chemistry and optimization are two of the most prominent applications of quantum computers. Variational quantum algorithms have been proposed for solving problems in these domains. However, the design of the quantum circuit ansatz…
Mapping logical quantum circuits to Noisy Intermediate-Scale Quantum (NISQ) devices is a challenging problem which has attracted rapidly increasing interests from both quantum and classical computing communities. This paper proposes an…
Quantum machine learning models use encoding circuits to map data into a quantum Hilbert space. While it is well known that the architecture of these circuits significantly influences core properties of the resulting model, they are often…
We study the computational power of shallow quantum circuits with $O(\log n)$ initialized and $n^{O(1)}$ uninitialized ancillary qubits, where $n$ is the input length and the initial state of the uninitialized ancillary qubits is arbitrary.…
A quantum compiler is a critical piece in the quantum computing pipeline since it allows an abstract quantum circuit to be run on a physical quantum computer. One extremely important subproblem in quantum compilation is the generation of a…
We use complexity theory to rigorously investigate the difficulty of classically simulating evolution under many-body localized (MBL) Hamiltonians. Using the defining feature that MBL systems have a complete set of quasilocal integrals of…
Standard quantum amplitude estimation algorithms provide quadratic speedup to Monte-Carlo simulations but require a circuit depth that scales as inverse of the estimation error. In view of the shallow depth in near-term devices, the…
Quantum simulation of the electronic structure problem is one of the most researched applications of quantum computing. The majority of quantum algorithms for this problem encode the wavefunction using $N$ Gaussian orbitals, leading to…
We construct quantum circuits which exactly encode the spectra of correlated electron models up to errors from rotation synthesis. By invoking these circuits as oracles within the recently introduced "qubitization" framework, one can use…
Quantum variational circuits have gained significant attention due to their applications in the quantum approximate optimization algorithm and quantum machine learning research. This work introduces a novel class of classical probabilistic…
Quantum embedding learning is an important step in the application of quantum machine learning to classical data. In this paper we propose a quantum few-shot embedding learning paradigm, which learns embeddings useful for training…
We present a polynomial-time classical algorithm for estimating expectation values of arbitrary observables on typical quantum circuits under any incoherent local noise, including non-unital or dephasing. Although previous research…
The theory of quantum algorithms promises unprecedented benefits of harnessing the laws of quantum mechanics for solving certain computational problems. A persistent obstacle to using such algorithms for solving a wide range of real-world…
There is no unique way to encode a quantum algorithm into a quantum circuit. With limited qubit counts, connectivities, and coherence times, circuit optimization is essential to make the best use of near-term quantum devices. We introduce…
We develop a phase estimation method with a distinct feature: its maximal runtime (which determines the circuit depth) is $\delta/\epsilon$, where $\epsilon$ is the target precision, and the preconstant $\delta$ can be arbitrarily close to…
Quantum circuit transformation (QCT), necessary for adapting any quantum circuit to the qubit connectivity constraints of the NISQ device, often introduces numerous additional SWAP gates into the original circuit, increasing the circuit…
Linear regression is a widely used technique to fit linear models and finds widespread applications across different areas such as machine learning and statistics. In most real-world scenarios, however, linear regression problems are often…