Capacity Approaching Coding for Low Noise Interactive Quantum Communication, Part I: Large Alphabets

• URL: http://arxiv.org/abs/2001.02818v1
• Date: Thu, 9 Jan 2020 02:48:43 GMT
• Title: Capacity Approaching Coding for Low Noise Interactive Quantum Communication, Part I: Large Alphabets
• Authors: Debbie Leung, Ashwin Nayak, Ala Shayeghi, Dave Touchette, Penghui Yao, Nengkun Yu
• Abstract summary: We consider the problem of implementing two-party interactive quantum communication over noisy channels. For a noiseless qudit channel over a $mathrmpoly(n)$ size alphabet, our main result is a simulation method that fails with probability less than $2-Theta(nepsilon)$ We conjecture that it is optimal up to a constant factor in the $sqrtepsilon$ term.
• Score: 15.078027648304115
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider the problem of implementing two-party interactive quantum communication over noisy channels, a necessary endeavor if we wish to fully reap quantum advantages for communication. For an arbitrary protocol with $n$ messages, designed for a noiseless qudit channel over a $\mathrm{poly}(n)$ size alphabet, our main result is a simulation method that fails with probability less than $2^{-\Theta(n\epsilon)}$ and uses a qudit channel over the same alphabet $n\left(1+\Theta \left(\sqrt{\epsilon}\right)\right)$ times, of which an $\epsilon$ fraction can be corrupted adversarially. The simulation is thus capacity achieving to leading order, and we conjecture that it is optimal up to a constant factor in the $\sqrt{\epsilon}$ term. Furthermore, the simulation is in a model that does not require pre-shared resources such as randomness or entanglement between the communicating parties. Our work improves over the best previously known quantum result where the overhead is a non-explicit large constant [Brassard et al., FOCS'14] for low $\epsilon$.

Related papers

• Nearly-Optimal Consensus Tolerating Adaptive Omissions: Why is a Lot of Randomness Needed? [4.465134753953128]
  We study the problem of reaching agreement in a synchronous distributed system by $n$ autonomous parties, when the communication links from/to faulty parties can omit messages. We design a randomized algorithm that works in $O(sqrtnlog2 n)$ rounds and sends $O(n2log3 n)$ communication bits. We prove that no MC algorithm can work in less than $Omega(fracn2maxR,nlog n)$ rounds if it uses less than $O(R)$ calls to
  arXiv  Detail & Related papers  (2024-05-08T02:17:10Z)
• Towards large-scale quantum optimization solvers with few qubits [59.63282173947468]
  We introduce a variational quantum solver for optimizations over $m=mathcalO(nk)$ binary variables using only $n$ qubits, with tunable $k>1$. We analytically prove that the specific qubit-efficient encoding brings in a super-polynomial mitigation of barren plateaus as a built-in feature.
  arXiv  Detail & Related papers  (2024-01-17T18:59:38Z)
• DADAO: Decoupled Accelerated Decentralized Asynchronous Optimization [0.0]
  DADAO is the first decentralized, accelerated, asynchronous, primal, first-order algorithm to minimize a sum of $L$-smooth and $mu$-strongly convex functions distributed over a given network of size $n$. We show that our algorithm requires $mathcalO(nsqrtchisqrtfracLmulog(frac1epsilon)$ local and only $mathcalO(nsqrtchisqrtfracLmulog(
  arXiv  Detail & Related papers  (2022-07-26T08:47:54Z)
• Quantum simulation of real-space dynamics [7.143485463760098]
  We conduct a systematic study of quantum algorithms for real-space dynamics. We give applications to several computational problems, including faster real-space simulation of quantum chemistry.
  arXiv  Detail & Related papers  (2022-03-31T13:01:51Z)
• A lower bound on the space overhead of fault-tolerant quantum computation [51.723084600243716]
  The threshold theorem is a fundamental result in the theory of fault-tolerant quantum computation. We prove an exponential upper bound on the maximal length of fault-tolerant quantum computation with amplitude noise.
  arXiv  Detail & Related papers  (2022-01-31T22:19:49Z)
• Random quantum circuits transform local noise into global white noise [118.18170052022323]
  We study the distribution over measurement outcomes of noisy random quantum circuits in the low-fidelity regime. For local noise that is sufficiently weak and unital, correlations (measured by the linear cross-entropy benchmark) between the output distribution $p_textnoisy$ of a generic noisy circuit instance shrink exponentially. If the noise is incoherent, the output distribution approaches the uniform distribution $p_textunif$ at precisely the same rate.
  arXiv  Detail & Related papers  (2021-11-29T19:26:28Z)
• A direct product theorem for quantum communication complexity with applications to device-independent cryptography [6.891238879512672]
  We show that for a distribution $p$ that is product across the input sets of the $l$ players, the success probability of any entanglement-assisted quantum communication protocol goes down exponentially in $n$. We also show that it is possible to do device-independent (DI) quantum cryptography without the assumption that devices do not leak any information.
  arXiv  Detail & Related papers  (2021-06-08T12:52:10Z)
• Interactive quantum advantage with noisy, shallow Clifford circuits [0.0]
  We show a strategy for adding noise tolerance to the interactive protocols of Grier and Schaeffer. A key component of this reduction is showing average-case hardness for the classical simulation tasks. We show that is true even for quantum tasks which are $oplus$L-hard to simulate.
  arXiv  Detail & Related papers  (2021-02-13T00:54:45Z)
• An Optimal Separation of Randomized and Quantum Query Complexity [67.19751155411075]
  We prove that for every decision tree, the absolute values of the Fourier coefficients of a given order $ellsqrtbinomdell (1+log n)ell-1,$ sum to at most $cellsqrtbinomdell (1+log n)ell-1,$ where $n$ is the number of variables, $d$ is the tree depth, and $c>0$ is an absolute constant.
  arXiv  Detail & Related papers  (2020-08-24T06:50:57Z)
• Bosonic quantum communication across arbitrarily high loss channels [68.58838842613457]
  A general attenuator $Phi_lambda, sigma$ is a bosonic quantum channel that acts by combining the input with a fixed environment state. We show that for any arbitrary value of $lambda>0$ there exists a suitable single-mode state $sigma(lambda)$. Our result holds even when we fix an energy constraint at the input of the channel, and implies that quantum communication at a constant rate is possible even in the limit of arbitrarily low transmissivity.
  arXiv  Detail & Related papers  (2020-03-19T16:50:11Z)
• Quantum Algorithms for Simulating the Lattice Schwinger Model [63.18141027763459]
  We give scalable, explicit digital quantum algorithms to simulate the lattice Schwinger model in both NISQ and fault-tolerant settings. In lattice units, we find a Schwinger model on $N/2$ physical sites with coupling constant $x-1/2$ and electric field cutoff $x-1/2Lambda$. We estimate observables which we cost in both the NISQ and fault-tolerant settings by assuming a simple target observable---the mean pair density.
  arXiv  Detail & Related papers  (2020-02-25T19:18:36Z)

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.