HonHai (Foxconn) QC meeting
HonHai (Foxconn) QC meeting
  • 108
  • 9 298
Single copy stabilizer testing
[2025-01-10 Marcel Hinsche]
We consider the problem of testing whether an unknown n-qubit quantum state |ψ⟩ is a stabilizer state, with only single-copy access. We give an algorithm solving this problem using O(n) copies, and conversely prove that Ω(n−−√) copies are required for any algorithm. The main observation behind our algorithm is that when repeatedly measuring in a randomly chosen stabilizer basis, stabilizer states are the most likely among the set of all pure states to exhibit linear dependencies in measurement outcomes. Our algorithm is designed to probe deviations from this extremal behavior. For the lower bound, we first reduce stabilizer testing to the task of distinguishing random stabilizer states from the maximally mixed state. We then argue that, without loss of generality, it is sufficient to consider measurement strategies that a) lie in the commutant of the tensor action of the Clifford group and b) satisfy a Positive Partial Transpose (PPT) condition. By leveraging these constraints, together with novel results on the partial transposes of the generators of the Clifford commutant, we derive the lower bound on the sample complexity.
Переглядів: 8

Відео

Halving the Cost of Quantum Algorithms with Randomization
Переглядів 13719 годин тому
[2025-01-03 John Martyn] Quantum signal processing (QSP) provides a systematic framework for implementing a polynomial transformation of a linear operator, and unifies nearly all known quantum algorithms. In parallel, recent works have developed randomized compiling, a technique that promotes a unitary gate to a quantum channel and enables a quadratic suppression of error (i.e., $\epsilon \righ...
On the sample complexity of purity and inner product estimation
Переглядів 4319 годин тому
[2024-12-27 Weiyuan Gong] We study the sample complexity of the prototypical tasks quantum purity estimation and quantum inner product estimation. In purity estimation, we are to estimate tr(ρ2) of an unknown quantum state ρ to additive error ϵ. Meanwhile, for quantum inner product estimation, Alice and Bob are to estimate tr(ρσ) to additive error ϵ given copies of unknown quantum state ρ and σ...
Pauli propagation for classically simulating quantum circuits
Переглядів 9021 день тому
[2024-12-20 Manuel Rudolph] Simulating quantum circuits classically is in general a hard task. However, certain families of quantum circuits may be practically or even provably efficiently simulable by use of specialized classical algorithms. In this talk, we will cover a simulation method called "Pauli propagation", which has recently been shown to enable efficient classical simulation of expe...
Small correlation is sufficient for optimal noisy quantum metrology
Переглядів 85Місяць тому
[2024-11-22 Chao Yin] We propose a class of metrological resource states whose quantum Fisher information scales optimally in both system size and noise rate. In these states, qubits are partitioned into sensing groups with relatively large correlations within a group but small correlations between groups. The states are obtainable from local Hamiltonian evolution, and we design a metrologicall...
Online learning of quantum processes
Переглядів 34Місяць тому
[2024-11-15 Asad Raza] Among recent insights into learning quantum states, online learning and shadow tomography procedures are notable for their ability to accurately predict expectation values even of adaptively chosen observables. In contrast to the state case, quantum process learning tasks with a similarly adaptive nature have received little attention. In this work, we investigate online ...
Incompressibility and spectral gaps of random circuits
Переглядів 452 місяці тому
[2024-11-08 Norah Tan] Random reversible and quantum circuits form random walks on the alternating group Alt(2n) and unitary group SU(2n), respectively. Known bounds on the spectral gap for the t-th moment of these random walks have inverse-polynomial dependence in both n and t. We prove that the gap for random reversible circuits is Ω(n−3) for all t≥1, and the gap for random quantum circuits i...
Bipartite entanglement of noisy stabilizer states through the lens of stabilizer codes
Переглядів 412 місяці тому
[2024-11-01 Kenneth Goodenough] Stabilizer states are a prime resource for a number of applications in quantum information science, such as secret-sharing and measurement-based quantum computation. This motivates us to study the entanglement of noisy stabilizer states across a bipartition. We show that the spectra of the corresponding reduced states can be expressed in terms of properties of an...
Building a Surface Code Logical Qubit with Superconducting Qubits
Переглядів 1762 місяці тому
[2024-10-25 Jorge Marques] Controlling quantum states with the fidelity required for useful quantum algorithms exceeds the capabilities of single physical qubits. Quantum error correction addresses this challenge by redundantly encoding a logical qubit across multiple physical qubits. In this talk, I will present the realization of an error-detected logical qubit in the surface code, along with...
Lossy and Constrained Extended Non Local Games with Applications to Cryptography
Переглядів 522 місяці тому
[2024-10-18 Llorenç Escolà-Farràs] Extended non-local games are a generalization of monogamy-of-entanglement games, played by two quantum parties and a quantum referee that performs a measurement on their local quantum system. Along the lines of the NPA hierarchy, the optimal winning probability of those games can be upper bounded by a hierarchy of semidefinite programs (SDPs) converging to the...
Permutation tests for quantum state identity
Переглядів 933 місяці тому
[2024-10-11 Philip Verduyn Lunel] The quantum analogue of the equality function, known as the quantum state identity problem, is the task of deciding whether n unknown quantum states are equal or unequal, given the promise that all states are either pairwise orthogonal or identical. Under the one-sided error requirement, it is known that the permutation test is optimal for this task, and for tw...
Simultaneous Haar Indistinguishability with Applications to Unclonable Cryptography
Переглядів 253 місяці тому
[2024-10-04 Fatih Kaleoglu] Unclonable cryptography is concerned with leveraging the no-cloning principle to build cryptographic primitives that are otherwise impossible to achieve classically. Understanding the feasibility of unclonable encryption, one of the key unclonable primitives, satisfying indistinguishability security in the plain model has been a major open question in the area. So fa...
Fault-tolerant Simulation of Lattice Gauge Theories with Gauge Covariant Codes
Переглядів 573 місяці тому
[2024-09-27 Luca Spagnoli] We show in this paper that a strong and easy connection exists between quantum error correction and Lattice Gauge Theories (LGT) by using the Gauge symmetry to construct an efficient error-correcting code for Abelian LGTs. We identify the logical operations on this gauge covariant code and show that the corresponding Hamiltonian can be expressed in terms of these logi...
Multivariate Fidelities
Переглядів 413 місяці тому
[2024-09-20 Theshani Nuradha] The main contribution of our paper is to introduce a number of multivariate quantum fidelities and show that they satisfy several desirable properties that are natural extensions of those of the Uhlmann and Holevo fidelities. We propose three variants that reduce to the average pairwise fidelity for commuting states: average pairwise z-fidelities, the multivariate ...
Triply efficient shadow tomography
Переглядів 1194 місяці тому
[2024-09-06 Robbie King] Given copies of a quantum state ρ, a shadow tomography protocol aims to learn all expectation values from a fixed set of observables, to within a given precision ϵ. We say that a shadow tomography protocol is triply efficient if it is sample- and time-efficient, and only employs measurements that entangle a constant number of copies of ρ at a time. The classical shadows...
Realization of an Andreev Spin qubit
Переглядів 2644 місяці тому
Realization of an Andreev Spin qubit
Certifying almost all quantum states with few single qubit measurements
Переглядів 894 місяці тому
Certifying almost all quantum states with few single qubit measurements
Verification of Recursively Defined Quantum Circuits
Переглядів 445 місяців тому
Verification of Recursively Defined Quantum Circuits
A fixed point algorithm for matrix projections with applications in quantum information
Переглядів 315 місяців тому
A fixed point algorithm for matrix projections with applications in quantum information
Two prover perfect zero knowledge for MIP*
Переглядів 765 місяців тому
Two prover perfect zero knowledge for MIP*
Useful entanglement can be extracted from noisy graph states
Переглядів 255 місяців тому
Useful entanglement can be extracted from noisy graph states
Unconditional quantum MAGIC advantage in shallow circuit computation
Переглядів 405 місяців тому
Unconditional quantum MAGIC advantage in shallow circuit computation
Polynomial Time Classical Simulation of Noisy IQP Circuits with Constant Depth
Переглядів 1056 місяців тому
Polynomial Time Classical Simulation of Noisy IQP Circuits with Constant Depth
Extending the Known Region of Nonlocal Boxes that Collapse Communication Complexity
Переглядів 726 місяців тому
Extending the Known Region of Nonlocal Boxes that Collapse Communication Complexity
Graph theoretical optimization of fusion based graph state generation
Переглядів 456 місяців тому
Graph theoretical optimization of fusion based graph state generation
Quantum complexity of testing signed graph clusterability
Переглядів 287 місяців тому
Quantum complexity of testing signed graph clusterability
Doubling the order of approximation via the randomized product formula
Переглядів 157 місяців тому
Doubling the order of approximation via the randomized product formula
Monogamy of highly symmetric states
Переглядів 197 місяців тому
Monogamy of highly symmetric states
Incorporating Zero Probability Constraints to Device Independent Randomness Expansion
Переглядів 187 місяців тому
Incorporating Zero Probability Constraints to Device Independent Randomness Expansion
Unbounded Quantum Advantage in One-Way SC Complexity of a Distributed Clique Labelling Relation
Переглядів 137 місяців тому
Unbounded Quantum Advantage in One-Way SC Complexity of a Distributed Clique Labelling Relation

КОМЕНТАРІ

  • @ChrisSargent-f5j
    @ChrisSargent-f5j 3 місяці тому

    Martinez Laura Thomas John Martinez Steven

  • @vanikaghajanyan7760
    @vanikaghajanyan7760 10 місяців тому

    43:00 It is generally accepted that a quantum transition occurs as a result of the evolution of the system over a finite period of time, and the moment of occurrence of each of the transitions is by no means the end of the disturbance. The course of a quantum transition (jump) in time deserves special analysis. A single transition is a random phenomenon and at what point each transition occurred, it is not possible to calculate* using quantum mechanics, which proceeds from the basic postulate of this theory: if an event is possible, then only its probability is reliable. Thus, QM is distributed in an infinitely small time interval (=0) in the vicinity of event P. That is, it is a pseudo-quantum theory that is internally and externally ~ consistent. However, the QM claims to a comprehensive description of the world and, moreover, extension of own limitations to reality are not modest. --------------------- *) - Instead, "Shut up and count." Feynman should have said: "Wake up and create a truly quantum theory.” Addition In fact, the observer's self-esteem in QM is underestimated to the level of the infamous ostrich. The observer is always involved in an unavoidable measurement process. It seems that there have never been any problems with QM already within the framework of GR (for example, in the case of the Schrodinger/Carroll cat). A live cat breathes and, accordingly, emits gravitational waves according to the formula GR with intensity: I(G)=(2G/45c^5)(M^2)(l^4)(w^6), where M is the mass of the cat, l is its characteristic size, w is its frequency breathing.The frequency of gravitational radiation should be on the order of w~ 2π/т where т is the characteristic time of accelerated mass movement (pulsation, rotation, collision, non-spherical explosion).It is clear that the dead cat is not breathing and I(G) =0*. In principle, all this lends itself to a certain (improbability) constant measurement without opening the "black box", since gravity is not shielded [w=w(m)]. Moreover, the behavior of the radiation source is also controlled, since it emits only in an excited state. ** Of course, Carroll's sleeping cat breathes, but differently (can be measured) than the waking one. Sweet dreams to you QM, on the interpretation of the Born wave function.*** P.S. Why didn't Einstein use this argument? He wasn't sure about the reality of gravitational waves and assumed only the presence of hidden parameters… --------------------- *) - By the way, a "smile" without a cat can be detected according to Einstein's equations. Raising one of the indices, substituting I=k and summing, we find: R=-(8πG/c^4)T, where T=T(n) is the trace of the energy-momentum tensor (~ "gravitational memory."). **) - If the cat is replaced with a detector, then with each absorption its state will change (which makes measurement possible). It is clear that this will also cause additional radiation of gravitational waves, since the included detector is already a source. ***) - “Smile gentlemen, a serious look on your face is not a sign of intelligence."(Gorin, "The same Munchausen").