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Universal variational quantum computation
Jacob Biamonte
PHYSICAL REVIEW A 103, L030401 (2021)
https://doi.org/10.1103/PhysRevA.103.L030401
Variational quantum algorithms dominate contemporary gatebased quantum enhanced optimization, eigenvalue estimation, and machine learning. Here we
establish the quantum computational universality of variational quantum computation by developing two objective functions which minimize to prepare
outputs of arbitrary quantum circuits. The fleeting resource of variational quantum computation is the number of expected values which must be
iteratively minimized using classicaltoquantum outer loop optimization. An efficient solution to this optimization problem is given by the quantum
circuit being simulated itself. The first construction is efficient in the number of expected values for nqubit circuits containing O(poly ln n)
nonClifford gates—the number of expected values has no dependence on Clifford gates appearing in the simulated circuit. The second approach yields
O(L 2 ) expected values whereas introducing not more than O(ln L) slack qubits for a quantum circuit partitioned into L gates. Hence, the utilitarian
variational quantum programming procedure—based on the classical evaluation of objective functions and iterated feedback—is, in principle, as
powerful as any other model of quantum computation. This result elevates the formal standing of the variational approach whereas establishing a
universal model of quantum computation.
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Quantum Information Scrambling on a Superconducting Qutrit Processor
M. S. Blok, V. V. Ramasesh , T. Schuster, K. O’Brien, J. M. Kreikebaum, D. Dahlen, A. Morvan, B. Yoshida, N. Y. Yao and I. Siddiqi
PHYSICAL REVIEW X 11, 021010 (2021)
DOI: 10.1103/PhysRevX.11.021010
The dynamics of quantum information in strongly interacting systems, known as quantum information scrambling, has recently become a common thread in
our understanding of black holes, transport in exotic nonFermi liquids, and manybody analogs of quantum chaos. To date, verified experimental
implementations of scrambling have focused on systems composed of twolevel qubits. Higherdimensional quantum systems, however, may exhibit different
scrambling modalities and are predicted to saturate conjectured speed limits on the rate of quantum information scrambling. We take the first steps
toward accessing such phenomena, by realizing a quantum processor based on superconducting qutrits (threelevel quantum systems). We demonstrate the
implementation of universal twoqutrit scrambling operations and embed them in a fivequtrit quantum teleportation protocol. Measured teleportation
fidelities F avg ¼ 0.568 0.001 confirm the presence of scrambling even in the presence of experimental imperfections and decoherence. Our
teleportation protocol, which connects to recent proposals for studying traversable wormholes in the laboratory, demonstrates how quantum technology
that encodes information in higherdimensional systems can exploit a larger and more connected state space to achieve the resource efficient encoding
of complex quantum circuits.
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Fabrication of lowloss quasisinglemode PPLN waveguide and its application to a modularized broadband highlevel
squeezer
Takahiro Kashiwazaki, Taichi Yamashima, Naoto Takanashi, Asuka Inoue, Takeshi Umeki and Akira Furusawa
Appl. Phys. Lett. 119, 251104 (2021);
https://doi.org/10.1063/5.0063118
A continuouswave (CW) broadband highlevel optical quadrature squeezer is essential for highspeed largescale faulttolerant quantum computing on a
timedomainmultiplexed continuousvariable optical cluster state. CW THzbandwidth squeezed light can be obtained with a waveguide optical parametric
ampliﬁer (OPA); however, the squeezing level has been insufﬁcient for applications of faulttolerant quantum computation because of degradation of
the squeezing level due to their optical losses caused by the structural perturbation and pumpinduced phenomena. Here, by using mechanical polishing
processes, we fabricated a lowloss quasisinglemode periodically poled LiNbO 3(PPLN) waveguide, which shows 7% optical propagation loss with a
waveguide length of 45 mm. Using the waveguide, we assembled a lowloss ﬁberpigtailed OPA module with a total insertion loss of 21%. Thanks to its
directly bonded core on a LiTaO 3 substrate, the waveguide does not show pumpinduced optical loss even under a condition of hundreds of milliwatts
pumping. Furthermore, the quasisinglemode structure prohibits excitation of higherorder spatial modes and enables us to obtain larger squeezing
level. Even with including optical coupling loss of the modularization, we observe 6.3dB squeezed light from the DC component up to a 6.0THz
sideband in a fully ﬁberclosed optical system. By excluding the losses due to imperfections of the modularization and detection, the squeezing
level at the output of the PPLN waveguide is estimated to be over 10 dB. Our waveguide squeezer is a promising quantum light source for highspeed
largescale faulttolerant quantum computing.
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Asymptotic Improvements to Quantum Circuits via Qutrits
Pranav Gokhale, Natalie C. Brown, Casey Duckering, Jonathan M. Baker, Kenneth R. Brown & Frederic T. Chong
https://www.researchgate.net/publication/333418921
Quantum computation is traditionally expressed in terms of quantum bits, or qubits. In this work, we instead consider threelevel qutrits. Past work
with qutrits has demonstrated only constant factor improvements, owing to the log 2 (3) binarytoternary compression factor. We present a novel
technique using qutrits to achieve a logarithmic depth (runtime) decomposition of the Generalized Toffoli gate using no ancilla a significant
improvement over linear depth for the best qubitonly equivalent. Our circuit construction also features a 70x improvement in twoqudit gate count
over the qubitonly equivalent decomposition. This results in circuit cost reductions for important algorithms like quantum neurons and Grover search.
We develop an opensource circuit simulator for qutrits, along with realistic nearterm noise models which account for the cost of operating qutrits.
Simulation results for these noise models indicate over 90% mean reliability (fidelity) for our circuit construction, versus under 30% for the
qubitonly baseline. These results suggest that qutrits offer a promising path towards scaling quantum computation.
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Prospects for Simulating a QuditBased Model of (1+1)d Scalar QED
Erik J. Gustafson
Phys. Rev. D 103, 114505 (2021)
DOI: 10.1103/PhysRevD.103.114505
We present a gauge invariant digitization of (1 + 1)d scalar quantum electrodynamics for an arbitrary spin truncation for quditbased quantum
computers. We provide a construction of the Trotter operator in terms of a universal quditgate set. The cost savings of using a qutrit based spin1
encoding versus a qubit encoding are illustrated. We show that a simple initial state could be simulated on current qutrit based hardware using noisy
simulations for two different native gate set.
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Experimental quantum cryptography with qutrits
Simon Gröblacher, Thomas Jennewein, Alipasha Vaziri, Gregor Weihs and Anton Zeilinger
New Journal of Physics 8 (2006) 75
doi:10.1088/13672630/8/5/075
We produce two identical keys using, for the first time, entangled trinary quantum systems (qutrits) for quantum key distribution. The advantage of
qutrits over the normally used binary quantum systems is an increased coding density and a higher security margin. The qutrits are encoded into the
orbital angular momentum of photons, namely Laguerre–Gaussian modes with azimuthal index l + 1, 0 and −1, respectively. The orbital angular
momentum is controlled with phase holograms. In an Ekerttype protocol the violation of a threedimensional Bell inequality verifies the security of
the generated keys.A key is obtained with a qutrit error rate of approximately 10%.
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Quantum Cryptography Based On Bell Inequalities for ThreeDimensional System
Dagomir Kaszlikowski, Kelken Chang, D. K. L. Oi, L.C. Kwek and C.H. Oh
https://arxiv.org/abs/quantph/0206170
We present a crytographic protocol based upon entangled qutrit pairs. We analyse the scheme under a symmetric incoherent attack and plot the region
for which the protocol is secure and compare this with the region of violations of certain Bell inequalities.
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Quantum Information Scrambling on a Superconducting Qutrit Processor
M. S. Blok, V. V. Ramasesh , T. Schuster, K. O’Brien, J. M. Kreikebaum, D. Dahlen, A. Morvan, B. Yoshida, 3 N. Y. Yao and I. Siddiqi .
PHYSICAL REVIEW X 11, 021010 (2021) DOI: 10.1103/PhysRevX.11.021010
The dynamics of quantum information in strongly interacting systems, known as quantum information scrambling, has recently become a common thread in
our understanding of black holes, transport in exotic nonFermi liquids, and manybody analogs of quantum chaos. To date, verified experimental
implementations of scrambling have focused on systems composed of twolevel qubits. Higherdimensional quantum systems, however, may exhibit different
scrambling modalities and are predicted to saturate conjectured speed limits on the rate of quantum information scrambling. We take the first steps
toward accessing such phenomena, by realizing a quantum processor based on superconducting qutrits (threelevel quantum systems). We demonstrate the
implementation of universal twoqutrit scrambling operations and embed them in a fivequtrit quantum teleportation protocol. Measured teleportation
fidelities F avg ¼ 0.568 0.001 confirm the presence of scrambling even in the presence of experimental imperfections and decoherence. Our
teleportation protocol, which connects to recent proposals for studying traversable wormholes in the laboratory, demonstrates how quantum technology
that encodes information in higherdimensional systems can exploit a larger and more connected state space to achieve the resource efficient encoding
of complex quantum circuits
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Improving waferscale Josephson junction resistance variation in superconducting quantum coherent circuits
J.M. Kreikebaum, K.P. O’Brien, A. Morvan, and I. Siddiqi
DOI: 10.1088/13616668/ab8617
Supercond. Sci. Technol. 33 06LT02 (2020)
Quantum bits, or qubits, are an example of coherent circuits envisioned for nextgeneration computers and detectors. A robust superconducting qubit
with a coherent lifetime of O(100 µs) is the transmon: a Josephson junction functioning as a nonlinear inductor shunted with a capacitor to form an
anharmonic oscillator. In a complex device with many such transmons, precise control over each qubit frequency is often required, and thus variations
of the junction area and tunnel barrier thickness must be sufficiently minimized to achieve optimal performance while avoiding spectral overlap
between neighboring circuits. Simply transplanting our recipe optimized for single, standalone devices to waferscale (producing 64, 1x1 cm dies from
a 150 mm wafer) initially resulted in global drifts in roomtemperature tunneling resistance of ± 30%. Inferring a critical current I c variation
from this resistance distribution, we present an optimized process developed from a systematic 38 wafer study that results in < 3.5% relative
standard deviation (RSD) in critical current (≡ σ I c / hI c i) for 3000 Josephson junctions (both singlejunctions and asymmetric SQUIDs) across
an area of 49 cm 2 . Looking within a 1x1 cm moving window across the substrate gives an estimate of the variation characteristic of a given qubit
chip. Our best process, utilizing ultrasonically assisted development, uniform ashing, and dynamic oxidation has shown σ I c / hI c i = 1.8% within
1x1 cm, on average, with a few 1x1 cm areas having σ I c / hI c i < 1.0% (equivalent to σ f / h f i < 0.5%). Such stability would drastically
improve the yield of multijunction chips with strict critical current requirements.
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Conditional teleportation of quantumdot spin states
Haifeng Qiao, Yadav P. Kandel, Sreenath K. Manikandan, Andrew N. Jordan Geoffrey C. Gardner, Michael J. Manfra, John M. Nichol & Saeed Fallahi
NATURE COMMUNICATIONS  (2020) 11:3022
https://doi.org/10.1038/s41467020167450
Among the different platforms for quantum information processing, individual electron spins in semiconductor quantum dots stand out for their long
coherence times and potential for scalable fabrication. The past years have witnessed substantial progress in the capabilities of spin qubits.
However, coupling between distant electron spins, which is required for quantum error correction, presents a challenge, and this goal remains the
focus of intense research. Quantum teleportation is a canonical method to transmit qubit states, but it has not been implemented in quantumdot spin
qubits. Here, we present evidence for quantum teleportation of electron spin qubits in semiconductor quantum dots. Although we have not performed
quantum state tomography to deﬁnitively assess the teleportation ﬁdelity, our data are consistent with conditional teleportation of spin
eigenstates, entanglement swapping, and gate teleportation. Such evidence for allmatter spinstate teleportation underscores the capabilities of
exchangecoupled spin qubits for quantuminformation transfer.
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Can the displacemon device test objective collapse models?
Journal of Vacuum Science & Technology B 40, 012802 (2022);
https://doi.org/10.1116/6.0001485
Lydia A. KanariNaish, Jack Clarke, Michael R. Vanner and Edward A. Laird
Testing the limits of the applicability of quantum mechanics will deepen our understanding of the universe and may shed light on the interplay between
quantum mechanics and gravity. At present there is a wide range of approaches for such macroscopic tests spanning from matterwave interferometry of
large molecules to precision measurements of heating rates in the motion of microscale cantilevers. The “displacemon” is a proposed
electromechanical device consisting of a mechanical resonator ﬂuxcoupled to a superconducting qubit enabling generation and readout of mechanical
quantum states. In the original proposal, the mechanical resonator was a carbon nanotube, containing 10 6 nucleons. Here, in order to probe quantum
mechanics at a more macroscopic scale, we propose using an aluminum mechanical resonator on two larger mass scales, one inspired by the
Marshall–Simon–Penrose–Bouwmeester movingmirror proposal, and one set by the Planck mass. For such a device, we examine the experimental
requirements needed to perform a more macroscopic quantum test and thus feasibly detect the decoherence effects predicted by two objective collapse
models: Di osi–Penrose and continuous spontaneous localization. Our protocol for testing these two theories takes advantage of the displacemon
architecture to create nonGaussian mechanical states out of equilibrium with their environment and then analyzes the measurement statistics of a
superconducting qubit. We ﬁnd that with improvements to the fabrication and vibration sensitivities of these electromechanical devices, the
displacemon device provides a new route to feasibly test decoherence mechanisms beyond standard quantum theory.
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MeasurementInduced Entanglement Transitions in the Quantum Ising Chain: From Infinite to Zero Clicks
Xhek Turkeshi, Alberto Biella, Rosario Fazio, Marcello Dalmonte and Marco Schiró
Phys. Rev. B 103, 224210 (2021) DOI: 10.1103/PhysRevB.103.224210
We investigate measurementinduced phase transitions in the Quantum Ising chain coupled to a monitoring environment. We compare two different limits
of the measurement problem, the stochastic quantumstate diffusion protocol corresponding to infinite small jumps per unit of time and the noclick
limit, corresponding to postselection and described by a nonHermitian Hamiltonian. In both cases we find a remarkably similar phenomenology as the
measurement strength γ is increased, namely a sharp transition from a critical phase with logarithmic scaling of the entanglement to an arealaw
phase, which occurs at the same value of the measurement rate in the two protocols. An effective central charge, extracted from the logarithmic
scaling of the entanglement, vanishes continuously at the common transition point, although with different critical behavior possibly suggesting
different universality classes for the two protocols. We interpret the central charge mismatch near the transition in terms of noiseinduced
disentanglement, as suggested by the entanglement statistics which displays emergent bimodality upon approaching the critical point. The nonHermitian
Hamiltonian and its associated subradiance spectral transition provide a natural framework to understand both the extended critical phase, emerging
here for a model which lacks any continuous symmetry, and the entanglement transition into the area law
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e Measurementinduced Transition in Longrange Interacting Quantum Circuits
Maxwell Block, Yimu Bao, Soonwon Choi, Ehud Altman and Norman Y. Yao
Phys. Rev. Lett. 128, 010604
https://arxiv.org/abs/2104.13372
The competition between scrambling unitary evolution and projective measurements leads to a phase transition in the dynamics of quantum entanglement.
Here, we demonstrate that the nature of this transition is fundamentally altered by the presence of longrange, powerlaw interactions. For
sufficiently weak powerlaws, the measurementinduced transition is described by conformal field theory, analogous to shortrangeinteracting hybrid
circuits. However, beyond a critical powerlaw, we demonstrate that longrange interactions give rise to a continuum of nonconformal universality
classes, with continuously varying critical exponents. We numerically determine the phase diagram for a onedimensional, longrangeinteracting hybrid
circuit model as a function of the powerlaw exponent and the measurement rate. Finally, by using an analytic mapping to a longrange quantum Ising
model, we provide a theoretical understanding for the critical powerlaw.
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Quantum State Complexity in Computationally Tractable Quantum Circuits
Jason Iaconis
PRX QUANTUM 2, 010329 (2021)
Characterizing the quantum complexity of local random quantum circuits is a very deep problem with implications to the seemingly disparate ﬁelds of
quantum information theory, quantum manybody physics, and highenergy physics. While our theoretical understanding of these systems has progressed in
recent years, numerical approaches for studying these models remains severely limited. In this paper, we discuss a special class of numerically
tractable quantum circuits, known as quantum automaton circuits, which may be particularly well suited for this task. These are circuits that preserve
the computational basis, yet can produce highly entangled output wave functions. Using ideas from quantum complexity theory, especially those
concerning unitary designs, we argue that automaton wave functions have high quantum state complexity. We look at a wide variety of metrics, including
measurements of the output bitstring distribution and characterization of the generalized entanglement properties of the quantum state, and ﬁnd
that automaton wave functions closely approximate the behavior of fully Haar random states. In addition to this, we identify the generalized
outoftime ordered 2kpoint correlation functions as a particularly useful probe of complexity in automaton circuits. Using these correlators, we are
able to numerically study the growth of complexity well beyond the scrambling time for very large systems. As a result, we are able to present
evidence of a linear growth of design complexity in local quantum circuits, consistent with conjectures from quantum information theory.
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Deterministic Shallow Dopant Implantation in Silicon with Detection Confidence Upper‐Bound to 99.85% by Ion‐Solid
Interactions
November 2021 Advanced Materials
DOI:10.1002/adma.202103235
Alexander M. Jakob, Simon G. Robson, Vivien Schmitt, Vincent Mourik, Matthias Posselt, Daniel Spemann, Brett C. Johnson, Hannes R. Firgau, Edwin
Mayes, Jeffrey C. McCallum, Andrea Morello, and David N. Jamieson
Silicon chips containing arrays of single dopant atoms could be the material of choice for both classical and quantum devices that exploit single
donor spins. For example, groupVdonors implanted in isotopically purified ²⁸Si crystals are attractive for largescale quantum computers. Useful
attributes include long nuclear and electron spin lifetimes of ³¹P, hyperfine clock transitions in ²⁰⁹Bi or electrically controllable ¹²³Sb
nuclear spins. Promising architectures require the ability to fabricate arrays of individual nearsurface dopant atoms with high yield. Here we employ
an onchip detector electrode system with 70 eV r.m.s. noise (∼20 electrons) to demonstrate near room temperature implantation of single 14 keV
³¹P⁺ ions. The physics model for the ionsolid interaction shows an unprecedented upperbound single ion detection confidence of 99.85±0.02% for
nearsurface implants. As a result, the practical controlled silicon doping yield is limited by materials engineering factors including surface gate
oxides in which detected ions may stop. For a device with 6 nm gate oxide and 14 keV ³¹P⁺ implants we demonstrate a yield limit of 98.1%. Thinner
gate oxides allow this limit to converge to the upperbound. Deterministic single ion implantation can therefore be a viable materials engineering
strategy for scalable dopant architectures in silicon devices.
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Spinorbit driven electrical manipulation of the zerofield splitting in highspin centers in solids
Biktagirov, Timur & Gerstmann, Uwe
PHYSICAL REVIEW RESEARCH 2, 023071 (2020) DOI:10.1103/PhysRevResearch.2.023071
In recent years, spinorbit coupling has attracted significant attention due to its promising applications in spintronic devices. In solidstate spin
qubits, the spinorbit coupling allows for the lifting of spin degeneracy in the absence of an external magnetic field. Such spinorbit driven
zerofield splitting can be directly tuned by external electric fields. Here we present a reliable theoretical framework to address this phenomenon in
extended periodic systems. We unravel the microscopic origin of the zerofield splitting in lightelement semiconductors and propose its implications
for coherent electrical control. The reported theoretical results open up promising possibilities for a rational design and tuning of highspin
centers suitable for quantum information processing. is attached
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A chemical path to quantum information
Stephen von Kugelgen & Danna E Freedman
DOI: 10.1126/science.aaz4044
Science 2019 Nov 29;366(6469):10701071
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Controllable freezing of the nuclear spin bath in a singleatom spin qubit
Mateusz T. Mądzik, Thaddeus D. Ladd, Fay E. Hudson, Kohei M. Itoh, Alexander M. Jakob, Brett C. Johnson, David N. Jamieson, Jeffrey C. McCallum,
Andrew S. Dzurak, Arne Laucht and Andrea Morello
Sci Adv. 2020 Jul 3;6(27):eaba3442.
doi: 10.1126/sciadv.aba3442.
The quantum coherence and gate fidelity of electron spin qubits in semiconductors is often limited by noise arising from coupling to a bath of nuclear
spins. Isotopic enrichment of spinzero nuclei such as 28 Si has led to spectacular improvements of the dephasing time T 2 ∗ which, surprisingly,
can extend two orders of magnitude beyond theoretical expectations. Using a singleatom 31 P qubit in enriched 28 Si, we show that the abnormally long
T 2 ∗ is due to the controllable freezing of the dynamics of the residual 29 Si nuclei close to the donor. Our conclusions are supported by a nearly
parameterfree modeling of the 29 Si nuclear spin dynamics, which reveals the degree of backaction provided by the electron spin as it interacts with
the nuclear bath. This study clarifies the limits of ergodic assumptions in analyzing manybody spinproblems under conditions of strong, frequent
measurement, and provides novel strategies for maximizing coherence and gate fidelity of spin qubits in semiconductors.
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Quantum tomography of an entangled threequbit state in silicon Kenta Takeda, Akito Noiri Seigo Tarucha & Takashi
Nakajima Nature Nanotechnology (2021) DOI: 10.1038/s41565021009250 Quantum entanglement is a fundamental property of coherent quantum states and
an essential resource for quantum computing. In largescale quantum systems, the error accumulation requires concepts for quantum error correction. A
first step toward error correction is the creation of genuinely multipartite entanglement, which has served as a performance benchmark for quantum
computing platforms such as superconducting circuits, trapped ions and nitrogenvacancy centres in diamond. Among the candidates for largescale
quantum computing devices, siliconbased spin qubits offer an outstanding nanofabrication capability for scalingup. Recent studies demonstrated
improved coherence times, highfidelity allelectrical control, hightemperature operation and quantum entanglement of two spin qubits.Here we
generated a threequbit Greenberger–Horne–Zeilinger state using a lowdisorder, fully controllable array of three spin qubits in silicon. We
performed quantum state tomography and obtained a state fidelity of 88.0%. The measurements witness a genuine Greenberger–Horne–Zeilinger class
quantum entanglement that cannot be separated into any biseparable state. Our results showcase the potential of siliconbased spin qubit platforms for
multiqubit quantum algorithms.
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Fidelity benchmarks for twoqubit gates in silicon
W. Huang, C. H. Yang, K. W. Chan, T. Tanttu, B. Hensen, R. C. C. Leon, M. A. Fogarty, J. C. C. Hwang, F. E. Hudson, K. M. Itoh, A. Morello, A. Laucht
& A. S. Dzurak
Nature 569, 532536 (2019)
DOI: 10.1038/s4158601911970
Universal quantum computation will require qubit technology based on a scalable platform, together with quantum error correction protocols that place
strict limits on the maximum infidelities for one and twoqubit gate operations. While a variety of qubit systems have shown high fidelities at the
onequbit level, superconductor technologies have been the only solidstate qubits manufactured via standard lithographic techniques which have
demonstrated twoqubit fidelities near the faulttolerant threshold. Siliconbased quantum dot qubits are also amenable to largescale manufacture and
can achieve high singlequbit gate fidelities (exceeding 99.9%) using isotopically enriched silicon. However, while twoqubit gates have been
demonstrated in silicon, it has not yet been possible to rigorously assess their fidelities using randomized benchmarking, since this requires
sequences of significant numbers of qubit operations (≳20) to be completed with nonvanishing fidelity. Here, for qubits encoded on the electron
spin states of gatedefined quantum dots, we demonstrate Bell state tomography with fidelities ranging from 80% to 89%, and twoqubit randomized
benchmarking with an average Clifford gate fidelity of 94.7% and average ControlledROT (CROT) fidelity of 98.0%. These fidelities are found to be
limited by the relatively low gate times employed here compared with the decoherence times T∗2 of the qubits. Silicon qubit designs employing fast
gate operations based on high Rabi frequencies, together with advanced pulsing techniques, should therefore enable significantly higher fidelities in
the near future.
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Quantum logic with spin qubits crossing the surface code threshold
https://doi.org/10.1038/s4158602104273w
Xiao Xue, Maximilian Russ, Nodar Samkharadze, Brennan Undseth, Amir Sammak, Giordano Scappucci & Lieven M. K. Vandersypen
Highfidelity control of quantum bits is paramount for the reliable execution of quantum algorithms and for achieving fault tolerance—the ability to
correct errors aster than they occur. The central requirement for fault tolerance is expressed in terms of an error threshold. Whereas the actual
threshold depends on many details, a common target is the approximately 1% error threshold of the wellknown surface code. Reaching twoqubit gate
fidelities above 99% has been a longstanding major goal for semiconductor spin qubits. These qubits are promising for scaling, as they can leverage
advanced semiconductor technology. Here we report a spinbased quantum processor in silicon with singlequbit and twoqubit gate fidelities, all of
which are above 99.5%, extracted from gateset tomography. The average singlequbit gate fidelities remain above 99% when including crosstalk and
idling errors on the neighbouring qubit. Using this highfidelity gate set, we execute the demanding task of calculating molecular groundstate
energies using a variational quantum eigensolver algorithm. Having surpassed the 99% barrier for the twoqubit gate fidelity, semiconductor qubits are
well positioned on the path to fault tolerance and to possible applications in the era of noisy intermediatescale quantum devices.
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Fast universal quantum control above the faulttolerance threshold in silicon
Akito Noiri, Kenta Takeda, Takashi Nakajima, Takashi Kobayashi, Amir Sammak, Giordano Scappucci, and Seigo Tarucha
Nature 2022 Jan;601(7893):338342.
doi: 10.1038/s4158602104182y.
Faulttolerant quantum computers which can solve hard problems rely on quantum error correction. One of the most promising error correction codes is
the surface code, which requires universal gate fidelities exceeding the error correction threshold of 99 per cent. Among many qubit platforms, only
superconducting circuits, trapped ions, and nitrogenvacancy centers in diamond have delivered those requirements. Electron spin qubits in silicon are
particularly promising for a largescale quantum computer due to their nanofabrication capability, but the twoqubit gate fidelity has been limited to
98 per cent due to the slow operation. Here we demonstrate a twoqubit gate fidelity of 99.5 per cent, along with singlequbit gate fidelities of 99.8
per cent, in silicon spin qubits by fast electrical control using a micromagnetinduced gradient field and a tunable twoqubit coupling. We identify
the condition of qubit rotation speed and coupling strength where we robustly achieve highfidelity gates. We realize DeutschJozsa and Grover search
algorithms with high success rates using our universal gate set. Our results demonstrate the universal gate fidelity beyond the faulttolerance
threshold and pave the way for scalable silicon quantum computers.
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leau
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The Potential Impact of Quantum Computers on Society
Ronald de Wolf
Ethics and Information Technology, 19(4):271276, 2017
https://arxiv.org/abs/1712.05380
This paper considers the potential impact that the nascent technology of quantum computing may have on society. It focuses on three areas:
cryptography, optimization, and simulation of quantum systems. We will also discuss some ethical aspects of these developments, and ways to mitigate
the risks.
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[Edited on 2512022 by leau]
[Edited on 2512022 by leau]
[Edited on 2512022 by leau]


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Probing Topological Spin Liquids on a Programmable Quantum Simulator
G. Semeghini, H. Levine, A. Keesling, S. Ebadi, T. T. Wang, D. Bluvstein, R. Verresen, H. Pichler, M. Kalinowski, R. Samajdar, A. Omran, S. Sachdev,
A. Vishwanath, M. Greiner, V. Vuletić & M. D. Lukin
https://arxiv.org/abs/2104.04119
DOI:10.1126/science.abi8794
Quantum spin liquids, exotic phases of matter with topological order, have been a major focus of explorations in physical science for the past several
decades. Such phases feature longrange quantum entanglement that can potentially be exploited to realize robust quantum computation.we use a 219atom
programmable quantum simulator to probe quantum spin liquid states. In our approach, arrays of atoms are placed on the links of a kagome lattice and
evolution under Rydberg blockade creates frustrated quantum states with no local order. The onset of a quantum spin liquid phase of the paradigmatic
toric code type is detected by evaluating topological string operators that provide direct signatures of topological order and quantum correlations.
Its properties are further revealed by using an atom array with nontrivial topology, representing a first step towards topological encoding. Our
observations enable the controlled experimental exploration of topological quantum matter and protected quantum information processing.
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The Search for the Quantum Spin Liquid in Kagome Antiferromagnets
J.J. Wen, Y. S. Lee
CHIN. PHYS. LETT. Vol. 36, No. 5 (2019) 050101
DOI: 10.1088/0256307X/36/5/050101
We systematically study the lowtemperature specific heats for the twodimensional kagome antiferromagnet, Cu3Zn(OH)6FBr. The specific heat exhibits a
T1.7 dependence at low temperatures and a shoulderlike feature above it. We construct a microscopic lattice model of Z2 quantum spin liquid and
perform largescale quantum Monte Carlo simulations to show that the above behaviors come from the contributions from gapped anyons and magnetic
impurities. Surprisingly, we find the entropy associated with the shoulder decreases quickly with grain size d, although the system is paramagnetic to
the lowest temperature. While this can be simply explained by a coreshell picture in that the contribution from the interior state disappears near
the surface, the 5.9nm shell width precludes any trivial explanations. Such a large length scale signifies the coherence length of the nonlocality of
the quantum entangled excitations in quantum spin liquid candidate, similar to Pippard's coherence length in superconductors. Our approach therefore
offers a new experimental probe of the intangible quantum state of matter with topological order.
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