The Quantum Esscher Transform
- URL: http://arxiv.org/abs/2401.07561v1
- Date: Mon, 15 Jan 2024 09:53:40 GMT
- Title: The Quantum Esscher Transform
- Authors: Yixian Qiu, Kelvin Koor, Patrick Rebentrost
- Abstract summary: We study the generalization of the Esscher Transform to the quantum setting.
We discuss potential applications of the quantum Esscher Transform.
Our algorithm is based on the modern techniques of block-encoding and quantum singular value transformation.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The Esscher Transform is a tool of broad utility in various domains of
applied probability. It provides the solution to a constrained minimum relative
entropy optimization problem. In this work, we study the generalization of the
Esscher Transform to the quantum setting. We examine a relative entropy
minimization problem for a quantum density operator, potentially of wide
relevance in quantum information theory. The resulting solution form motivates
us to define the \textit{quantum} Esscher Transform, which subsumes the
classical Esscher Transform as a special case. Envisioning potential
applications of the quantum Esscher Transform, we also discuss its
implementation on fault-tolerant quantum computers. Our algorithm is based on
the modern techniques of block-encoding and quantum singular value
transformation (QSVT). We show that given block-encoded inputs, our algorithm
outputs a subnormalized block-encoding of the quantum Esscher transform within
accuracy $\epsilon$ in $\tilde O(\kappa d \log^2 1/\epsilon)$ queries to the
inputs, where $\kappa$ is the condition number of the input density operator
and $d$ is the number of constraints.
Related papers
- Estimating quantum amplitudes can be exponentially improved [11.282486674587236]
Estimating quantum amplitudes is a fundamental task in quantum computing.
We present a novel framework for estimating quantum amplitudes by transforming pure states into their matrix forms.
Our framework achieves the standard quantum limit $epsilon-2$ and the Heisenberg limit $epsilon-1$, respectively.
arXiv Detail & Related papers (2024-08-25T04:35:53Z) - 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) - Quantum Worst-Case to Average-Case Reductions for All Linear Problems [66.65497337069792]
We study the problem of designing worst-case to average-case reductions for quantum algorithms.
We provide an explicit and efficient transformation of quantum algorithms that are only correct on a small fraction of their inputs into ones that are correct on all inputs.
arXiv Detail & Related papers (2022-12-06T22:01:49Z) - Variational Quantum Non-Orthogonal Optimization [0.0]
We show that it is possible to significantly reduce the number of qubits required to solve complex optimization problems.
Our proposal opens the path towards solving real-life useful optimization problems in today's limited quantum hardware.
arXiv Detail & Related papers (2022-10-06T18:00:02Z) - Constrained Quantum Optimization for Extractive Summarization on a
Trapped-ion Quantum Computer [13.528362112761805]
We show the largest-to-date execution of a quantum optimization algorithm that preserves constraints on quantum hardware.
We execute XY-QAOA circuits that restrict the quantum evolution to the in-constraint subspace, using up to 20 qubits and a two-qubit gate depth of up to 159.
We discuss the respective trade-offs of the algorithms and implications for their execution on near-term quantum hardware.
arXiv Detail & Related papers (2022-06-13T16:21:04Z) - Configurable sublinear circuits for quantum state preparation [1.9279780052245203]
We show a configuration that encodes an $N$-dimensional state by a quantum circuit with $O(sqrtN)$ width and depth and entangled information in ancillary qubits.
We show a proof-of-principle on five quantum computers and compare the results.
arXiv Detail & Related papers (2021-08-23T13:52:43Z) - 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) - Adiabatic Quantum Graph Matching with Permutation Matrix Constraints [75.88678895180189]
Matching problems on 3D shapes and images are frequently formulated as quadratic assignment problems (QAPs) with permutation matrix constraints, which are NP-hard.
We propose several reformulations of QAPs as unconstrained problems suitable for efficient execution on quantum hardware.
The proposed algorithm has the potential to scale to higher dimensions on future quantum computing architectures.
arXiv Detail & Related papers (2021-07-08T17:59:55Z) - Fast algorithm for quantum polar decomposition, pretty-good
measurements, and the Procrustes problem [0.0]
We show that the problem of quantum polar decomposition has a simple and concise implementation via the quantum singular value QSVT.
We focus on the applications to pretty-good measurements, a close-to-optimal measurement to distinguish quantum states, and the quantum Procrustes problem.
arXiv Detail & Related papers (2021-06-14T17:50:41Z) - Space-efficient binary optimization for variational computing [68.8204255655161]
We show that it is possible to greatly reduce the number of qubits needed for the Traveling Salesman Problem.
We also propose encoding schemes which smoothly interpolate between the qubit-efficient and the circuit depth-efficient models.
arXiv Detail & Related papers (2020-09-15T18:17:27Z) - Quantum Gram-Schmidt Processes and Their Application to Efficient State
Read-out for Quantum Algorithms [87.04438831673063]
We present an efficient read-out protocol that yields the classical vector form of the generated state.
Our protocol suits the case that the output state lies in the row space of the input matrix.
One of our technical tools is an efficient quantum algorithm for performing the Gram-Schmidt orthonormal procedure.
arXiv Detail & Related papers (2020-04-14T11:05:26Z)
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.