In recent years at HRL, I have published fewer and fewer papers relative to the number of topics I have worked on in experimental and theoretical evaluation of quantum technologies. This is largely because the most interesting directions for quantum technologies are valuable, and that value can certainly be compromised with public release. Nonetheless, every once in a while, we release some data. Here is a reasonably complete list of papers I have worked on, with all co-authors listed, and a very brief teaser or annotation for each.
Takeaway: Spin qubits truly are scalable: when using multilevel interconnect to make an array that can scale in two dimensions, performance gets no worse.
Takeaway: Spin qubits idle well: one can nearly eliminate the impact of gradients from nuclear spins in exchange-only silicon qubits, reducing to the error of exchange pulses, which can be extremely low.
Takeaway: There exists an extremely scalable, transistor-like solution for semiconductor qubits, in which all quantum control is accomplished with DC voltages. Multiqubit logic gates are tricky, but poth possible and performant.
Invitation: Consider starting with this review paper to learn about the many kinds of semiconductor spin qubits and why they present such a compelling path to scalable quantum computing.
Takeaway: Semiconductor spin qubits have an excellent ability to be initialized and measured.
Takeaway: Single hole in MOS is a very interesting qubit possibility, although more understanding is needed to predict or engineer its electromagnetic couplings.
Takeaway: Spin decoherence in Si/SiGe cares about many nuclei, and nuclear quadrupolar splittings of 73Ge play an especially critical role.
Takeaway: How long does it take for a qubit to dephase? In many cases, including this one, it depends on how often you measure it. For a single donor qubit, frequency shifts due to nearby nuclei will drift faster or slower depending on how often the donor electron slows diffusion.
Takeaway: Strong coupling of silicon qubits to microwave photons is possible with an appropriate coupling design.
Takeaway: Strong coupling of exchange-only silicon qubits to microwave photons is possible with an appropriate bias and control strategy, but finding that strategy takes a sophisticated numeric model of the device.
Takeaway: MOS dots are so small, and isotopic purification so effective, that it is possible to isolate a single 29Si nucleus inside a dot, and to measure its dynamics. More recently, single 73Ge implanted isoelectronic nuclei have also been detected, and donor-dot hybrids have been studied for some time. Considering all control timescales and fabrication challenges, is a nucleus a better memory than the electron for semiconductor spin qubits?
Takeaway: Of spin-qubit divisions, we talk of Loss-Divincenzo vs. Exchange-Only, MOS vs. SiGe, etc. It is an oversimplification to assume LD qubits, or MOS qubits, always require a high magnetic field: this largely has to do with measurement (Elzerman vs. Pauli Spin Blockade). This pre-pandemic paper is one of the first studies of MOS LD Si qubits at low-magnetic field. The participation of nuclear diffusion has very interesting field dependence, here and in many studies since!
Takeaway: Voltage-controlled spin qubits work! "Blind" randomized benchmarking of exchange-only qubits proves both that we can program and run long circuits using triple-dot exchange-only, but also that they are performant.
"Silicon Qubits," T. D. Ladd. and M. S. Carroll, Encyclopedia of Modern Optics (Second Edition), B. D. Guenther and D. G. Steel, eds., Elsevier, 467 (2018) [preprint]
Invitation: I was invited to contribute to this encyclopedia article, and opted to increase coverage of my expertise by cowriting it with Malcolm Carroll (who has since left the field). It is now rather out of date, but the preprint here is still available.
Takeaway: Early tests of fault-tolerance for spin qubits can be done in easier-to-fabricate one-dimensional arrays.
Takeaway: Many device components coming together for MOS spin qubits.
Takeaway: In III-V semiconductor systems, self-assembled InGaAs quantum dots have such strong optical cross sections, but electrostatically gated arrays have so much more promise for quantum memory registers. This paper describes what it might take to leverage both at once.
Takeaway: Charge-noise in exchange-based qubits can have its impact reduced by choosing an insensitive bias point for control. This paper introduces the critically important "fingerprint" plot and the concept of "insensitivity," characterizing how insensitive exchange is to gate-referred voltage noise (J/|dJ/dV|).
Takeaway: In the presence of realistic amounts of loss, quantum communication protocols benefit from memory buffers and the use of high-speed, repeat-until-success entanglement sources.
Takeaway: This was the first-ever publication of a Si/SiGe isotopically enhanced triple-dot qubit undergoing calibrated exchange-only gates. Some of the noise analysis hidden in this paper remains critically important for similar devices even today.
Invitation: David DiVincenzo kindly invited me to contribute to a spring school on quantum technology at Juelich, and so I wrote this chapter summarizing many things about optical quantum dot qubits and their use for both quantum computing and quantum communication.
Takeaway: A summary of work detecting resonant phonons at the charge sensor of GaAs multi-dot devices.
Takeaway: A summary of work tuning out splittings in self-assembled quantum dots using both strain and field, to make better entanglement sources.
Takeaway: The equation for the shape of an exchange-Rabi curve in the presence of field gradients derived in this short paper has been used many, many times at HRL to analyze data. Ironically, I wrote it to offer Charlie Marcus and Jim Medford something to cite as they were doing similar work in GaAs.
Takeaway: This paper received so much attention that I wish we had broadened its scope. Its initial goal was to provide an architecture for using optical, III-V quantum dots in a complete quantum computer architecture. But the division of that architecture into layers ended up being the more valuable contribution to the literature at the time that this was published, and a more generic consideration and even standardization of layers would have been ever more highly valued.
Takeaway: A quantum network will to balance limited resources in forming connections, and benefits from methods in classical networking.
Takeaway: The result of the first HRL internship with Cody Jones, who later became an employee and then moved to Google. The decoupling scheme here is a continuous generalization of the UDD scheme. A hidden technical gem here is a proof of why UDD filter functions come out as simple Bessel functions.
Takeaway: The fluorine impurity in ZnSe had promise as a single-photon or entanglement source.
Takeaway: The first demonstration of coherent exchange oscillations in Si/SiGe double-quantum dots, upon which much of the work at HRL, Intel, and many other places is subsequently based. This paper was deliberately written to mimic the similarly seminal result in GaAs from Jason Petta, Charlie Marcus, Amir Yacoby, and others from 2005.
Takeaway: Unlike today, in 2011 little had been done in the development of semiconductor holes as qubits. Using the optical self-assempled InGaAs quantum dot system, we showed many of the expected phenomena for a hole and its hyperfine couplings, but also introduced some mysteries, most of which were later solved by others.
Takeaway: If a multi-quantum-dot cavity QED system has sufficiently high cooperativity, a single detuned optical pulse is sufficient to achieve a full entangling gate. Much of the analysis here has been replicated, especially by the CQED efforts with superconducting qubits. Unfortunately, sufficiently high cooperativities did not emerge during the time I was doing this analysis.
Invitation: Despite considerable age, this 2010 review of quantum computers still holds value today, I believe. It was by no means the first review of quantum computer technologies (those began in the 1990s), and has not been the last, but 2010 was an interesting year, as NMR and ion traps were at a kind of peak while photonics, superconductors, silicon spin qubits, and neutral atoms were just starting to emerge as realistic.
Takeaway: When you optically pump a single electron spin in an InAs quantum dot, the nuclei respond. The "sawtooth pattern" in single-quantum-dot optical Ramsey, observed by our Stanford but also many other groups, was a bizarre mystery at first, and I remain proud of this simple model for nuclear feedback I assembled to explain it.
Takeaway: If InAs quantum dots are truly to be a good quantum memory, we'd better be able to reduce dephasing with a spin-echo. Here we do that optically. Later work (especially from Oxford) has taken this to much better places. I wish I had better understood nuclear quadrupole dynamics at this time!
Takeaway: Quantum communication using error correction meets the surface code! All such schemes require less that 50% loss, but for scenarios for which that is the case, this is a very high-speed way of connecting modules. Although no one is proposing to do quantum communication this way, I think this paper was influential on multi-module quantum computation, lattice-surgery techniques, and a variety of other ways of architecting quantum networks.
Takeaway: Semiconductor photons with quantum dot memories, coupled with cavities and waveguides, just might be able to make a scalable architecture. This paper was perhaps written too soon, and so has little resemblance to things that companies like PsiQuantum and Phonotic, Inc. are doing. But it carries a similar dream.
Takeaway: The fluorine donor in ZnSe might have been a very interesting single-photon source!
Takeaway: The fluorine donor in ZnSe might have been a very interesting single-photon source!
Takeaway: The fluorine donor in ZnSe might have been a very interesting single-photon source!
Takeaway: This paper was written in 2010. Even in 2025, similar thoughts abound, noting the remarkable properties about the donor-bound exciton transitions for phosphorus in silicon and ways to detect spin-dependent transitions using transport. However, many experimental efforts have not succeeded. Many things are hard and sadly the hard parts are not well captured by this proposal.
Takeaway: I worked on (and did not sufficiently publish) a very successful quantitative model for the nuclear hyperpolarization using selective excitation of the donor-bound exciton transitions in isotopically enhanced silicon.
Takeaway: I am a coauthor of this paper about pnictide superconductors because the study used a cryogenic magneto-optical microscope I helped develop in our Stanford lab. I do not really understand superconductors.
Takeaway: A theoretical derivation of spin-echo techniques using ultrafast pulses in optical quantum dots, in anticipation of the later experimental demonstration.
Takeaway: The two papers above are review papers about how one might use InAs quantum dots, ultrafast pulses, and photonics to do many cool quantum things.
Takeaway: This Nature paper is one of my most-cited papers, since the use of ultrafast pulses to induce a spin-dependent AC Stark shift became a popular technique of many groups studying similar systems.
Takeaway: This paper is from 2008 and leverages the thesis work of my friend Rod Van Meter to make very early estimates for actual execution time of Shor's algorithm. Although out-of-date relative to better estimates given fault-tolerant gate sets and some implementation improvements made much more recently, I believe such meticulous resource counting was already important in 2008 (or really in 2005, when this was actually done), and one key conclusion has not changed: having fast physical gate times is critical for a practical utility-scale quantum computer.
Takeaway: If we could make an optical-dot, ultra-fast pulse quantum computer, it would be very fast.
Takeaway: Results from a detailed simulation of entanglement purification and entanglement swapping in a chain of quantum repeaters, using code I first drafted and then further developed by Rod Van Meter.
Takeaway: We were targeting single-photon emitters, but made these microdisk lasers on the way there.
Takeaway: Some fun and perhaps overly complicated way to leverage entangled phases of quasiclassical control fields to entangle weakly coupled qubits.
Takeaway: The above two papers show how simple, off-resonant coherent pulses in cavity QED systems can be used to entangle distant memories.
Takeaway: The primary result of my doctoral thesis, employing high-power RF decoupling pulses in pure silicon to push decoherence times above 25 seconds. This was a record until isotopically purified silicon and ion trap experiments exceeeded it some years later.
Takeaway: To make a nuclear quantum computer in semiconductors, you need to polarize nuclei far beyond thermal amounts. This has been known to be possible in GaAs for many years, but in 2005 and even today, microscopic details and limitations were poorly understood.
"Multispin dynamics of the solid-state NMR free induction decay," H. Cho, T. D. Ladd, J. Baugh, D. G. Cory, and C. Ramanathan, Physical Review B 72, 54427 (2005)
Takeaway: A nice way to analyze entanglement in nuclei as they undergo dipole-dipole-induced evolution.
"Optical detection of the spin state of a single nucleus in silicon," K.-M. C. Fu, T. D. Ladd, C. Santori, and Y. Yamamoto, Physical Review B 69, 125306 (2004)
Takeaway: The proposal at the beginning of a quest by us and many others to do single-phosphorus-in-silicon measurement optically. If you are thinking about doing this because this paper suggests it's a good idea, reach out to me first! There's a reason 20+ years have gone by without a strong experiment doing this. A hidden gem in this paper is a back-of-the-envelope analysis of a phenomenon now known as "ionization shock."
"All-silicon quantum computer," T. D. Ladd, J. R. Goldman, F. Yamaguchi, Y. Yamamoto, E. Abe, and K. M. Itoh, Physical Review Letters 89, 17901 (2002)
Also: "Solid-State Silicon NMR Quantum Computer," E. Abe, and K. M. Itoh, T. D. Ladd, J. R. Goldman, F. Yamaguchi, and Y. Yamamoto, Journal of Superconductivity: Incorporating Novel Magnetism 16(1), (2003)
Takeaway: Then and now, the known advantage of silicon for quantum computing is a clean material with long coherence times, but the known concerns are for charge noise and fabrication pitch challenges for the gates needed to create electrostatic gates. The dream of this paper was to imagine a silicon-based quantum computer in which there are no gates at all, a minimum of surfaces, and just a solid crystal. This motivation has proven worthwhile in the subsequent decades, however the actual proposal here is definitely impractical in its means for initializing and measuring qubits (and perhaps other things as well.) We can continue to dream, but I think we need to wrestle with tight-pitch fab, charge noise, and other things, although notably global RF is making something of a comeback as a path toward scalability in silicon qubit arrays.
"Solid-state crystal lattice NMR quantum computation," T. D. Ladd, Y. Yamamoto, J. R. Goldman, and F. Yamaguchi, Quantum Information and Computation 1, 56 (2001)
Also in Experimental Quantum Computation and Information: Proceedings of the CXLVIII Course of the International School of Physics "Enrico Fermi," IOS Press, Amsterdam (2002)
Also: “Quantum computation in a one-dimensional crystal lattice with nuclear magnetic resonance force microscopy,” J. R. Goldman, T. D. Ladd, F. Yamaguchi, and Y. Yamamoto, Proceedings of the 15th International Conference on Laser Spectroscopy, 333 (2002)
"Decoherence in crystal lattice quantum computation," T. D. Ladd, J. R. Goldman, F. Yamaguchi, and Y. Yamamoto, Appl. Phys. A 71, 27 (2000)
"Magnet designs for a crystal lattice quantum computer," J. R. Goldman, T. D. Ladd, F. Yamaguchi, and Y. Yamamoto, Appl. Phys. A 71, 11 (2000)
Takeaway: The series of papers above were based on "crystal lattice quantum computation", the notion that an array of spin qubits could be based on a suitably chosen, naturally grown crystal rather than a tight-pitch fabricated device, an idea of my advisor Yoshi Yamamoto. This was the start of my graduate career.
"Nonlinear AC response and noise of a giant magnetoresistive sensor," J. R. Petta, Thaddeus Ladd, and M. B. Weissman, IEEE Transactions on Magnetics 36, 2057 (2000)
Takeaway: Noise gets weird in GMR field sensors. A notable pre-qubit coauthorship between myself and Jason Petta, in my case resulting from work as an REU at UIUC prior to graduate studies.
"Knots in the æther: Theories of matter in the past and present," Thaddeus Ladd, Interface Journal 17, 3 (2000)
Takeaway: String theory looks a light like a bonkers theory for atoms as knotted vortices of aether. The latter was abandoned as being too mathematically hard, well before the invalidity of the aether would have killed it. And how's string theory doing?
"A model for arbitrary plane imaging, or the brain in pain falls mainly on the plane," Jeff Miller, Dylan Helliwell, and Thaddeus Ladd, The UMAP Journal 19(3), 223 (1998)
Takeaway: My first paper, resulting from the undergraduate Mathematical Contest in Modeling. Looking at it now, I am proud to have chosen such a silly title as a youth, and look forward to returning to such practices as I approach more elderly senility.