Reconstructing a quantum state with a variational autoencoder

Quantum state tomography (QST) is an important and challenging task in the field of quantum information, which has attracted a lot of attentions in recent years. Machine learning models can provide a classical representation of the quantum state after trained on the measurement outcomes, which are part of effective techniques to solve QST problem. In this work, we use a variational autoencoder (VAE) to learn the measurement distribution of two quantum states generated by MPS circuits. We first consider the Greenberger–Horne–Zeilinger (GHZ) state which can be generated by a simple MPS circuit. Simulation results show that a VAE can reconstruct 3- to 8-qubit GHZ states with a high fidelity, i.e., 0.99, and is robust to depolarizing noise. The minimum number ([Formula: see text]) of training samples required to reconstruct the GHZ state up to 0.99 fidelity scales approximately linearly with the number of qubits ([Formula: see text]). However, for the quantum state generated by a complex MPS circuit, [Formula: see text] increases exponentially with [Formula: see text], especially for the quantum state with high entanglement entropy.

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Entanglement

10.1093/oso/9780198714057.003.0003 ◽

2017 ◽

Author(s):

Richard Healey

Keyword(s):

Quantum Theory ◽

Quantum State ◽

Physical Condition ◽

Physical System ◽

Polarization State ◽

Quantum Systems ◽

Ghz State ◽

Mathematical Representation ◽

Entangled State ◽

Physical Relation

Often a pair of quantum systems may be represented mathematically (by a vector) in a way each system alone cannot: the mathematical representation of the pair is said to be non-separable: Schrödinger called this feature of quantum theory entanglement. It would reflect a physical relation between a pair of systems only if a system’s mathematical representation were to describe its physical condition. Einstein and colleagues used an entangled state to argue that its quantum state does not completely describe the physical condition of a system to which it is assigned. A single physical system may be assigned a non-separable quantum state, as may a large number of systems, including electrons, photons, and ions. The GHZ state is an example of an entangled polarization state that may be assigned to three photons.

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A phononic interface between a superconducting quantum processor and quantum networked spin memories

npj Quantum Information ◽

10.1038/s41534-021-00457-4 ◽

2021 ◽

Vol 7 (1) ◽

Author(s):

Tomáš Neuman ◽

Matt Eichenfield ◽

Matthew E. Trusheim ◽

Lisa Hackett ◽

Prineha Narang ◽

...

Keyword(s):

Quantum State ◽

Piezoelectric Transducers ◽

High Fidelity ◽

Hybrid Architecture ◽

Quantum Networks ◽

Superconducting Circuit ◽

Artificial Atom ◽

Experimental Parameters ◽

Quantum Processor ◽

State Spin

AbstractWe introduce a method for high-fidelity quantum state transduction between a superconducting microwave qubit and the ground state spin system of a solid-state artificial atom, mediated via an acoustic bus connected by piezoelectric transducers. Applied to present-day experimental parameters for superconducting circuit qubits and diamond silicon-vacancy centers in an optimized phononic cavity, we estimate quantum state transduction with fidelity exceeding 99% at a MHz-scale bandwidth. By combining the complementary strengths of superconducting circuit quantum computing and artificial atoms, the hybrid architecture provides high-fidelity qubit gates with long-lived quantum memory, high-fidelity measurement, large qubit number, reconfigurable qubit connectivity, and high-fidelity state and gate teleportation through optical quantum networks.

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Adaptive quantum state tomography with neural networks

npj Quantum Information ◽

10.1038/s41534-021-00436-9 ◽

2021 ◽

Vol 7 (1) ◽

Author(s):

Yihui Quek ◽

Stanislav Fort ◽

Hui Khoon Ng

Keyword(s):

Machine Learning ◽

Quantum State ◽

The State ◽

Learning To Learn ◽

Seamless Integration ◽

Quantum State Tomography ◽

Flexible Machine ◽

Meta Learning ◽

Long Time ◽

State Tomography

AbstractCurrent algorithms for quantum state tomography (QST) are costly both on the experimental front, requiring measurement of many copies of the state, and on the classical computational front, needing a long time to analyze the gathered data. Here, we introduce neural adaptive quantum state tomography (NAQT), a fast, flexible machine-learning-based algorithm for QST that adapts measurements and provides orders of magnitude faster processing while retaining state-of-the-art reconstruction accuracy. As in other adaptive QST schemes, measurement adaptation makes use of the information gathered from previous measured copies of the state to perform a targeted sensing of the next copy, maximizing the information gathered from that next copy. Our NAQT approach allows for a rapid and seamless integration of measurement adaptation and statistical inference, using a neural-network replacement of the standard Bayes’ update, to obtain the best estimate of the state. Our algorithm, which falls into the machine learning subfield of “meta-learning” (in effect “learning to learn” about quantum states), does not require any ansatz about the form of the state to be estimated. Despite this generality, it can be retrained within hours on a single laptop for a two-qubit situation, which suggests a feasible time-cost when extended to larger systems and potential speed-ups if provided with additional structure, such as a state ansatz.

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Understanding boundary effects in quantum state tomography – One qubit case

10.1063/1.4903103 ◽

2014 ◽

Author(s):

Takanori Sugiyama ◽

Peter S. Turner ◽

Mio Murao

Keyword(s):

Quantum State ◽

Boundary Effects ◽

Quantum State Tomography ◽

State Tomography

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Finiteness of the set of virtual knots with a given state number

Journal of Knot Theory and Its Ramifications ◽

10.1142/s0218216518500499 ◽

2018 ◽

Vol 27 (08) ◽

pp. 1850049

Author(s):

Takuji Nakamura ◽

Yasutaka Nakanishi ◽

Shin Satoh

Keyword(s):

The Real ◽

Virtual Knot ◽

Virtual Knots ◽

Minimum Number ◽

Number Formula

A state of a virtual knot diagram [Formula: see text] is a collection of circles obtained from [Formula: see text] by splicing all the real crossings. For each integer [Formula: see text], we denote by [Formula: see text] the number of states of [Formula: see text] with [Formula: see text] circles. The [Formula: see text]-state number [Formula: see text] of a virtual knot [Formula: see text] is the minimum number of [Formula: see text] for [Formula: see text] of [Formula: see text]. Let [Formula: see text] be the set of virtual knots [Formula: see text] with [Formula: see text] for an integer [Formula: see text]. In this paper, we study the finiteness of [Formula: see text]. We determine the finiteness of [Formula: see text] for any [Formula: see text] and [Formula: see text] for any [Formula: see text].

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Nonlocal realism tests and quantum state tomography in Sagnac-based type-II polarization-entanglement SPDC-source

Heliyon ◽

10.1016/j.heliyon.2021.e07384 ◽

2021 ◽

pp. e07384

Author(s):

Ali Motazedifard ◽

S.A. Madani ◽

J.J. Dashkasan ◽

N.S. Vayaghan

Keyword(s):

Quantum State ◽

Type Ii ◽

Quantum State Tomography ◽

State Tomography

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On the double total dominator chromatic number of graphs

Discrete Mathematics Algorithms and Applications ◽

10.1142/s1793830921501548 ◽

2021 ◽

pp. 2150154

Author(s):

Fairouz Beggas ◽

Hamamache Kheddouci ◽

Walid Marweni

Keyword(s):

Chromatic Number ◽

Minimum Degree ◽

Domination Number ◽

Vertex Coloring ◽

Total Domination Number ◽

Close Relationship ◽

Minimum Number ◽

Number Formula ◽

Dominator Coloring ◽

Proper Vertex

In this paper, we introduce and study a new coloring problem of graphs called the double total dominator coloring. A double total dominator coloring of a graph [Formula: see text] with minimum degree at least 2 is a proper vertex coloring of [Formula: see text] such that each vertex has to dominate at least two color classes. The minimum number of colors among all double total dominator coloring of [Formula: see text] is called the double total dominator chromatic number, denoted by [Formula: see text]. Therefore, we establish the close relationship between the double total dominator chromatic number [Formula: see text] and the double total domination number [Formula: see text]. We prove the NP-completeness of the problem. We also examine the effects on [Formula: see text] when [Formula: see text] is modified by some operations. Finally, we discuss the [Formula: see text] number of square of trees by giving some bounds.

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