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Li Z, Roy T, Rodríguez Pérez D, Lee KH, Kapit E, Schuster DI. Autonomous error correction of a single logical qubit using two transmons. Nat Commun 2024; 15:1681. [PMID: 38395989 PMCID: PMC10891116 DOI: 10.1038/s41467-024-45858-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2023] [Accepted: 02/05/2024] [Indexed: 02/25/2024] Open
Abstract
Large-scale quantum computers will inevitably need quantum error correction to protect information against decoherence. Traditional error correction typically requires many qubits, along with high-efficiency error syndrome measurement and real-time feedback. Autonomous quantum error correction instead uses steady-state bath engineering to perform the correction in a hardware-efficient manner. In this work, we develop a new autonomous quantum error correction scheme that actively corrects single-photon loss and passively suppresses low-frequency dephasing, and we demonstrate an important experimental step towards its full implementation with transmons. Compared to uncorrected encoding, improvements are experimentally witnessed for the logical zero, one, and superposition states. Our results show the potential of implementing hardware-efficient autonomous quantum error correction to enhance the reliability of a transmon-based quantum information processor.
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Affiliation(s)
- Ziqian Li
- James Franck Institute, University of Chicago, Chicago, IL, 60637, USA
- Department of Physics, University of Chicago, Chicago, IL, 60637, USA
- Department of Applied Physics, Stanford University, Stanford, CA, 94305, USA
| | - Tanay Roy
- James Franck Institute, University of Chicago, Chicago, IL, 60637, USA
- Department of Physics, University of Chicago, Chicago, IL, 60637, USA
| | | | - Kan-Heng Lee
- James Franck Institute, University of Chicago, Chicago, IL, 60637, USA
- Department of Physics, University of Chicago, Chicago, IL, 60637, USA
| | - Eliot Kapit
- Department of Physics, Colorado School of Mines, Golden, CO, 80401, USA
| | - David I Schuster
- James Franck Institute, University of Chicago, Chicago, IL, 60637, USA.
- Department of Physics, University of Chicago, Chicago, IL, 60637, USA.
- Department of Applied Physics, Stanford University, Stanford, CA, 94305, USA.
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL, 60637, USA.
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Jones EB, Hillberry LE, Jones MT, Fasihi M, Roushan P, Jiang Z, Ho A, Neill C, Ostby E, Graf P, Kapit E, Carr LD. Small-world complex network generation on a digital quantum processor. Nat Commun 2022; 13:4483. [PMID: 35918333 PMCID: PMC9345974 DOI: 10.1038/s41467-022-32056-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/30/2021] [Accepted: 07/13/2022] [Indexed: 11/09/2022] Open
Abstract
Quantum cellular automata (QCA) evolve qubits in a quantum circuit depending only on the states of their neighborhoods and model how rich physical complexity can emerge from a simple set of underlying dynamical rules. The inability of classical computers to simulate large quantum systems hinders the elucidation of quantum cellular automata, but quantum computers offer an ideal simulation platform. Here, we experimentally realize QCA on a digital quantum processor, simulating a one-dimensional Goldilocks rule on chains of up to 23 superconducting qubits. We calculate calibrated and error-mitigated population dynamics and complex network measures, which indicate the formation of small-world mutual information networks. These networks decohere at fixed circuit depth independent of system size, the largest of which corresponding to 1,056 two-qubit gates. Such computations may enable the employment of QCA in applications like the simulation of strongly-correlated matter or beyond-classical computational demonstrations.
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Affiliation(s)
- Eric B Jones
- National Renewable Energy Laboratory, Golden, CO, 80401, USA. .,ColdQuanta Inc., Boulder, CO, 80301, USA.
| | | | - Matthew T Jones
- Department of Physics, Colorado School of Mines, Golden, CO, 80401, USA.,NVIDIA Corporation, Boulder, CO, 80302, USA
| | - Mina Fasihi
- Department of Physics, Colorado School of Mines, Golden, CO, 80401, USA
| | | | - Zhang Jiang
- Google Quantum AI, Santa Barbara, CA, 93117, USA
| | - Alan Ho
- Google Quantum AI, Santa Barbara, CA, 93117, USA
| | | | - Eric Ostby
- Google Quantum AI, Santa Barbara, CA, 93117, USA
| | - Peter Graf
- National Renewable Energy Laboratory, Golden, CO, 80401, USA
| | - Eliot Kapit
- Department of Physics, Colorado School of Mines, Golden, CO, 80401, USA. .,Quantum Engineering Program, Colorado School of Mines, Golden, CO, 80401, USA.
| | - Lincoln D Carr
- Department of Physics, Colorado School of Mines, Golden, CO, 80401, USA. .,Quantum Engineering Program, Colorado School of Mines, Golden, CO, 80401, USA.
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Bai X, Paddison JAM, Kapit E, Koohpayeh SM, Wen JJ, Dutton SE, Savici AT, Kolesnikov AI, Granroth GE, Broholm CL, Chalker JT, Mourigal M. Magnetic Excitations of the Classical Spin Liquid MgCr_{2}O_{4}. Phys Rev Lett 2019; 122:097201. [PMID: 30932548 DOI: 10.1103/physrevlett.122.097201] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/28/2018] [Indexed: 06/09/2023]
Abstract
We report a comprehensive inelastic neutron-scattering study of the frustrated pyrochlore antiferromagnet MgCr_{2}O_{4} in its cooperative paramagnetic regime. Theoretical modeling yields a microscopic Heisenberg model with exchange interactions up to third-nearest neighbors, which quantitatively explains all of the details of the dynamic magnetic response. Our work demonstrates that the magnetic excitations in paramagnetic MgCr_{2}O_{4} are faithfully represented in the entire Brillouin zone by a theory of magnons propagating in a highly correlated paramagnetic background. Our results also suggest that MgCr_{2}O_{4} is proximate to a spiral spin-liquid phase distinct from the Coulomb phase, which has implications for the magnetostructural phase transition in MgCr_{2}O_{4}.
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Affiliation(s)
- X Bai
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - J A M Paddison
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
- Churchill College, University of Cambridge, Storey's Way, Cambridge CB3 0DS, United Kingdom
| | - E Kapit
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Parks Road, Oxford OX1 3NP, United Kingdom
- Department of Physics, Colorado School of Mines, Golden, Colorado 80401, USA
| | - S M Koohpayeh
- Institute for Quantum Matter and Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - J-J Wen
- Institute for Quantum Matter and Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - S E Dutton
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
| | - A T Savici
- Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - A I Kolesnikov
- Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - G E Granroth
- Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - C L Broholm
- Institute for Quantum Matter and Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, Maryland 21218, USA
- Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - J T Chalker
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Parks Road, Oxford OX1 3NP, United Kingdom
| | - M Mourigal
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
- Institute for Quantum Matter and Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, Maryland 21218, USA
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Abstract
One of the largest obstacles to building a quantum computer is gate error, where the physical evolution of the state of a qubit or group of qubits during a gate operation does not match the intended unitary transformation. Gate error stems from a combination of control errors and random single qubit errors from interaction with the environment. While great strides have been made in mitigating control errors, intrinsic qubit error remains a serious problem that limits gate fidelity in modern qubit architectures. Simultaneously, recent developments of small error-corrected logical qubit devices promise significant increases in logical state lifetime, but translating those improvements into increases in gate fidelity is a complex challenge. In this Letter, we construct protocols for gates on and between small logical qubit devices which inherit the parent device's tolerance to single qubit errors which occur at any time before or during the gate. We consider two such devices, a passive implementation of the three-qubit bit flip code, and the author's own [E. Kapit, Phys. Rev. Lett. 116, 150501 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.150501] very small logical qubit (VSLQ) design, and propose error-tolerant gate sets for both. The effective logical gate error rate in these models displays superlinear error reduction with linear increases in single qubit lifetime, proving that passive error correction is capable of increasing gate fidelity. Using a standard phenomenological noise model for superconducting qubits, we demonstrate a realistic, universal one- and two-qubit gate set for the VSLQ, with error rates an order of magnitude lower than those for same-duration operations on single qubits or pairs of qubits. These developments further suggest that incorporating small logical qubits into a measurement based code could substantially improve code performance.
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Affiliation(s)
- Eliot Kapit
- Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, USA
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Lu Y, Chakram S, Leung N, Earnest N, Naik RK, Huang Z, Groszkowski P, Kapit E, Koch J, Schuster DI. Universal Stabilization of a Parametrically Coupled Qubit. Phys Rev Lett 2017; 119:150502. [PMID: 29077454 DOI: 10.1103/physrevlett.119.150502] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2017] [Indexed: 06/07/2023]
Abstract
We autonomously stabilize arbitrary states of a qubit through parametric modulation of the coupling between a fixed frequency qubit and resonator. The coupling modulation is achieved with a tunable coupling design, in which the qubit and the resonator are connected in parallel to a superconducting quantum interference device. This allows for quasistatic tuning of the qubit-cavity coupling strength from 12 MHz to more than 300 MHz. Additionally, the coupling can be dynamically modulated, allowing for single-photon exchange in 6 ns. Qubit coherence times exceeding 20 μs are maintained over the majority of the range of tuning, limited primarily by the Purcell effect. The parametric stabilization technique realized using the tunable coupler involves engineering the qubit bath through a combination of photon nonconserving sideband interactions realized by flux modulation, and direct qubit Rabi driving. We demonstrate that the qubit can be stabilized to arbitrary states on the Bloch sphere with a worst-case fidelity exceeding 80%.
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Affiliation(s)
- Yao Lu
- The James Franck Institute and Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
| | - S Chakram
- The James Franck Institute and Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
| | - N Leung
- The James Franck Institute and Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
| | - N Earnest
- The James Franck Institute and Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
| | - R K Naik
- The James Franck Institute and Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
| | - Ziwen Huang
- Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA
| | - Peter Groszkowski
- Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA
| | - Eliot Kapit
- Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, USA
| | - Jens Koch
- Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA
| | - David I Schuster
- The James Franck Institute and Department of Physics, University of Chicago, Chicago, Illinois 60637, USA
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Kapit E. Hardware-Efficient and Fully Autonomous Quantum Error Correction in Superconducting Circuits. Phys Rev Lett 2016; 116:150501. [PMID: 27127945 DOI: 10.1103/physrevlett.116.150501] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/2015] [Indexed: 06/05/2023]
Abstract
Superconducting qubits are among the most promising platforms for building a quantum computer. However, individual qubit coherence times are not far past the scalability threshold for quantum error correction, meaning that millions of physical devices would be required to construct a useful quantum computer. Consequently, further increases in coherence time are very desirable. In this Letter, we blueprint a simple circuit consisting of two transmon qubits and two additional lossy qubits or resonators, which is passively protected against all single-qubit quantum error channels through a combination of continuous driving and engineered dissipation. Photon losses are rapidly corrected through two-photon drive fields implemented with driven superconducting quantum interference device couplings, and dephasing from random potential fluctuations is heavily suppressed by the drive fields used to implement the multiqubit Hamiltonian. Comparing our theoretical model to published noise estimates from recent experiments on flux and transmon qubits, we find that logical state coherence could be improved by a factor of 40 or more compared to the individual qubit T_{1} and T_{2} using this technique. We thus demonstrate that there is substantial headroom for improving the coherence of modern superconducting qubits with a fairly modest increase in device complexity.
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Affiliation(s)
- Eliot Kapit
- Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, USA and Initiative for Theoretical Science, The Graduate Center, City University of New York, New York, New York 10016, USA
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Abstract
We report on a numerical experiment in which we use time-dependent potentials to braid non-Abelian quasiparticles. We consider lattice bosons in a uniform magnetic field within the fractional quantum Hall regime, where ν, the ratio of particles to flux quanta, is near 1/2, 1, or 3/2. We introduce time-dependent potentials which move quasiparticle excitations around one another, explicitly simulating a braiding operation which could implement part of a gate in a quantum computation. We find that different braids do not commute for ν near 1 and 3/2, with Berry matrices, respectively, consistent with Ising and Fibonacci anyons. Near ν=1/2, the braids commute.
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Affiliation(s)
- Eliot Kapit
- Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853-2501, USA.
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Kapit E, Mueller E. Exact parent Hamiltonian for the quantum Hall states in a lattice. Phys Rev Lett 2010; 105:215303. [PMID: 21231318 DOI: 10.1103/physrevlett.105.215303] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2010] [Revised: 07/13/2010] [Indexed: 05/30/2023]
Abstract
We study lattice models of charged particles in uniform magnetic fields. We show how longer range hopping can be engineered to produce a massively degenerate manifold of single-particle ground states with wave functions identical to those making up the lowest Landau level of continuum electrons in a magnetic field. We find that in the presence of local interactions, and at the appropriate filling factors, Laughlin's fractional quantum Hall wave function is an exact many-body ground state of our lattice model. The hopping matrix elements in our model fall off as a Gaussian, and when the flux per plaquette is small compared to the fundamental flux quantum one only needs to include nearest and next-nearest neighbor hoppings. We suggest how to realize this model using atoms in optical lattices, and describe observable consequences of the resulting fractional quantum Hall physics.
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Affiliation(s)
- Eliot Kapit
- Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York, USA
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Schroeter DF, Kapit E, Thomale R, Greiter M. Spin hamiltonian for which the chiral spin liquid is the exact ground state. Phys Rev Lett 2007; 99:097202. [PMID: 17931030 DOI: 10.1103/physrevlett.99.097202] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2006] [Revised: 05/15/2007] [Indexed: 05/25/2023]
Abstract
We construct a Hamiltonian that singles out the chiral spin liquid on a square lattice with periodic boundary conditions as the exact and, apart from the twofold topological degeneracy, unique ground state.
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Abstract
The membrane-binding matrix (MA) domain of the human immunodeficiency virus type 1 (HIV-1) structural precursor Gag (PrGag) protein oligomerizes in solution as a trimer and crystallizes in three dimensions as a trimer unit. A number of models have been proposed to explain how MA trimers might align with respect to PrGag capsid (CA) N-terminal domains (NTDs), which assemble hexagonal lattices. We have examined the binding of naturally myristoylated HIV-1 matrix (MyrMA) and matrix plus capsid (MyrMACA) proteins on membranes in vitro. Unexpectedly, MyrMA and MyrMACA proteins both assembled hexagonal cage lattices on phosphatidylserine-cholesterol membranes. Membrane-bound MyrMA proteins did not organize into trimer units but, rather, organized into hexamer rings. Our results yield a model in which MA domains stack directly above NTD hexamers in immature particles, and they have implications for HIV assembly and interactions between MA and the viral membrane glycoproteins.
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Affiliation(s)
- Ayna Alfadhli
- Vollum Institute and Department of Molecular Microbiology and Immunology, Oregon Health & Sciences University, Mail Code L220, 3181 SW Sam Jackson Park Road, Portland, OR 97201-3098, USA
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