Multivariate trace estimation in constant quantum depth
- URL: http://arxiv.org/abs/2206.15405v3
- Date: Thu, 4 Jan 2024 04:24:11 GMT
- Title: Multivariate trace estimation in constant quantum depth
- Authors: Yihui Quek and Eneet Kaur and Mark M. Wilde
- Abstract summary: A folkloric belief is that a depth-$Theta(m)$ quantum circuit is needed to estimate the trace of a $m$ density matrix.
We prove that this belief is overly conservative by constructing a constant quantum-depth circuit for the task.
We show how to implement our circuit in a highly parallelized way on an architecture similar to that of Google's Sycamore processor.
- Score: 5.908471365011943
- License: http://creativecommons.org/licenses/by-nc-sa/4.0/
- Abstract: There is a folkloric belief that a depth-$\Theta(m)$ quantum circuit is
needed to estimate the trace of the product of $m$ density matrices (i.e., a
multivariate trace), a subroutine crucial to applications in condensed matter
and quantum information science. We prove that this belief is overly
conservative by constructing a constant quantum-depth circuit for the task,
inspired by the method of Shor error correction. Furthermore, our circuit
demands only local gates in a two dimensional circuit -- we show how to
implement it in a highly parallelized way on an architecture similar to that of
Google's Sycamore processor. With these features, our algorithm brings the
central task of multivariate trace estimation closer to the capabilities of
near-term quantum processors. We instantiate the latter application with a
theorem on estimating nonlinear functions of quantum states with "well-behaved"
polynomial approximations.
Related papers
- Equivalence Checking of Quantum Circuits via Intermediary Matrix Product Operator [4.306566710489809]
Equivalence checking plays a vital role in identifying errors that may arise during compilation and optimization of quantum circuits.
We introduce a novel method based on Matrix Product Operators (MPOs) for determining the equivalence of quantum circuits.
arXiv Detail & Related papers (2024-10-14T18:00:00Z) - Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits [63.733312560668274]
Given a quantum circuit containing d tunable RZ gates and G-d Clifford gates, can a learner perform purely classical inference to efficiently predict its linear properties?
We prove that the sample complexity scaling linearly in d is necessary and sufficient to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d.
We devise a kernel-based learning model capable of trading off prediction error and computational complexity, transitioning from exponential to scaling in many practical settings.
arXiv Detail & Related papers (2024-08-22T08:21:28Z) - Robust Implementation of Discrete-time Quantum Walks in Any Finite-dimensional Quantum System [2.646968944595457]
discrete-time quantum walk (DTQW) model one of most suitable choices for circuit implementation.
In this paper, we have successfully cut down the circuit cost concerning gate count and circuit depth by half.
For the engineering excellence of our proposed approach, we implement DTQW in any finite-dimensional quantum system with akin efficiency.
arXiv Detail & Related papers (2024-08-01T13:07:13Z) - Reductive Quantum Phase Estimation [0.0]
We show a circuit that distinguishes an arbitrary set of phases with a fewer number of qubits and unitary applications.
We show a trade-off between measurement precision and phase distinguishability, which allows one to tune the circuit to be optimal for a specific application.
arXiv Detail & Related papers (2024-02-06T23:38:36Z) - Lightcone Bounds for Quantum Circuit Mapping via Uncomplexity [1.0360348400670518]
We show that a minimal SWAP-gate count for executing a quantum circuit on a device emerges via the minimization of the distance between quantum states.
This work constitutes the first use of quantum circuit uncomplexity to practically-relevant quantum computing.
arXiv Detail & Related papers (2024-02-01T10:32:05Z) - Symmetry-Based Quantum Circuit Mapping [2.51705778594846]
We introduce a quantum circuit remapping algorithm that leverages the intrinsic symmetries in quantum processors.
This algorithm identifies all topologically equivalent circuit mappings by constraining the search space using symmetries and accelerates the scoring of each mapping using vector computation.
arXiv Detail & Related papers (2023-10-27T10:04:34Z) - End-to-end resource analysis for quantum interior point methods and portfolio optimization [63.4863637315163]
We provide a complete quantum circuit-level description of the algorithm from problem input to problem output.
We report the number of logical qubits and the quantity/depth of non-Clifford T-gates needed to run the algorithm.
arXiv Detail & Related papers (2022-11-22T18:54:48Z) - Quantum circuit debugging and sensitivity analysis via local inversions [62.997667081978825]
We present a technique that pinpoints the sections of a quantum circuit that affect the circuit output the most.
We demonstrate the practicality and efficacy of the proposed technique by applying it to example algorithmic circuits implemented on IBM quantum machines.
arXiv Detail & Related papers (2022-04-12T19:39:31Z) - Numerical Simulations of Noisy Quantum Circuits for Computational
Chemistry [51.827942608832025]
Near-term quantum computers can calculate the ground-state properties of small molecules.
We show how the structure of the computational ansatz as well as the errors induced by device noise affect the calculation.
arXiv Detail & Related papers (2021-12-31T16:33:10Z) - 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) - QUANTIFY: A framework for resource analysis and design verification of
quantum circuits [69.43216268165402]
QUANTIFY is an open-source framework for the quantitative analysis of quantum circuits.
It is based on Google Cirq and is developed with Clifford+T circuits in mind.
For benchmarking purposes QUANTIFY includes quantum memory and quantum arithmetic circuits.
arXiv Detail & Related papers (2020-07-21T15:36:25Z)
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.