Quantum Advantage in Reversing Unknown Unitary Evolutions
- URL: http://arxiv.org/abs/2403.04704v1
- Date: Thu, 7 Mar 2024 17:59:11 GMT
- Title: Quantum Advantage in Reversing Unknown Unitary Evolutions
- Authors: Yu-Ao Chen, Yin Mo, Yingjian Liu, Lei Zhang, Xin Wang
- Abstract summary: We introduce the Quantum Unitary Reversal Algorithm (QURA), a deterministic and exact approach to universally reverse arbitrary unknown unitary transformations.
QURA ensures an exact unitary inversion while the classical counterpart can never achieve exact inversion using a finite number of unitary calls.
- Score: 9.259390080722206
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We introduce the Quantum Unitary Reversal Algorithm (QURA), a deterministic
and exact approach to universally reverse arbitrary unknown unitary
transformations using $\mathcal{O}(d^2)$ calls of the unitary, where $d$ is the
system dimension. Our construction resolves a fundamental problem of
time-reversal simulations for closed quantum systems by affirming the
feasibility of reversing any unitary evolution without knowing the exact
process. The algorithm also provides the construction of a key oracle for
unitary inversion in quantum algorithm frameworks such as quantum singular
value transformation. Notably, our work demonstrates that compared with
classical methods relying on process tomography, reversing an unknown unitary
on a quantum computer holds a quadratic quantum advantage in computation
complexity. QURA ensures an exact unitary inversion while the classical
counterpart can never achieve exact inversion using a finite number of unitary
calls.
Related papers
- Towards Quantum Computational Mechanics [1.7201069233638664]
We show how quantum computing can be used to solve representative volume element (RVE) problems in computational homogenisation.
Our quantum RVE solver attains exponential acceleration with respect to classical solvers.
arXiv Detail & Related papers (2023-12-06T12:53:02Z) - Taming Quantum Time Complexity [50.10645865330582]
We show how to achieve both exactness and thriftiness in the setting of time complexity.
We employ a novel approach to the design of quantum algorithms based on what we call transducers.
arXiv Detail & Related papers (2023-11-27T14:45:19Z) - Hamiltonian Encoding for Quantum Approximate Time Evolution of Kinetic
Energy Operator [2.184775414778289]
The time evolution operator plays a crucial role in the precise computation of chemical experiments on quantum computers.
We have proposed a new encoding method, namely quantum approximate time evolution (QATE) for the quantum implementation of the kinetic energy operator.
arXiv Detail & Related papers (2023-10-05T05:25:38Z) - Unitary Complexity and the Uhlmann Transformation Problem [41.67228730328207]
We introduce a framework for unitary synthesis problems, including notions of reductions and unitary complexity classes.
We use this framework to study the complexity of transforming one entangled state into another via local operations.
Our framework for unitary complexity thus provides new avenues for studying the computational complexity of many natural quantum information processing tasks.
arXiv Detail & Related papers (2023-06-22T17:46:39Z) - Quantum process tomography of continuous-variable gates using coherent
states [49.299443295581064]
We demonstrate the use of coherent-state quantum process tomography (csQPT) for a bosonic-mode superconducting circuit.
We show results for this method by characterizing a logical quantum gate constructed using displacement and SNAP operations on an encoded qubit.
arXiv Detail & Related papers (2023-03-02T18:08:08Z) - Two-Unitary Decomposition Algorithm and Open Quantum System Simulation [0.17126708168238122]
We propose a quantum two-unitary decomposition (TUD) algorithm to decompose a $d$-dimensional operator $A$ with non-zero singular values.
The two unitaries can be deterministically implemented, thus requiring only a single call to the state preparation oracle for each.
Since the TUD method can be used to implement non-unitary operators as only two unitaries, it also has potential applications in linear algebra and quantum machine learning.
arXiv Detail & Related papers (2022-07-20T16:09:28Z) - Realization of arbitrary doubly-controlled quantum phase gates [62.997667081978825]
We introduce a high-fidelity gate set inspired by a proposal for near-term quantum advantage in optimization problems.
By orchestrating coherent, multi-level control over three transmon qutrits, we synthesize a family of deterministic, continuous-angle quantum phase gates acting in the natural three-qubit computational basis.
arXiv Detail & Related papers (2021-08-03T17:49:09Z) - Nonlinear transformation of complex amplitudes via quantum singular value transformation [0.8009842832476994]
This paper defines a task called nonlinear transformation of complex amplitudes on a quantum computer.
We construct a block-encoding of complex amplitudes from a state preparation unitary.
We discuss its possible applications to quantum machine learning, where complex amplitudes encoding classical or quantum data are processed.
arXiv Detail & Related papers (2021-07-22T15:47:50Z) - Variational Hamiltonian simulation for translational invariant systems
via classical pre-processing [0.0]
We introduce a variational algorithm which uses solutions of classical optimizations to predict efficient quantum circuits.
Our strategy can improve upon the Trotter- Suzuki accuracy by several orders of magnitude.
We can extrapolate our method to beyond classically simulatable system sizes.
arXiv Detail & Related papers (2021-06-07T14:59:50Z) - Synthesis of Quantum Circuits with an Island Genetic Algorithm [44.99833362998488]
Given a unitary matrix that performs certain operation, obtaining the equivalent quantum circuit is a non-trivial task.
Three problems are explored: the coin for the quantum walker, the Toffoli gate and the Fredkin gate.
The algorithm proposed proved to be efficient in decomposition of quantum circuits, and as a generic approach, it is limited only by the available computational power.
arXiv Detail & Related papers (2021-06-06T13:15:25Z) - Error mitigation and quantum-assisted simulation in the error corrected
regime [77.34726150561087]
A standard approach to quantum computing is based on the idea of promoting a classically simulable and fault-tolerant set of operations.
We show how the addition of noisy magic resources allows one to boost classical quasiprobability simulations of a quantum circuit.
arXiv Detail & Related papers (2021-03-12T20:58:41Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.