Feedback-assisted quantum optimization.

We propose a quantum-inspired classical algorithm for combinatorial optimization problems, named the counterdiabaticity-assisted classical algorithm for optimization (CACAO). In this algorithm, a solution of a given combinatorial optimization problem is heuristically searched with classical spin dynamics based on quantum Lyapunov control of local counterdiabatic driving. We compare the performance of CACAO with that of quantum time-evolution algorithms, i.e., quantum annealing, the feedback-based algorithm for quantum optimization (known as FALQON), and the counterdiabatic feedback-based quantum algorithm (known as CD-FQA). We also study the performance of CACAO applied to large systems up to 10000 spins.We propose a quantum-inspired classical algorithm for combinatorial optimization problems, named the counterdiabaticity-assisted classical algorithm for optimization (CACAO). In this algorithm, a solution of a given combinatorial optimization problem is heuristically searched with classical spin dynamics based on quantum Lyapunov control of local counterdiabatic driving. We compare the performance of CACAO with that of quantum time-evolution algorithms, i.e., quantum annealing, the feedback-based algorithm for quantum optimization (known as FALQON), and the counterdiabatic feedback-based quantum algorithm (known as CD-FQA). We also study the performance of CACAO applied to large systems up to 10000 spins.

arXiv:2506.09214Physical review. EOct 8, 20250 citations

Quantum Optimization Algorithms.

Ojas Parekh

Jun 19, 20190 citations

Finite-blocklength classical communication over the quantum erasure channel with and without classical feedback

Mark M. Wilde

We determine the optimal success probability for transmitting a fixed number of classical messages through a finite number of uses of the quantum erasure channel, assisted by noiseless classical feedback and without initial shared entanglement. For an input dimension $d$ , an erasure probability $p$ , a blocklength $n$ , and $M$ equiprobable messages, the optimal success probability is equal to $E[\min\{1,d^K/M\}]$ , where $K$ is binomial with parameters $n$ and $1-p$ . The converse allows arbitrary adaptive quantum encoders, quantum memories, and receiver instruments. Its main ingredient is an elementary dimension bound for noiseless quantum communication with classical feedback, proved by fixing the classical controls without conditioning the sender's state on the observed transcript. A classical protocol that transmits the base- $d$ digits of an integer representing the message, repeating each digit until the receiver acknowledges its reception or the prescribed blocklength is reached, attains the bound for every integer $M$ . We also establish a relative-majorization property of erasure-channel outputs and exactly evaluate a hypothesis-testing converse, recovering the same numerical bound without feedback. That converse need not be achievable without feedback: four uses of the qubit erasure channel and four messages give a strict gap. A product-state code employing tetrahedral qubit states nevertheless outperforms every classical binary erasure code with these parameters. We give an explicit message-size formula and show that the bounded-remainder normal approximation and the average-success strong-converse exponent are unchanged without feedback. We also determine the feedback-assisted error exponent below capacity, prove that it agrees with the no-feedback exponent above a critical rate, and give no-feedback bounds at lower rates.We determine the optimal success probability for transmitting a fixed number of classical messages through a finite number of uses of the quantum erasure channel, assisted by noiseless classical feedback and without initial shared entanglement. For an input dimension $d$, an erasure probability $p$, a blocklength $n$, and $M$ equiprobable messages, the optimal success probability is equal to $E[\min\{1,d^K/M\}]$, where $K$ is binomial with parameters $n$ and $1-p$. The converse allows arbitrary adaptive quantum encoders, quantum memories, and receiver instruments. Its main ingredient is an elementary dimension bound for noiseless quantum communication with classical feedback, proved by fixing the classical controls without conditioning the sender's state on the observed transcript. A classical protocol that transmits the base-$d$ digits of an integer representing the message, repeating each digit until the receiver acknowledges its reception or the prescribed blocklength is reached, attains the bound for every integer $M$. We also establish a relative-majorization property of erasure-channel outputs and exactly evaluate a hypothesis-testing converse, recovering the same numerical bound without feedback. That converse need not be achievable without feedback: four uses of the qubit erasure channel and four messages give a strict gap. A product-state code employing tetrahedral qubit states nevertheless outperforms every classical binary erasure code with these parameters. We give an explicit message-size formula and show that the bounded-remainder normal approximation and the average-success strong-converse exponent are unchanged without feedback. We also determine the feedback-assisted error exponent below capacity, prove that it agrees with the no-feedback exponent above a critical rate, and give no-feedback bounds at lower rates.

quant-pharXiv:2610.00440Oct 1, 20260 citations

Two‐Parameter Estimation Via Photon Subtraction Operation Within a Feedback‐Assisted Interferometer

Qingqian Kang, Zekun Zhao, Qisi Zhou +5 more

Abstract In this paper, the effect of multi‐photon subtraction operations in a feedback‐assisted interferometer can enhance measurement precision for single‐parameter and two‐parameter estimation is analyzed under both ideal and photon‐loss conditions. The effects of the feedback strength , the optical parametric amplifier's gain , the coherent state amplitude , and the order of multi‐photon subtraction on system performance are examined. It is demonstrated that an optimal feedback strength exists in both conditions. Selecting a suitable can significantly boost the system's robustness to photon loss, and markedly improve measurement precision. And the photon subtraction operations within a feedback‐assisted interferometer can further enhance measurement precision effectively. Additionally, it is found that increasing intramode correlations while decreasing intermode correlations can improve estimation accuracy. This work investigates a new method through the synergistic integration of feedback topology and non‐Gaussian operations into a multiparameter estimation system, along with their systematic study under both ideal and loss conditions. The findings may contribute to improving quantum‐enhanced measurements and hold promise for high‐precision quantum sensing research.Abstract In this paper, the effect of multi‐photon subtraction operations in a feedback‐assisted interferometer can enhance measurement precision for single‐parameter and two‐parameter estimation is analyzed under both ideal and photon‐loss conditions. The effects of the feedback strength , the optical parametric amplifier's gain , the coherent state amplitude , and the order of multi‐photon subtraction on system performance are examined. It is demonstrated that an optimal feedback strength exists in both conditions. Selecting a suitable can significantly boost the system's robustness to photon loss, and markedly improve measurement precision. And the photon subtraction operations within a feedback‐assisted interferometer can further enhance measurement precision effectively. Additionally, it is found that increasing intramode correlations while decreasing intermode correlations can improve estimation accuracy. This work investigates a new method through the synergistic integration of feedback topology and non‐Gaussian operations into a multiparameter estimation system, along with their systematic study under both ideal and loss conditions. The findings may contribute to improving quantum‐enhanced measurements and hold promise for high‐precision quantum sensing research.

arXiv:2506.05756Advanced Quantum TechnologiesOct 6, 20251 citation

Quantum optimization

Tad Hogg, Dmitriy Portnov

Information SciencesOct 1, 2000111 citations

d

, an erasure probability

p

, a blocklength

n

, and

M

equiprobable messages, the optimal success probability is equal to

E[\min\{1,d^K/M\}]

, where

K

is binomial with parameters

n

and

1-p

. The converse allows arbitrary adaptive quantum encoders, quantum memories, and receiver instruments. Its main ingredient is an elementary dimension bound for noiseless quantum communication with classical feedback, proved by fixing the classical controls without conditioning the sender's state on the observed transcript. A classical protocol that transmits the base-

d

digits of an integer representing the message, repeating each digit until the receiver acknowledges its reception or the prescribed blocklength is reached, attains the bound for every integer

M

. We also establish a relative-majorization property of erasure-channel outputs and exactly evaluate a hypothesis-testing converse, recovering the same numerical bound without feedback. That converse need not be achievable without feedback: four uses of the qubit erasure channel and four messages give a strict gap. A product-state code employing tetrahedral qubit states nevertheless outperforms every classical binary erasure code with these parameters. We give an explicit message-size formula and show that the bounded-remainder normal approximation and the average-success strong-converse exponent are unchanged without feedback. We also determine the feedback-assisted error exponent below capacity, prove that it agrees with the no-feedback exponent above a critical rate, and give no-feedback bounds at lower rates.