Kevin Satzinger
Kevin Satzinger is a research scientist on the Google AI Quantum hardware team, focusing on the deployment, automatic calibration, and characterization of superconducting quantum processors. He received his Ph.D. in physics from the University of California Santa Barbara in 2018 for research on quantum surface acoustic waves.
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Model-based Optimization of Superconducting Qubit Readout
Alex Opremcak
Alexandre Bourassa
Alexander Korotkov
Jimmy Chen
Physical Review Letters, 132 (2024), pp. 100603
Preview abstract
Measurement is one of the essential components of quantum algorithms, and for superconducting qubits it is often the most error prone. Here, we demonstrate a model-based readout optimization achieving low measurement errors while avoiding detrimental side-effects. For simultaneous and mid-circuit measurements across 17 qubits we observe 1.5% error per qubit with a duration of 500 ns end-to-end and minimal excess reset error from residual resonator photons. We also suppress measurement-induced state transitions and achieve a qubit leakage rate limited by natural heating.This technique can scale to hundreds of qubits, and be used to enhance performance of error-correcting codes as well as near-term applications
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Dynamics of magnetization at infinite temperature in a Heisenberg spin chain
Trond Andersen
Rhine Samajdar
Andre Petukhov
Jesse Hoke
Dmitry Abanin
ILYA Drozdov
Xiao Mi
Alexis Morvan
Charles Neill
Rajeev Acharya
Richard Ross Allen
Kyle Anderson
Markus Ansmann
Frank Arute
Kunal Arya
Juan Atalaya
Gina Bortoli
Alexandre Bourassa
Leon Brill
Michael Broughton
Bob Buckley
Tim Burger
Nicholas Bushnell
Juan Campero
Hung-Shen Chang
Jimmy Chen
Benjamin Chiaro
Desmond Chik
Josh Cogan
Roberto Collins
Paul Conner
William Courtney
Alex Crook
Ben Curtin
Agustin Di Paolo
Andrew Dunsworth
Clint Earle
Lara Faoro
Edward Farhi
Reza Fatemi
Vinicius Ferreira
Ebrahim Forati
Brooks Foxen
Gonzalo Garcia
Élie Genois
William Giang
Dar Gilboa
Raja Gosula
Alejo Grajales Dau
Steve Habegger
Michael Hamilton
Monica Hansen
Sean Harrington
Paula Heu
Gordon Hill
Markus Hoffmann
Trent Huang
Ashley Huff
Bill Huggins
Sergei Isakov
Justin Iveland
Cody Jones
Pavol Juhas
Marika Kieferova
Alexei Kitaev
Andrey Klots
Alexander Korotkov
Fedor Kostritsa
John Mark Kreikebaum
Dave Landhuis
Pavel Laptev
Kim Ming Lau
Lily Laws
Joonho Lee
Kenny Lee
Yuri Lensky
Alexander Lill
Wayne Liu
Salvatore Mandra
Orion Martin
Steven Martin
Seneca Meeks
Amanda Mieszala
Shirin Montazeri
Ramis Movassagh
Wojtek Mruczkiewicz
Ani Nersisyan
Michael Newman
JiunHow Ng
Murray Ich Nguyen
Tom O'Brien
Seun Omonije
Alex Opremcak
Rebecca Potter
Leonid Pryadko
David Rhodes
Charles Rocque
Negar Saei
Kannan Sankaragomathi
Henry Schurkus
Christopher Schuster
Mike Shearn
Aaron Shorter
Noah Shutty
Vladimir Shvarts
Vlad Sivak
Jindra Skruzny
Clarke Smith
Rolando Somma
George Sterling
Doug Strain
Marco Szalay
Doug Thor
Alfredo Torres
Guifre Vidal
Cheng Xing
Jamie Yao
Ping Yeh
Juhwan Yoo
Grayson Young
Yaxing Zhang
Ningfeng Zhu
Jeremy Hilton
Anthony Megrant
Yu Chen
Vadim Smelyanskiy
Vedika Khemani
Sarang Gopalakrishnan
Tomaž Prosen
Science, 384 (2024), pp. 48-53
Preview abstract
Understanding universal aspects of quantum dynamics is an unresolved problem in statistical mechanics. In particular, the spin dynamics of the one-dimensional Heisenberg model were conjectured as to belong to the Kardar-Parisi-Zhang (KPZ) universality class based on the scaling of the infinite-temperature spin-spin correlation function. In a chain of 46 superconducting qubits, we studied the probability distribution of the magnetization transferred across the chain’s center, P(M). The first two moments of P(M) show superdiffusive behavior, a hallmark of KPZ universality. However, the third and fourth moments ruled out the KPZ conjecture and allow for evaluating other theories. Our results highlight the importance of studying higher moments in determining dynamic universality classes and provide insights into universal behavior in quantum systems.
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Optimizing quantum gates towards the scale of logical qubits
Alexandre Bourassa
Andrew Dunsworth
Will Livingston
Vlad Sivak
Trond Andersen
Yaxing Zhang
Desmond Chik
Jimmy Chen
Charles Neill
Alejo Grajales Dau
Anthony Megrant
Alexander Korotkov
Vadim Smelyanskiy
Yu Chen
Nature Communications, 15 (2024), pp. 2442
Preview abstract
A foundational assumption of quantum error correction theory is that quantum gates can be scaled to large processors without exceeding the error-threshold for fault tolerance. Two major challenges that could become fundamental roadblocks are manufacturing high-performance quantum hardware and engineering a control system that can reach its performance limits. The control challenge of scaling quantum gates from small to large processors without degrading performance often maps to non-convex, high-constraint, and time-dynamic control optimization over an exponentially expanding configuration space. Here we report on a control optimization strategy that can scalably overcome the complexity of such problems. We demonstrate it by choreographing the frequency trajectories of 68 frequency-tunable superconducting qubits to execute single- and two-qubit gates while mitigating computational errors. When combined with a comprehensive model of physical errors across our processor, the strategy suppresses physical error rates by ~3.7× compared with the case of no optimization. Furthermore, it is projected to achieve a similar performance advantage on a distance-23 surface code logical qubit with 1057 physical qubits. Our control optimization strategy solves a generic scaling challenge in a way that can be adapted to a variety of quantum operations, algorithms, and computing architectures.
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Stable quantum-correlated many-body states through engineered dissipation
Xiao Mi
Alexios Michailidis
Sara Shabani
Jerome Lloyd
Rajeev Acharya
Igor Aleiner
Trond Andersen
Markus Ansmann
Frank Arute
Kunal Arya
Juan Atalaya
Gina Bortoli
Alexandre Bourassa
Leon Brill
Michael Broughton
Bob Buckley
Tim Burger
Nicholas Bushnell
Jimmy Chen
Benjamin Chiaro
Desmond Chik
Charina Chou
Josh Cogan
Roberto Collins
Paul Conner
William Courtney
Alex Crook
Ben Curtin
Alejo Grajales Dau
Dripto Debroy
Agustin Di Paolo
ILYA Drozdov
Andrew Dunsworth
Lara Faoro
Edward Farhi
Reza Fatemi
Vinicius Ferreira
Ebrahim Forati
Brooks Foxen
Élie Genois
William Giang
Dar Gilboa
Raja Gosula
Steve Habegger
Michael Hamilton
Monica Hansen
Sean Harrington
Paula Heu
Markus Hoffmann
Trent Huang
Ashley Huff
Bill Huggins
Sergei Isakov
Justin Iveland
Cody Jones
Pavol Juhas
Kostyantyn Kechedzhi
Marika Kieferova
Alexei Kitaev
Andrey Klots
Alexander Korotkov
Fedor Kostritsa
John Mark Kreikebaum
Dave Landhuis
Pavel Laptev
Kim Ming Lau
Lily Laws
Joonho Lee
Kenny Lee
Yuri Lensky
Alexander Lill
Wayne Liu
Orion Martin
Amanda Mieszala
Shirin Montazeri
Alexis Morvan
Ramis Movassagh
Wojtek Mruczkiewicz
Charles Neill
Ani Nersisyan
Michael Newman
JiunHow Ng
Murray Ich Nguyen
Tom O'Brien
Alex Opremcak
Andre Petukhov
Rebecca Potter
Leonid Pryadko
Charles Rocque
Negar Saei
Kannan Sankaragomathi
Henry Schurkus
Christopher Schuster
Mike Shearn
Aaron Shorter
Noah Shutty
Vladimir Shvarts
Jindra Skruzny
Clarke Smith
Rolando Somma
George Sterling
Doug Strain
Marco Szalay
Alfredo Torres
Guifre Vidal
Cheng Xing
Jamie Yao
Ping Yeh
Juhwan Yoo
Grayson Young
Yaxing Zhang
Ningfeng Zhu
Jeremy Hilton
Anthony Megrant
Yu Chen
Vadim Smelyanskiy
Dmitry Abanin
Science, 383 (2024), pp. 1332-1337
Preview abstract
Engineered dissipative reservoirs have the potential to steer many-body quantum systems toward correlated steady states useful for quantum simulation of high-temperature superconductivity or quantum magnetism. Using up to 49 superconducting qubits, we prepared low-energy states of the transverse-field Ising model through coupling to dissipative auxiliary qubits. In one dimension, we observed long-range quantum correlations and a ground-state fidelity of 0.86 for 18 qubits at the critical point. In two dimensions, we found mutual information that extends beyond nearest neighbors. Lastly, by coupling the system to auxiliaries emulating reservoirs with different chemical potentials, we explored transport in the quantum Heisenberg model. Our results establish engineered dissipation as a scalable alternative to unitary evolution for preparing entangled many-body states on noisy quantum processors.
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Measurement-induced entanglement and teleportation on a noisy quantum processor
Jesse Hoke
Matteo Ippoliti
Dmitry Abanin
Rajeev Acharya
Trond Andersen
Markus Ansmann
Frank Arute
Kunal Arya
Juan Atalaya
Gina Bortoli
Alexandre Bourassa
Leon Brill
Michael Broughton
Bob Buckley
Tim Burger
Nicholas Bushnell
Jimmy Chen
Benjamin Chiaro
Desmond Chik
Josh Cogan
Roberto Collins
Paul Conner
William Courtney
Alex Crook
Ben Curtin
Alejo Grajales Dau
Agustin Di Paolo
ILYA Drozdov
Andrew Dunsworth
Daniel Eppens
Edward Farhi
Reza Fatemi
Vinicius Ferreira
Ebrahim Forati
Brooks Foxen
William Giang
Dar Gilboa
Raja Gosula
Steve Habegger
Michael Hamilton
Monica Hansen
Paula Heu
Markus Hoffmann
Trent Huang
Ashley Huff
Bill Huggins
Sergei Isakov
Justin Iveland
Cody Jones
Pavol Juhas
Kostyantyn Kechedzhi
Marika Kieferova
Alexei Kitaev
Andrey Klots
Alexander Korotkov
Fedor Kostritsa
John Mark Kreikebaum
Dave Landhuis
Pavel Laptev
Kim Ming Lau
Lily Laws
Joonho Lee
Kenny Lee
Yuri Lensky
Alexander Lill
Wayne Liu
Orion Martin
Amanda Mieszala
Shirin Montazeri
Alexis Morvan
Ramis Movassagh
Wojtek Mruczkiewicz
Charles Neill
Ani Nersisyan
Michael Newman
JiunHow Ng
Murray Ich Nguyen
Tom O'Brien
Seun Omonije
Alex Opremcak
Andre Petukhov
Rebecca Potter
Leonid Pryadko
Charles Rocque
Negar Saei
Kannan Sankaragomathi
Henry Schurkus
Christopher Schuster
Mike Shearn
Aaron Shorter
Noah Shutty
Vladimir Shvarts
Jindra Skruzny
Clarke Smith
Rolando Somma
George Sterling
Doug Strain
Marco Szalay
Alfredo Torres
Guifre Vidal
Cheng Xing
Jamie Yao
Ping Yeh
Juhwan Yoo
Grayson Young
Yaxing Zhang
Ningfeng Zhu
Jeremy Hilton
Anthony Megrant
Yu Chen
Vadim Smelyanskiy
Xiao Mi
Vedika Khemani
Nature, 622 (2023), 481–486
Preview abstract
Measurement has a special role in quantum theory: by collapsing the wavefunction, it can enable phenomena such as teleportation and thereby alter the ‘arrow of time’ that constrains unitary evolution. When integrated in many-body dynamics, measurements can lead to emergent patterns of quantum information in space–time that go beyond the established paradigms for characterizing phases, either in or out of equilibrium. For present-day noisy intermediate-scale quantum (NISQ) processors, the experimental realization of such physics can be problematic because of hardware limitations and the stochastic nature of quantum measurement. Here we address these experimental challenges and study measurement-induced quantum information phases on up to 70 superconducting qubits. By leveraging the interchangeability of space and time, we use a duality mapping to avoid mid-circuit measurement and access different manifestations of the underlying phases, from entanglement scaling to measurement-induced teleportation. We obtain finite-sized signatures of a phase transition with a decoding protocol that correlates the experimental measurement with classical simulation data. The phases display remarkably different sensitivity to noise, and we use this disparity to turn an inherent hardware limitation into a useful diagnostic. Our work demonstrates an approach to realizing measurement-induced physics at scales that are at the limits of current NISQ processors.
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Readout of a quantum processor with high dynamic range Josephson parametric amplifiers
Aaron Shorter
Alejandro Grajales Dau
Alex Crook
Alex Opremcak
Alexander Korotkov
Alexander Lill
Alexandre Bourassa
Alexis Morvan
Alfredo Torres
Andrew Dunsworth
Ani Nersisyan
Anthony Megrant
Ashley Anne Huff
Ben Curtin
Benjamin Chiaro
Bob Benjamin Buckley
Brooks Riley Foxen
Charles Neill
Christopher Schuster
Dave Landhuis
Ebrahim Forati
Fedor Kostritsa
Frank Carlton Arute
Grayson Robert Young
Jamie Yao
Jeremy Patterson Hilton
Jimmy Chen
JiunHow Ng
John Mark Kreikebaum
Josh Godfrey Cogan
Juhwan Yoo
Justin Thomas Iveland
Kannan Aryaperumal Sankaragomathi
Kenny Lee
Kunal Arya
Leon Brill
Lily MeeKit Laws
Marco Szalay
Marika Kieferova
Markus Ansmann
Markus Rudolf Hoffmann
Michael C. Hamilton
Mike Shearn
Murray Nguyen
Nicholas Bushnell
Ningfeng Zhu
Pavel Laptev
Ping Yeh
Rajeev Acharya
Rebecca Potter
Reza Fatemi
Roberto Collins
Sean Harrington
Shirin Montazeri
Tim Burger
Trent Huang
Trevor Johnathan Mccourt
Vladimir Shvarts
Wayne Liu
William Giang
Xiao Mi
Yu Chen
Applied Physics Letters, 122 (2023), pp. 014001
Preview abstract
We demonstrate a high dynamic range Josephson parametric amplifier (JPA) in which the active nonlinear element is implemented using an array of rf-SQUIDs. The device is matched to the 50 $\Omega$ environment with a Klopfenstein-taper impedance transformer and achieves a bandwidth of 250-300 MHz, with input saturation powers up to $-95$~dBm at 20 dB gain. A 54-qubit Sycamore processor was used to benchmark these devices, providing a calibration for readout power, an estimate of amplifier added noise, and a platform for comparison against standard impedance matched parametric amplifiers with a single dc-SQUID. We find that the high power rf-SQUID array design has no adverse effect on system noise, readout fidelity, and qubit dephasing, and we estimate an upper bound on amplifier added noise at 1.6 times the quantum limit. Lastly, amplifiers with this design show no degradation in readout fidelity due to gain compression, which can occur in multi-tone multiplexed readout with traditional JPAs.
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Suppressing quantum errors by scaling a surface code logical qubit
Anthony Megrant
Cody Jones
Jeremy Hilton
Jimmy Chen
Juan Atalaya
Kenny Lee
Michael Newman
Vadim Smelyanskiy
Yu Chen
Nature (2023)
Preview abstract
Practical quantum computing will require error rates that are well below what is achievable with
physical qubits. Quantum error correction [1, 2] offers a path to algorithmically-relevant error rates
by encoding logical qubits within many physical qubits, where increasing the number of physical
qubits enhances protection against physical errors. However, introducing more qubits also increases
the number of error sources, so the density of errors must be sufficiently low in order for logical
performance to improve with increasing code size. Here, we report the measurement of logical qubit
performance scaling across multiple code sizes, and demonstrate that our system of superconducting
qubits has sufficient performance to overcome the additional errors from increasing qubit number.
We find our distance-5 surface code logical qubit modestly outperforms an ensemble of distance-3
logical qubits on average, both in terms of logical error probability over 25 cycles and logical error
per cycle (2.914%±0.016% compared to 3.028%±0.023%). To investigate damaging, low-probability
error sources, we run a distance-25 repetition code and observe a 1.7 × 10−6 logical error per round
floor set by a single high-energy event (1.6 × 10−7 when excluding this event). We are able to
accurately model our experiment, and from this model we can extract error budgets that highlight
the biggest challenges for future systems. These results mark the first experimental demonstration
where quantum error correction begins to improve performance with increasing qubit number, and
illuminate the path to reaching the logical error rates required for computation.
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Purification-Based Quantum Error Mitigation of Pair-Correlated Electron Simulations
Thomas E O'Brien
Gian-Luca R. Anselmetti
Fotios Gkritsis
Vincent Elfving
Stefano Polla
William J. Huggins
Oumarou Oumarou
Kostyantyn Kechedzhi
Dmitry Abanin
Rajeev Acharya
Igor Aleiner
Richard Ross Allen
Trond Ikdahl Andersen
Kyle Anderson
Markus Ansmann
Frank Carlton Arute
Kunal Arya
Juan Atalaya
Michael Blythe Broughton
Bob Benjamin Buckley
Alexandre Bourassa
Leon Brill
Tim Burger
Nicholas Bushnell
Jimmy Chen
Yu Chen
Benjamin Chiaro
Desmond Chun Fung Chik
Josh Godfrey Cogan
Roberto Collins
Paul Conner
William Courtney
Alex Crook
Ben Curtin
Ilya Drozdov
Andrew Dunsworth
Daniel Eppens
Lara Faoro
Edward Farhi
Reza Fatemi
Ebrahim Forati
Brooks Riley Foxen
William Giang
Dar Gilboa
Alejandro Grajales Dau
Steve Habegger
Michael C. Hamilton
Sean Harrington
Jeremy Patterson Hilton
Markus Rudolf Hoffmann
Trent Huang
Ashley Anne Huff
Sergei Isakov
Justin Thomas Iveland
Cody Jones
Pavol Juhas
Marika Kieferova
Andrey Klots
Alexander Korotkov
Fedor Kostritsa
John Mark Kreikebaum
Dave Landhuis
Pavel Laptev
Kim Ming Lau
Lily MeeKit Laws
Joonho Lee
Kenny Lee
Alexander T. Lill
Wayne Liu
Orion Martin
Trevor Johnathan Mccourt
Anthony Megrant
Xiao Mi
Masoud Mohseni
Shirin Montazeri
Alexis Morvan
Ramis Movassagh
Wojtek Mruczkiewicz
Charles Neill
Ani Nersisyan
Michael Newman
Jiun How Ng
Murray Nguyen
Alex Opremcak
Andre Gregory Petukhov
Rebecca Potter
Kannan Aryaperumal Sankaragomathi
Christopher Schuster
Mike Shearn
Aaron Shorter
Vladimir Shvarts
Jindra Skruzny
Vadim Smelyanskiy
Clarke Smith
Rolando Diego Somma
Doug Strain
Marco Szalay
Alfredo Torres
Guifre Vidal
Jamie Yao
Ping Yeh
Juhwan Yoo
Grayson Robert Young
Yaxing Zhang
Ningfeng Zhu
Christian Gogolin
Nature Physics (2023)
Preview abstract
An important measure of the development of quantum computing platforms has been the simulation of increasingly complex physical systems. Prior to fault-tolerant quantum computing, robust error mitigation strategies are necessary to continue this growth. Here, we study physical simulation within the seniority-zero electron pairing subspace, which affords both a computational stepping stone to a fully correlated model, and an opportunity to validate recently introduced ``purification-based'' error-mitigation strategies. We compare the performance of error mitigation based on doubling quantum resources in time (echo verification) or in space (virtual distillation), on up to 20 qubits of a superconducting qubit quantum processor. We observe a reduction of error by one to two orders of magnitude below less sophisticated techniques (e.g. post-selection); the gain from error mitigation is seen to increase with the system size. Employing these error mitigation strategies enables the implementation of the largest variational algorithm for a correlated chemistry system to-date. Extrapolating performance from these results allows us to estimate minimum requirements for a beyond-classical simulation of electronic structure. We find that, despite the impressive gains from purification-based error mitigation, significant hardware improvements will be required for classically intractable variational chemistry simulations.
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Noise-resilient Majorana Edge Modes on a Chain of Superconducting Qubits
Alejandro Grajales Dau
Alex Crook
Alex Opremcak
Alexa Rubinov
Alexander Korotkov
Alexandre Bourassa
Alexei Kitaev
Alexis Morvan
Andre Gregory Petukhov
Andrew Dunsworth
Andrey Klots
Anthony Megrant
Ashley Anne Huff
Benjamin Chiaro
Bernardo Meurer Costa
Bob Benjamin Buckley
Brooks Foxen
Charles Neill
Christopher Schuster
Cody Jones
Daniel Eppens
Dar Gilboa
Dave Landhuis
Dmitry Abanin
Doug Strain
Ebrahim Forati
Edward Farhi
Emily Mount
Fedor Kostritsa
Frank Carlton Arute
Guifre Vidal
Igor Aleiner
Jamie Yao
Jeremy Patterson Hilton
Joao Basso
John Mark Kreikebaum
Joonho Lee
Juan Atalaya
Juhwan Yoo
Justin Thomas Iveland
Kannan Aryaperumal Sankaragomathi
Kenny Lee
Kim Ming Lau
Kostyantyn Kechedzhi
Kunal Arya
Lara Faoro
Leon Brill
Marco Szalay
Markus Rudolf Hoffmann
Masoud Mohseni
Michael Blythe Broughton
Michael Newman
Michel Henri Devoret
Mike Shearn
Nicholas Bushnell
Orion Martin
Paul Conner
Pavel Laptev
Ping Yeh
Rajeev Acharya
Rebecca Potter
Reza Fatemi
Roberto Collins
Sergei Isakov
Shirin Montazeri
Steve Habegger
Thomas E O'Brien
Trent Huang
Trond Ikdahl Andersen
Vadim Smelyanskiy
Vladimir Shvarts
Wayne Liu
William Courtney
William Giang
William J. Huggins
Wojtek Mruczkiewicz
Xiao Mi
Yaxing Zhang
Yu Chen
Yuan Su
Zijun Chen
Science (2022) (to appear)
Preview abstract
Inherent symmetry of a quantum system may protect its otherwise fragile states. Leveraging such protection requires testing its robustness against uncontrolled environmental interactions. Using 47 superconducting qubits, we implement the kicked Ising model which exhibits Majorana edge modes (MEMs) protected by a $\mathbb{Z}_2$-symmetry. Remarkably, we find that any multi-qubit Pauli operator overlapping with the MEMs exhibits a uniform decay rate comparable to single-qubit relaxation rates, irrespective of its size or composition. This finding allows us to accurately reconstruct the exponentially localized spatial profiles of the MEMs. Spectroscopic measurements further indicate exponentially suppressed hybridization between the MEMs over larger system sizes, which manifests as a strong resilience against low-frequency noise. Our work elucidates the noise sensitivity of symmetry-protected edge modes in a solid-state environment.
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Direct Measurement of Nonlocal Interactions in the Many-Body Localized Phase
Amit Vainsencher
Andrew Dunsworth
Anthony Megrant
Ben Chiaro
Brooks Foxen
Charles Neill
Dave Landhuis
Fedor Kostritsa
Frank Carlton Arute
Jimmy Chen
John Martinis
Josh Mutus
Kostyantyn Kechedzhi
Kunal Arya
Rami Barends
Roberto Collins
Trent Huang
Vadim Smelyanskiy
Yu Chen
Physical Review Research, 4 (2022), pp. 013148
Preview abstract
The interplay of interactions and strong disorder can lead to an exotic quantum many-body localized (MBL) phase of matter. Beyond the absence of transport, the MBL phase has distinctive signatures, such as slow dephasing and logarithmic entanglement growth; they commonly result in slow and subtle modifications of the dynamics, rendering their measurement challenging. Here, we experimentally characterize these properties of the MBL phase in a system of coupled superconducting qubits. By implementing phase sensitive techniques, we map out the structure of local integrals of motion in the MBL phase. Tomographic reconstruction of single and two-qubit density matrices allows us to determine the spatial and temporal entanglement growth between the localized sites. In addition, we study the preservation of entanglement in the MBL phase. The interferometric protocols implemented here detect affirmative quantum correlations and exclude artifacts due to the imperfect isolation of the system. By measuring elusive MBL quantities, our work highlights the advantages of phase sensitive measurements in studying novel phases of matter.
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