Communication Cost of Quantum Processes
- URL: http://arxiv.org/abs/2002.06840v3
- Date: Mon, 26 Oct 2020 15:42:33 GMT
- Title: Communication Cost of Quantum Processes
- Authors: Yuxiang Yang, Giulio Chiribella, and Masahito Hayashi
- Abstract summary: A common scenario in distributed computing involves a client who asks a server to perform a computation on a remote computer.
An important problem is to determine the minimum amount of communication needed to specify the desired computation.
We analyze the total amount of (classical and quantum) communication needed by a server in order to accurately execute a quantum process chosen by a client.
- Score: 49.281159740373326
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: A common scenario in distributed computing involves a client who asks a
server to perform a computation on a remote computer. An important problem is
to determine the minimum amount of communication needed to specify the desired
computation. Here we extend this problem to the quantum domain, analyzing the
total amount of (classical and quantum) communication needed by a server in
order to accurately execute a quantum process chosen by a client from a
parametric family of quantum processes. We derive a general lower bound on the
communication cost, establishing a relation with the precision limits of
quantum metrology: if a $\nu$-dimensional family of processes can be estimated
with mean squared error $n^{-\beta}$ by using $n$ parallel queries, then the
communication cost for $n$ parallel executions of a process in the family is at
least $(\beta\nu/2-\epsilon)\log n$ qubits at the leading order in $n$, for
every $\epsilon>0$. For a class of quantum processes satisfying the standard
quantum limit ($\beta=1$), we show that the bound can be attained by
transmitting an approximate classical description of the desired process. For
quantum processes satisfying the Heisenberg limit ($\beta=2$), our bound shows
that the communication cost is at least twice as the cost of communicating
standard quantum limited processes with the same number of parameters.
Related papers
- On the sample complexity of purity and inner product estimation [8.94496959777308]
We study the sample complexity of the tasks quantum purity estimation and quantum inner product estimation.
In purity estimation, we are to estimate $tr(rho2)$ of an unknown quantum state $rho$ to additive error $epsilon$.
For quantum inner product estimation, Alice and Bob are to estimate $tr(rhosigma)$ to additive error $epsilon$ given copies of unknown quantum state $rho$ and $sigma$.
arXiv Detail & Related papers (2024-10-16T16:17:21Z) - 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) - Single Qubit Multi-Party Transmission Using Universal Symmetric Quantum
Cloning [1.0878040851638]
We consider a hypothetical quantum network where Alice wishes to transmit one qubit of information to $M$ parties.
We show that Alice can send significantly fewer qubits compared to direct transmission of the message qubits to each of the $M$ remote receivers.
arXiv Detail & Related papers (2023-10-07T21:19:54Z) - Tools for the analysis of quantum protocols requiring state generation
within a time window [1.9021200954913475]
Quantum protocols commonly require a certain number of quantum resource states to be available simultaneously.
Here, we consider a setting in which a process generates a quantum resource state with some probability $p$ in each time step.
To maintain sufficient quality for an application, each resource state is discarded from the memory after $w$ time steps.
arXiv Detail & Related papers (2023-04-25T09:22:16Z) - Oblivious Quantum Computation and Delegated Multiparty Quantum
Computation [61.12008553173672]
We propose a new concept, oblivious computation quantum computation, where secrecy of the input qubits and the program to identify the quantum gates are required.
Exploiting quantum teleportation, we propose a two-server protocol for this task.
Also, we discuss delegated multiparty quantum computation, in which, several users ask multiparty quantum computation to server(s) only using classical communications.
arXiv Detail & Related papers (2022-11-02T09:01:33Z) - Halving the cost of quantum multiplexed rotations [0.0]
We improve the number of $T$ gates needed for a $b$-bit approximation of a multiplexed quantum gate with $c$ controls.
Our results roughly halve the cost of state-of-art electronic structure simulations based on qubitization of double-factorized or tensor-hypercontracted representations.
arXiv Detail & Related papers (2021-10-26T06:49:44Z) - 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) - Fault-tolerant Coding for Quantum Communication [71.206200318454]
encode and decode circuits to reliably send messages over many uses of a noisy channel.
For every quantum channel $T$ and every $eps>0$ there exists a threshold $p(epsilon,T)$ for the gate error probability below which rates larger than $C-epsilon$ are fault-tolerantly achievable.
Our results are relevant in communication over large distances, and also on-chip, where distant parts of a quantum computer might need to communicate under higher levels of noise.
arXiv Detail & Related papers (2020-09-15T15:10:50Z) - Succinct Blind Quantum Computation Using a Random Oracle [0.8702432681310399]
We give a new universal blind quantum computation protocol.
The protocol's first phase is succinct, that is, its complexity is independent of circuit size.
arXiv Detail & Related papers (2020-04-27T07:47:11Z) - 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.