### How the Cross Resonance Gate Works

By Moein Malekakhlagh IBM Quantum, IBM Thomas J. Watson Research center

Pushing for higher quantum volume, and reaching the thresholds necessary for error correction, requires extremely precise elementary single- and two-qubit gates. These gates are the quantum analogue of elementary operations in classical computation. For instance, NOT is a classical single-bit operation through which the logical state is flipped, while XOR is a two-bit operation, which essentially adds the inputs modulo 2 (so, 0 + 1 = 1, but 1 + 1 = 0). However, in quantum systems, we can also perform rotations on the quantum state of the qubits. For instance, if we think of a qubit’s possible states as sitting on a sphere, where |0> sits at the top and |1> sits at the bottom, then the quantum NOT gate corresponds to a rotation around the X axis of the qubit. Analogously, the Controlled-NOT (CNOT) gate, quantum analog of the XOR, is a two-qubit gate in which the target qubit goes through a rotation around its X axis only when the control is in logical state |1> (see figure 1).

 Figure 1: Correspondence between the classical XOR and the quantum controlled-NOT (CNOT) gates. The state of the target qubit is flipped when the control is in state |1>. A generic multi-qubit quantum operation can always be decomposed into single-qubit operations and pairwise CNOTs.
Whereas single-qubit gates have reached a high fidelity (that is, 99.99%), two-qubit gates still trail behind. In superconducting circuits, two-qubit gate schemes fall into two main categories; flux tunable two-qubit gates provide fast operation and flexibility in frequency allocation at the expense of flux noise. Microwave-activated gates, meanwhile, employ fixed-frequency qubits and are controlled via microwave pulses.

Cross-resonance (CR) [1, 2] is a microwave-activated two-qubit gate performed by driving one of the qubits (control) at the frequency of the other (target) (see figure 2). The qubits are connected through effective capacitors in a superconducting circuit. The CR drive protocol produces entanglement between the qubits, mainly through an interaction of the form ZX—rotation of the two-qubit wavefunction around the Z-X axis—with which a CNOT gate can be calibrated. Simplicity in implementation, resilience to noise and acceptable overhead has made architectures based on CR gates with fixed-frequency transmon qubits a favorable choice for current IBM processors.

 Figure 2 : (top left) IBM Hummingbird processor based on CR architecture. (bottom left) A schematic of the qubit layout for the processor, where each node represents a “physical” transmon qubit and each edge is the pairwise coupling. (top right) Schematic of a CR pair with frequencies $\omega_{c,t}$, anharmonicities $\alpha_{c,t}$, effective capacitive coupling J and drive amplitude $\Omega (t)$ . The drive frequency is set to be the same as the target qubit frequency. (bottom right) Energy diagram in the rotating frame of the drive. Vertical (horizontal) ladders show states of the control (target) qubit. The desired CR interactions are the ZX and the IX rates found as the effective coupling between the adjacent ladders (shown with a question mark).

Optimizing the CR gate fidelity requires an accurate understanding of the underlying interactions as well as the ability for precise control. Initial proposals [1, 2] considered a two energy level model for the qubits. This assumption captures only the dominant two-qubit interactions, such as the ZX rate and the drive-induced frequency shift on the control qubit known as Stark shift. Since the CR gate is implemented using weakly anharmonic transmon qubits, there are additional unwanted interactions due to higher quantum states of the qubits (figure 2). Therefore, more accurate multi-level modeling of the aforementioned error terms is necessary [3, 4, 5].

There are two main approaches towards understanding involved time-dependent quantum interactions. First, we could attempt to do precise numerical solution of the dynamics. This is essential in making reliable comparisons with experiment. However, it is typically not straightforward to gain immediate intuition about the nature of this system’s underlying interactions. In our recent paper [5], we used a perturbative approach, called Schrieffer-Wolff perturbation theory (SWPT), to solve for an effective gate Hamiltonian starting from a multi-level physical model for the system. Perturbation here means that we add the effective interactions, in this case due to the CR drive, as a small addition to the static Hamiltonian of the qubits.

In the SWPT method, we take an average of the off-resonant high-frequency states, arriving at effective low-frequency models of these interactions for the system. For the CR gate, this means that the impact of all higher qubit states is encoded in the effective two-qubit interaction rates. Contrary to rotating-wave approximation, which discards off-resonant interactions, SWPT accounts for their effect by solving for a series of perturbative frame transformations. The choice of effective frame is set by the drive scheme for the gate. For the CR gate, where the drive is resonant with the target qubit frequency, the effective frame is block-diagonal (a matrix whose diagonal elements are square matrices, and all other elements are 0) with respect to the control qubit, resulting in an effective Hamiltonian of the form: [3, 5]

$$\hat{H}_{eff} = \omega_{ix} \frac{\hat{I}\hat{X}}{2} + \omega_{iz} \frac{\hat{I}\hat{Z}}{2} + \omega_{zi} \frac{\hat{Z}\hat{I}}{2} + \omega_{zx} \frac{\hat{Z}\hat{X}}{2} + \omega_{zz} \frac{\hat{Z}\hat{Z}}{2}. \quad (1)$$

The CNOT gate is typically calibrated using the ZX and IX rates, while the rest result in coherent error for the gate. State of the art CR implementation using transmon qubits can approximately result in 1 MHz of IX, 2 MHz of ZX, 10 MHz of ZI, 20 KHz of IZ and 100 KHz of ZZ interactions (see figure 3).

The effective gate parameters in Eq. (1) depend on qubit-qubit frequency difference (detuning)  $\Delta_{ct}$, qubit anharmonicities  $\alpha_c,\alpha_t$ (that is, the anharmonicity of the control and of the target, respectively), exchange coupling $J$ and drive amplitude $\Omega$ (see figure 2). For instance, the leading order desired ZX and parasitic ZZ rates are found as:

$$\omega^{(1)}_{ZX} = \frac{J\Omega}{\Delta_{ct} + \alpha_c} - \frac{J\Omega}{\Delta_{ct}}, \quad (2)$$

$$\omega^{(0)}_{ZZ} = \frac{J^2}{\Delta_{ct} - \alpha_t} - \frac{J^2}{\Delta_{ct} + \alpha_c}. \quad (3)$$

According to Eqs. (2) and (3), effective CR rates are very sensitive to the ratio of qubit-qubit detuning and anharmonicity and various regions of operation emerge [4, 5] (see figure 3). To maximize the intended ZX rate, the detuning must be in regions II and III of the graph below—close to the positive side of the straddling regime 0 < $\Delta_{ct}$ < $- \alpha_{c}$ . The unwanted ZZ rate, however, is maximized close to the resonance with the third level of each qubit, i.e. $\Delta_{ct} = \alpha_c$, and  $\Delta_{ct} = -\alpha_t$, and suppressed in the middle of regions I and II.

 Figure 3 (from Ref. [5]): ZX and ZZ rates as a function of drive Ω and qubit-qubit detuning Δ_ct. The effective rates are calculated using SWPT up to fourth order in drive amplitude Ω.

The average gate error is what typically governs the performance of any gate, and we can estimate it experimentally using randomized benchmarking (RB) [6, 7]. Generally, to optimize for average CR error, one needs to maximize the ZX (IX) rate and minimize other unwanted interactions in Eq. (1). One strategy is to employ an echo pulse sequence as shown in figure 3 [8, 9]. It consists of two CR pulses with opposite amplitude, accompanied with $\pi$ rotations on the control qubit. The echo creates constructive/destructive interference between the effective gate parameters. Through this procedure, it removes unwanted rates such as ZI, ZZ and IX, at the expense of inducing higher order error terms. We find that optimal choices for qubit-qubit detuning are achieved in the middle of regions II, I and III, consistent with the behavior of ZX and ZZ rates in figure 4. For typical qubit anharmonicity of -330 MHz, these sweet spots are approximately centered around -100, 100 and 200 MHz, respectively.

 Figure 4 (from Ref. [5]): An echo sequence consisting of two CR tones with flipped drive amplitude with two π pulses on the control qubit [8, 9] and the resulting average gate error.

An alternative gate calibration based on the CR architecture is to tune a direct CNOT gate without echoing [10, 11]. To achieve this, we want no action on the target qubit when the control is in state |0>  and a $\pi$ rotation on the target when the control is in state |1> . For this calibration, the IX rate is not an error term anymore, and the gate speed is determined by IX-ZX rates resulting in a faster operation. Equipped with interference couplers to suppress the static ZZ rate, and using a virtual frame change to cancel out Stark shifts, Ref. [10] demonstrates a 180 ns gate with 99.77% gate fidelity.

In a quantum processor, CR pairs are connected to neighboring spectator qubits that can influence the gate operation due to frequency crowding—the operating frequencies between neighboring qubits being close enough to cause unwanted interactions. This poses further restrictions on the optimization of both two-qubit gate fidelity as well as multi-qubit interactions that affect holistic measures such as quantum volume [12]. An immediate three-qubit extension of the CR gate involves a third qubit that is either coupled to the control (control spectator) or the target qubit (target spectator). Applying SWPT on these toy problems reveal a series of two- and three-qubit frequency collisions (resonances) that need to be avoided in processor design (see figure 5).

In conclusion, CR offers a very promising platform for two-qubit gate implementation. State of the art calibrations of the CR gate using IBM quantum processors can reach 99.40% fidelity with overall gate time of approximately 280 ns for an echo sequence [10], and 99.78% fidelity with an overall gate time of 180 ns for a direct CNOT with interference couplers [11]. Further improvement of the gate fidelity requires a continual interplay between theory and experiment.

 Figure 5 (from Ref. [5]): An example of three-qubit effective rate with a control spectator qubit as a function of spectator-target detuning (order: s⊗c⊗t ). We have categorized numerous multi-qubit collisions [5] (II denotes adjacent and III denotes between all three qubits).

Acknowledgements: Optimal control techniques for CR gate has been a long-standing research and engineering effort among the IBM quantum team, for which we appreciate helpful discussions with and acknowledge earlier works by Easwar Magesan, Emily Pritchett, David C McKay, Sarah Sheldon, Ken Wei, Abhinav Kandala, Neereja Sundaresan, Peter Jurcevic, Isaac Lauer, Jerry M Chow, and Jay M Gambetta.

References:

[1] GS Paraoanu, “Microwave-induced coupling of superconducting qubits”. Physical Review B, 74(14):140504, 2006.

[2] Chad Rigetti and Michel Devoret. “Fully microwave-tunable universal gates in superconducting qubits with linear couplings and fixed transition frequencies". Physical Review B, 81(13):134507, 2010.

[3] Easwar Magesan and Jay M. Gambetta. “Effective Hamiltonian models of the cross-resonance gate”. Phys. Rev. A, 101:052308, May 2020.

[4] Vinay Tripathi, Mostafa Khezri, and Alexander N. Korotkov, “Operation and intrinsic error budget of a two qubit cross-resonance gate”. Phys. Rev. A, 100:012301, July 2019.

[5] Moein Malekakhlagh, Easwar Magesan, and David C. McKay. “First-principles analysis of cross-resonance gate operation”. Phys. Rev. A, 102:042605, Oct 2020.

[6] Easwar Magesan, Jay M. Gambetta and Joseph Emerson. “Scalable and robust randomized benchmarking of quantum processes”. Phys. Rev. Lett. 106.180504, 2011

[7] Easwar Magesan, Jay M. Gambetta and Joseph Emerson. “Characterizing quantum gates via randomized benchmarking”. Phys. Rev. A, 85:042311, 2011

[8] Sarah Sheldon, Easwar Magesan, Jerry M Chow, and Jay M Gambetta. “Procedure for systematically tuning up cross-talk in the cross-resonance gate”. Phys. Rev. A, 93(6):060302, 2016.

[9] Neereja Sundaresan, Isaac Lauer, Emily Pritchett, Easwar Magesan, Petar Jurcevic and Jay M. Gambetta. “Reducing unitary and spectator errors in cross-resonance with optimized rotary echos”. Phys. Rev. X Quantum 1.020318.

[10] Petar Jurcevic, Ali Javadi-Abhari, Lev S Bishop, Isaac Lauer, Daniela F. Bogorin, Markus Brink, Lauren Capeluto, Oktay Gunluk, Toshinari Itoko, Naoki Kanazawa et al. “Demonstration of  quantum volume 64 on a superconducting quantum computing system”. Quantum Science and Technology, 6(2):025020, 2021.

[11] Abhinav Kandala, Ken X. Wei, Srikanth Srinivasan, Easwar Magesan, Santino Carnevale, George A. Keefe, David Klaus, Oliver Dial and David C. McKay. “Demonstration of a high-fidelity CNOT for fixed-frequency transmons with engineered ZZ suppression”.

[12] Andrew W. Cross, Lev S. Bishop, Sarah Sheldon, Paul Nation and Jay M. Gambetta. “validating quantum computers using randomized model circuits”. Phys. Rev. A. 100:032328, 2019

### Introducing: A Motherboard for Quantum Computers

By Eric Michiels

As quantum systems scale up, high fidelity and high-speed qubit readout—without bulky components—is a critical success factor. An IBM Research Team led by Baleegh Abdo has demonstrated the proof-of-principle of a high-performance qubit readout motherboard, free from the disturbances of hardware like circulators and isolators.

Reading out qubits is a huge challenge: stable superconducting qubits operate in a dilution refrigerator at 15 mK, but must be reliably measured using room-temperature electronics.  In order to carry out measurement today, quantum computers employ low-power microwave signals and then amplify those outgoing signals using Josephson Parametric Amplifiers (JPAs) followed by High Electron Mobility Transistor (HEMT) amplifiers—learn more about those here. However, the amplification chain comes with bothersome noise, against which the qubits must be isolated. In state-of-the-art systems, researchers solve these problems by incorporating additional microwave devices at the 15 mK stage, such as circulators and isolators, which route readout signals in a single direction, i.e., from input to output, and protect the qubits by blocking some of the noise coming from the readout chain, respectively. While this solution might enable high-fidelity qubit readout, the reliance on these large microwave components introduces a scalability limitation—which is an issue when the IBM Quantum team has their eyes set on a million-qubit quantum computer in the coming decades. In short, qubit readout chains urgently require innovative improvements.

“The challenge with the current technology is that we use commercial magnetic isolators and circulators that do work well in cryogenic circumstances, but have the disadvantage of being big in size, expensive, and heavy. If you have a lot of them, because you would need to read out a lot of qubits, they will occupy a large volume in our dilution fridges,” said Baleegh Abdo, Master Inventor and Research Staff Member on the IBM Quantum team. Moreover, these isolators and circulators are magnetic, which can have adverse effects on superconducting qubits, further requiring that the quantum chips be placed inside magnetic shield cans, which inevitably degrade the readout fidelity due to the separation they impose between the various components in the readout chain.

Fortunately, a team of IBM Yorktown and Almaden, led by Abdo, are inventing new on-chip devices to eliminate these big magnetic components. Josephson Directional Amplifiers (JDA) amplify signals in only one direction, replacing the need for combining circulators with JPAs,  and Josephson Isolator (JIS) devices work to block output noise in the microwave frequency band used for readout. Both of these Josephson junction-based directional devices are compatible with superconducting circuits, devoid of magnetic materials, and can be operated using a single microwave drive or pump.  They are constructed by using two Josephson Parametric Converters (JPCs), a Josephson Junction-based amplifier. Josephson junctions are lossless, nonlinear inductors named after Brian David Josephson, a Welsh theoretical physicist; If you want to learn more, check out this post.

“Our new solution uses technologies that allow for miniaturization while being compatible with the superconducting qubit technology,” said Abdo.

The team envisioned creating a readout motherboard that combines these Josephson Junction-based devices with other on-chip microwave components and wire bonding them to the printed circuit board. And, indeed, at the 2020 American Physical Society March Meeting, they successfully demonstrated the construction and testing of such a motherboard.

However, since this motherboard was mainly a proof-of-concept, there’s still a considerable amount of work left before it’s ready for incorporation into an IBM Quantum device. Some of the questions which the team had to tackle are: How do we improve its performance? How do we integrate it, and how do we facilitate its packaging?

The team provided some possible answers to these important questions at this year's APS March meeting (2021).

A first improvement that the team made to both the JIS and JDA devices was getting rid of wire bonds. Leveraging IBM’s historical experience with bump bonds, the researchers produced JIS and JDA devices that they bump bonded directly to the PCBs. The bump bonds not only deliver incoming and outgoing signals, they also ground chip ports, carry the chip mechanically (you can think of these bonds as “glue”) and provide good impedance matching for broadband devices. The bump bond strategy is not brand new—they found use in the Quantum Hummingbird Processor, although in that case the quantum chip was not directly bump bonded to a PCB but to a silicon interposer, which, in turn, was bump bonded to a PCB.  A second improvement was increasing the JPC frequency (that is used to build the JIS and JDA devices) to better match the qubit readout frequency, requiring an update of the JPC design. Third, the team increased the strength of the couplings of the JPCs to the intermediate transmission line that is part of the JIS and JDA devices.

The tests showed great results: the JISs transmit signals in one direction with little added loss of about 0.5 dB when they are on versus off, whereas they attenuate signals in the opposite direction by more than 20 dB within a 10 MHz bandwidth.

“We get a Josephson Isolator that allows the signal to propagate in one direction… and it blocks the signals that are propagating in the opposite direction. So, this is an important component that protects the qubit against noise coming from the output chain," said Abdo.

 Schematic of a JDA
The JDA was also subject to improvements. In addition to being bump-bonded to the PCB in a similar manner as the JIS, the research team developed another breakthrough innovation: for the first time, they realized an on-chip 90-degree hybrid for the high-frequency pump needed for amplification. This achievement was made possible due to the use of the bump bonding providing good impedance matching for high frequency components. The new JDA device is capable of amplifying signals by 18 dB in one direction in a bandwidth of 3 MHz, whereas signals in the opposite direction are slightly attenuated. Here also, the insertion loss is limited to approximately 1 dB.

Core to these two directional devices is the JPC, a three-wave lossless mixing device operating at the quantum noise limit with two differential modes (often called “a” and “b”) that couple to a Josephson Ring Modulator or “JRM”. A JRM consists of four relatively large Josephson Junctions assembled in a loop and shunted by linear inductance. The differential modes are enabled by coupling two orthogonal microwave resonators having different resonance modes “a” and “b” to the JRM.

Apart from the differential modes, the JRM has a common mode that is driven off-resonance by the pump, which is a strong coherent microwave tone. The a-modes of the two JPCs in the JIS and JDA devices are coupled via a 90-dgree hybrid and the b-modes are coupled to an intermediate transmission line and 50 Ohm terminations. In the case of the JIS, the JPCs are operated in mixing or conversion mode, while in the case of the JDA, they are operated in amplification mode. Please look at the illustration figures in the sidebar. In short, JPCs which include the JRMs are used for building both the JIS and JDA devices, but the assembled devices operate in different ways.

 Schematic of a JIS
While all of these deliverables are a huge step forward in the journey towards building a universal fault tolerant quantum computer, further challenges are on the horizon, such as reducing the size of the motherboard and increasing the bandwidth of the JPCs so the JDA and JIS can support frequency multiplexed qubit readout. Multiplexing allows a single set of readout circuitry to measure a large number of qubits, which is key because the number of high-coherent qubits in quantum processors is expected to keep growing over the next years.

Abdo said: “In the long run, after we overcome both of these technological and research challenges, we believe we can use the motherboard device in much larger systems than 1000 qubits. And with our team we are currently designing JPCs that are more compact and have a larger bandwidth. We hope to get some preliminary results in the coming months."

Solving these issues successfully is of critical importance to scaling superconducting quantum hardware. Another interesting evolution is the possibility of moving from aluminum to niobium junctions, when building these directional devices.

“Since our current JDA and JIS devices are based on aluminum junctions, they must be tested and operated at temperatures much lower than 1 K. At some point, it would be nice to build them using niobium junctions, which will make them more resilient, have higher saturation power, and easier to test and characterize,” said Abdo.

This is just one of a few solutions to tackle the challenge of scaling up and miniaturizing superconducting quantum systems. IBM's team might converge on a solution like the one that Abdo’s team is working on, i.e., a motherboard which supports multiplexed qubit readout, which integrates multiple devices, or rely on state-of-the-art research into other components as a potential alternative.

Ultimately, the IBM team will draw on the best available research in the field when it comes to finding a solution to the problem of scaling up. As for the motherboard, down the road, it is likely that it will also host extra functional components, just like the classical version of the motherboard in our general-purpose computers of today.

### Finding the Ground State of Quantum Many-Body Systems

By Ieva Čepaitė, University of Strathclyde, Glasgow

Ground states of many-body quantum systems (especially systems made of spins) are cool – and I don’t just mean their temperature. Finding a system's ground state is often equivalent to solving a very hard optimization problem. Being able to prepare and manipulate such ground states is also incredibly important in understanding various quantum phenomena, such as high-temperature superfluidity and superconductivity as well as, say, topological quantum computing.

So—how do we do it? One way is counterdiabatic driving, and it's a lot like running with a glass of water on a tray. Let me explain.

We think of quantum states in terms of their Hamiltonian, an operator that represents a system's potential and kinetic energy as an equation. In order to represent the ground state, we begin with a pared-down, time-dependent version of the Hamiltonian called H(0). This state is easy to prepare, but isn't particularly useful—it's basically just a snapshot of the system. However, we can then evolve this Hamiltonian for a time T to Hamiltonian H(T)—like combining snapshots into a movie—whose ground state encodes something interesting (say, the solution to the aforementioned optimization problem or some novel phase of matter). If we perform this evolution slowly enough, we can keep the quantum system in the instantaneous ground state for every point in time (assuming all ground states are non-degenerate, meaning they represent unique energies throughout the evolution).

Importantly, the change from H(0) to H(T) has to be slow enough. This is because of something called the Quantum Adiabatic Theorem [1], which tells us, simply, that functions describing states evolving slowly will adapt to the slowly-changing conditions. However, if the time T is too short, the system has a high chance of transitioning out of the ground state into an excited one. Preparing ground states in this way, or adiabatically, is difficult; evolving a quantum system for very long times makes it difficult to maintain coherence, but evolving it too quickly excites it out of the required state. The question then becomes how to speed up these Hamiltonian dynamics without exciting unwanted transitions.

One way of achieving this is to use something called counterdiabatic driving (CD) [2], which involves counteracting potential excitations by applying an external drive. The concept of CD can be made clear using a very popular analogy (see Fig. 1):

 This may LOOK like a waiter's hand carrying a tray with a glass of water (or whatever suits your fancy), but really it's a quantum system in (A) its ground state at t = 0, (B) evolving via time-dependent Hamiltonian H(t) and (C) evolving via H(t) with an added counterdiabatic drive.

Imagine a waiter carrying a glass of water on a tray from the bar to a customer at a table. When the waiter starts moving they accelerate and induce a ‘force’ on the glass, making it wobble and splash around. The faster the waiter moves, the stronger the force, so the only way to keep the glass from spilling is to move very slowly. One way the waiter can counteract this force and walk quicker is by tilting the tray with the glass so as to keep the water from spilling, modifying the tilt as they weave around the restaurant to account for the shifting direction and magnitude of the force. Note that we don’t care what position the glass is while it’s being carried, only that it is upright, still, and full of water at the beginning and end of its journey.

If we now imagine the glass of water and tray to be the quantum system, then its ground state at time t=0 is standing still and upright on the bar and its ground state at t=T is standing perfectly still and upright on the customer’s table. The time-dependent Hamiltonian is, therefore, the path of the waiter from the bar to the customer. When the waiter moves too fast, the glass wobbles – equally, when the Hamiltonian changes too quickly in time, the quantum system may "wobble" too much and get excited from the ground state. The trick in the quantum case is to try and imitate what the waiter does and tilt the tray.

As you may have already guessed, this tilting is a stand-in for the idea of CD. As in the case of the waiter, we want to counteract the possible excitations that varying the Hamiltonian with time induces in the quantum state, and we can do this by applying an external ‘drive’ (tilt of the tray) on top of the original Hamiltonian. In essence, if we could exactly derive the form of these possible excitations throughout the state evolution, then we would know the CD exactly, too. This would allow us to perform something called transitionless driving, meaning that no excitations would even be possible no matter how quickly our Hamiltonian changed. This is a consequence of work done by Michael Berry [3], who showed that there can be a Hamiltonian which doesn’t allow for transitions to other states regardless of speed, although this Hamiltonian is hard to find. Sounds fantastic, right?

Well, the issue here is that deriving the exact form of the CD required to have lossless Hamiltonian evolution is very very hard, and we’d need to have exact knowledge of the entire energy spectrum of the system at every point in time to be able to do this. Even for systems of only a few spins (or qubits, should you prefer) and very simple dynamics this becomes almost impossible. In practice, we need to try something a little different: approximate CD.

A good example of this is the approach in a paper by D. Sels and A. Polkovnikov [4], where they take inspiration from the waiter example in a more practical way. When the waiter tilts the glass as in Fig. 1, they don’t actually know the exact microscopic movements of each molecule of water in the glass that they need to counteract, only the approximate direction and magnitude of the tilt to keep the glass from tipping over. In this vein, Sels and Polkovnikov propose an approximate CD protocol where we can make a decent guess for the form of the CD based on the system we’re working with and can optimize it by treating it as a sort of perturbation theory. These approximate drives – extra terms in the Hamiltonian like an additional magnetic field gradient or electric field pulse – can be incredibly effective even to first-order, as in the case of the waiter and they can be applied to essentially any closed system with a time-dependent Hamiltonian (though not always as efficiently depending on the application at hand).

Several approaches now exist that are inspired by approximate CD in one way or another for various applications (see, for example, this paper where a two-parameter CD drive is applied to investigating quantum phase transitions in for the p-spin model [5]). It looks like a promising new direction with many improvements still to be made, applications in many-body physics, and even potential benefits for optimization problems.

[1] A. Childs, LECTURE 18: The quantum adiabatic theorem, University of Waterloo Quantum Algorithms course, 2008
[2] S. A. Rice, M. Demirplak, Adiabatic Population Transfer with Control Fields, J. Phys. Chem. A 107, 46, 9937–9945, 2003
[3] M.V. Berry, Transitionless quantum driving, J. Phys. A: Math. Theor. 42 365303, 2009
[4] D. Sels, A. Polkovnikov, Minimizing irreversible losses in quantum systems by local counterdiabatic driving, 2 PNAS  114 (20) E3909-E3916, 2017
[5] L. Prielinger, A. Hartmann, Y. Yamashiro, K. Nishimura, W. Lechner, H. Nishimori, Two-parameter counter-diabatic driving in quantum annealing, Phys. Rev. Research 3, 013227, 2021

### Op Ed: Quantum Intranet is Key to Scaling Quantum Hardware

By Jerry Chow

Classical computers just won't cut it when it comes to tackling the greatest challenges in biology and medicine. Even accurately simulating the relatively simple caffeine molecule, far simpler than DNA or even proteins, would take an impossibly large classical computer. That's why we need a paradigm shift in the field of computing, like a shift from the steam locomotive to a starship's warp drive. That's why we need quantum computers.

At IBM Quantum, we've already started building quantum computers based on superconducting transmon qubit technology, and have been making this transformative technology available to the world. Back in 2016, we made history when we put our quantum computers on the Cloud for anyone from enterprise developers to students to program. Last fall, we announced an aggressive roadmap toward building a 1121‐qubit device by 2023. However, even that device will not be large enough to solve science's greatest challenges. That will require fault‐tolerant quantum processors containing potentially millions or even billions of qubits working together.

The technology required to build a processor with a few million superconducting qubits will likely surpass the limits of dilution refrigerator scaling (Figure 1), so we have to come up with alternative ideas for scaling up our devices efficiently. We think that constructing the fault‐tolerant quantum computers of the future will require a distributed approach similar to today's supercomputers, where smaller processors each in their own fridge share quantum information coherently and without loss to tackle problems in parallel. This will only be possible if we can develop quantum interconnects to link processors together into a quantum intranet.

This requirement for a quantum intranet is distinct from the more commonly discussed context of a quantum Internet. Quantum communications advances typically center around data transfer security such as long‐distance entanglement and quantum key distribution. IBM has long been involved in this field; IBM researchers debuted the BB84 QKD protocol in 1984 [1], for example. However, we must not lose sight of the fact that short‐distance quantum interconnect technology may play a key role in extending computational systems to a scale sufficient for solving practical problems. A quantum Internet connecting and interfacing such scaled quantum computers would follow as a next step to enable new applications. [2].

Quantum interconnects capable of supporting our vision of a quantum intranet will require fundamental advances in physics. The no‐cloning theorem makes it impossible to convert an arbitrary, unknown quantum state into classical bits and then use these bits to recreate that exact state elsewhere, so we must devise schemes that stay coherent as we transfer quantum information from the states of superconducting qubits onto the states of photons, transmit these photons over wires, and recreate the quantum state on the superconducting qubits of another processor.

At the same time, the microwave photons we use to manipulate and read out our superconducting qubits require wiring overheads, and a significantly different cryogenic infrastructure to permit coherent transfer of quantum states even over short distances. Hence, converting microwave photons into optical photons allows for low‐loss quantum state transfer through fiber optic infrastructure that the telecom industry has spent decades maturing.

Academic groups have been working for over a decade to transfer quantum information from microwave to optical photons in a coherent manner with a variety of systems and mechanisms, and while this has not been conclusively demonstrated, progress has been made [3]. At IBM Research's Thomas J. Watson Research Center in Yorktown Heights, NY, we have been developing a silicon‐germanium microwave‐optical transducer (funded by the Army Research Office and the Laboratory for Physical Sciences) that's integrated with our own transmon qubit platform. Meanwhile, our IBM Research lab in Zurich is exploring a different platform, to develop piezo‐optomechanical transducers in gallium phosphide. Implementing and perfecting each of these solutions will be challenges on their own—plus, we must devise distributed error correcting codes to run on these systems.

 IBM is developing a suite of scalable and increasingly larger and better processors, with a 1000‐plus qubit device targeted for the end of 2023. In order to house even more advanced processors to the thousands and eventually million‐plus qubit systems of the future, the IBM Quantum team is building a dilution refrigerator larger than any currently available commercially. (Credit: Connie Zhou for IBM)

Our primary research focus is in scaling up transmon qubit processors, but the issues surrounding scale‐up are important to every qubit architecture. We think that quantum interconnect research, and a quantum intranet, will be the likely solution to scale‐up across the field. The community has already deemed quantum interconnects as "crucial for sustained development of a national quantum science and technology program" [4]. Other recent work involving connecting spatially separated qubits with microwave includes Zhong, Y. et al.’s “Deterministic multi‐qubit entanglement in a quantum network,” [5], and Magnard, P. et al.’s “Microwave Quantum Link between Superconducting Circuits Housed in Spatially Separated Cryogenic Systems.” [6]

Given the importance of these devices, and the impact of scale, we cannot tackle these challenges alone. In August of last year, the US Department of Energy announced that it would allocate up to \$625 million in funding over five years to support multidisciplinary Quantum Information Science (QIS) Research Centers. We expect that the work carried out at these centers will be essential to realizing the quantum intranet. Specifically, IBM Quantum will work with the Q‐NEXT center led by Argonne National Laboratory to co‐design technological building blocks and system needs that will allow us to realize these quantum interconnects.

The IBM Quantum team is developing quantum computers because we think that these devices have the capability to change the world, but seeing them through to completion will take innovative solutions to physics problems that physicists have never faced before. If we can realize quantum interconnects and a quantum intranet, then we think we have a clear path to making these devices, and their abilities, a reality.

References:

[1] , : Quantum cryptography: public key distribution and coin tossing. Theor. Comput. Sci. 560(1), 711 (1984). https://doi.org/10.1016/j.tcs.2014.05.025

[2] K: The quantum internet. Nature (2008). https://doi.org/10.1038/nature07127

[3] , et al.: Quantum transduction of optical photons from a superconducting qubit. Nature (2020). https://doi.org/10.1038/s41586‐020‐3038‐6

[4] , et al.: Development of Quantum InterConnects for Next‐Generation Information Technologies (2019). https://arxiv.org/abs/1912.06642

[5] et al.: Deterministic multi‐qubit entanglement in a quantum network. Nature. 590, 571575 (2021). https://doi.org/10.1038/s41586‐021‐03288‐7

[6] et al.: Microwave Quantum Link between Superconducting Circuits Housed in Spatially Separated Cryogenic Systems. Phys. Rev. Lett. 125, 260502 (2020). https://link.aps.org/doi/10.1103/PhysRevLett.125.260502

### What Were Your Favorite APS March Talks?

Like many other physicists, we spent the past week in the APS March meeting, sitting in video conference rooms watching PowerPoints, wondering if we should maybe have joined a different video conference to watch a different PowerPoint, all while worrying about how our own presentation would go and hoping that our pet wouldn't make noise during it. But the dust is finally settling. Despite both the chaos of trying to keep track of dozens of quantum computing talks combined with the fatigue that comes with forgetting to get up from our chair for an entire day, we were able to sit in on a host of amazing talks about quantum hardware.

We've roped together a few talks we liked that represent some of the more interesting pieces of work to come out of the meeting, showing advances in qubit architectures, control mechanisms, and other hardware topics. We've intentionally left out any IBM results so as not to look tacky (most of the blog's authors work there), but feel free to discuss any IBM results in the comments. This isn't a comprehensive list or a list of "best," and given how many talks there were, we definitely left off some other cool presentations; these are just some of the ones we noticed and wanted to share. Sound off in the comments (or on Twitter or elsewhere!) with what you thought about the meeting, these talks, or any other research that got you thinking this past week.

Presenter: Farah Fahim (Fermi National Accelerator Laboratory)
Abstract: Deadzone-less, large area camera systems can be assembled by connecting wafer scale sensors to an array of almost reticule size, 4-side tileable, edgeless readout integrated circuits (ROIC). The design of truly edgeless ROICs, with active area extending to their edges, has been made possible with the advent of 3D integration technologies with high-density interconnects, which enable new routing and I/O paradigms. Despite their obvious potential, the realization and widespread development of truly edgeless ROICs to create gapless dectors has faced several obstacles including manufacturing processes related to 3D integration, identification of known good dies and edgeless design methodologies. The advancements required in "thru via" approaches and wafer bonding and its impact on developing integrated electronics required for Quantum and AI will be discussed.

We thought it was really interesting to see how other physicists have dealt with scaling up experiments to ridiculous levels of complexity, and provides some inspiration (and hope!) for the future of quantum devices.

Presenter: Jacob Blumoff (HRL Laboratories LLC)
Abstract: Existing architectures for silicon quantum-dot qubits have enabled high-fidelity state preparation and measurement1, low-error randomized benchmarking2, and millisecond-scale dynamical decoupling3. To facilitate improved control of the underlying electrostatic potential and scaling to larger arrays, we present a more advanced design called Single-Layer Etch-Defined Gate Electrode, or “SLEDGE.” These devices feature a single layer of non-overlapping gate electrodes and employ vias to break the plane to backend routing. Using this process, we demonstrate exchange-only qubit initialization, measurement, and randomized benchmarking with fidelities that compare favorably to the previous design. This architecture provides a path to scalable and high-performance silicon-based quantum devices.
1. Blumoff et al., APS March Meeting 2020, R38.00001
2. Andrews et al., Nat. Nano. 14, 747 (2019)
3. Sun et al., APS March Meeting 2020, L17.00008

This talk was a great intro on exchange-only qubits in Si/SiGe. Blumoff discussed scalability and the fabrication aspect, including improvement made with vias—and the new architecture performs about as well as the architecture it was attempting to improve upon.

Presenter: Phillipe Campagne-Ibarcq (Quantic Team, Inria Paris)
Abstract: In 2001, Gottesman, Kitaev and Preskill (GKP) proposed to encode a fully correctable logical qubit in grid states of a single harmonic oscillator. Although this code was originally designed to correct against shift errors, GKP qubits are robust against virtually all realistic error channels. Since this proposal, other bosonic codes have been extensively investigated, but only recently were the exotic GKP states experimentally synthesized and stabilized. These experiments relied on stroboscopic interactions between a target oscillator and an ancillary two-level system to measure non-destructively the GKP code error syndromes.
In this talk, I will review the fascinating properties of the GKP code and the conceptual and experimental tools developed for trapped ions and superconducting circuits, which enabled quantum error correction of a logical GKP qubit encoded in a microwave cavity. I will describe ongoing efforts to suppress further logical errors, and in particular to avoid the apparition of uncorrectable errors stemming from the noisy ancilla involved in error syndrome detection.

This talk started with a very clear introduction to GKP states, and the experiments themselves were amazing. The degree of technical skill that went into making and manipulating these states was really cool. Plus the states are really cool looking.

Presenter: Andras Gyenis (Princeton University)
Abstract: Encoding a qubit in logical quantum states with wavefunctions characterized by disjoint support and robust energies can offer simultaneous protection against relaxation and pure dephasing. One of the most promising candidates for such a fully-protected superconducting qubit is the 0-π circuit [Brooks et al., Phys. Rev. A 87, 052306 (2013)]. Here, we realize the proposed circuit topology in an experimentally obtainable parameter regime and show that the device, which we call as the soft 0-π qubit, hosts logical states with disjoint support that are exponentially (first-order) protected against charge (flux) noise. Multi-tone spectroscopy measurements reveal the energy-level structure of the system, which can be precisely described by a simple two-mode Hamiltonian. Using a Raman-type protocol, we exploit a higher-lying charge-insensitive energy level of the device to realize coherent population transfer and logical operations. The measured relaxation (T_1 = 1.6 ms) and dephasing (T_R = 9 μs, T_2E = 25 µs) times demonstrate that the soft 0-π circuit not only broadens the family of superconducting qubits, but also constitutes an important step towards quantum computing with intrinsically protected superconducting qubits.

The 0-π qubit lives! It was great to see how far along protected qubits have come. We're also still laughing about the authors claim that the qubit is "so well protected, even from experimentalists."

Presenter: Mahdi Naghiloo (MIT)
Abstract: We propose a new scheme that combines parametric mode conversion and adiabatic techniques in a pair of coupled nonlinear Josephson junction transmission lines to realize broadband isolation without magnetic elements. The idea is to induce an effective unidirectional parametric coupling between two otherwise orthogonal modes of propagation and engineer the dispersion to have an adiabatic conversion between two modes. Our realistic analysis suggests more than 20 dB isolation over an octave of bandwidth (4-8 GHz) with less than 0.1 dB of insertion loss. Our scheme is compatible with the current superconducting qubit technology. We report on progress toward implementing this device.

This was a proposal for making a TRWPA like device to replace a macroscopic magnetic isolator. This was very exciting to see because the devices performance looks almost identical to the commercial components. Looks like it will be a difficult microwave engineering challenge but the payoff would be enormous.
Presenter: Teruaki Yoshioka (Tokyo Univ of Science, Kagurazaka)
Abstract: We report an experiment of fast initialization of superconducting qubit using SINIS.
Active and unconditional initialization is required for NISQ, surface code and quantum computation.
By applying a bias voltage to the SINIS, photon assisted tunneling occurs, and the Q value of the resonator can be temporarily deteriorated. A qubit is coupled to the resonator, energy is transferred from the qubit to the resonator by applying two drive pulses which are an existing initialization scheme, and energy is efficiently emitted to the environment by natural relaxation of the resonator. Further, when initialization is not performed, that is, when a bias voltage is not applied to SINIS, the Q value of the resonator returns, so that the Q value does not affect readout and gate operation.
In this presentation, we report the experimental results and fabrication of the device.

The superconductor-insulator-normal metal-insulator-superconductor sandwich (SINIS) idea has been knocking around for a while. It's a cool attempt to take a piece of physics we'd normally say was a big problem—exciting quasiparticles—and turn it into a reset mechanism for resonators.

Presenter: Chuanhong Liu (University of Wisconsin-Madison)
Abstract: The Single Flux Quantum (SFQ) digital logic family has been proposed as a scalable approach for the control of next-generation multiqubit arrays. In an initial implementation, the fidelity of SFQ-based qubit gates was limited by quasiparticle (QP) poisoning induced by the dissipative SFQ driver. Here we introduce superconducting bandgap engineering as a mitigation strategy to suppress QP poisoning in this system. We explore low-gap moats and high-gap fences surrounding the qubit structure, along with a geometry involving extensive coverage of the high-gap groundplane with low-gap traps. We use charge-sensitive transmon qubits to evaluate the effectiveness of the various mitigation strategies in experiments involving direct QP injection.

This is the first time I've see an interface SFQ logic to qubits without destroying the qubits; they still had good coherence times. This was a cool introduction to superconducting bandgap engineering as a mitigation strategy to suppress quasiparticle poisoning in this system.

Presenter: Helin Zhang (University of Chicago)
Abstract: The heavy-fluxonium qubit is a promising building block for superconducting quantum processors due to its long relaxation and dephasing times at the flux-frustration point. However, the suppressed charge matrix elements and small splitting between computational states have made it challenging to perform fast single and two-qubit gates with conventional methods. In order to achieve high-fidelity initialization and readout, we demonstrate protocols utilizing higher levels beyond the computational subspace. We realize fast qubit control using a universal set of single-cycle flux gates, which are comprised of directly synthesizable pulses, and reach fidelities exceeding 99.8%. Finally, we discuss a set of flux-controlled two-qubit gates for inductively coupled fluxonium qubits. We believe that the fast, flux-based control combined with the coherence properties of the heavy fluxonium make this circuit one of the most promising candidates for next-generation superconducting qubits.

This took a good look at extremely low frequency fluxonium qubits at only a couple hundred MHz. It was really neat to see people control things that are at or below the thermal limit since they have to cool these qubits before thy even begin the experiment. Also, the fast flux gates look similar to something we would see in a spin qubit gate, so its interesting to see that come together, the control is very atypical.

Presenter: Nico Hendrickx (QuTech and Kavli Institute of Nanoscience, Delft University of Technology)
Abstract: Quantum dot spin qubits are a promising platform for large-scale quantum computers. Their inherent compatibility with semiconductor fabrication technology promises the ability to scale up to large numbers of qubits. However, all prior experiments are limited to two-qubit logic.
Here, we go beyond these demonstrations and operate a four-qubit quantum processor. Furthermore, we define the quantum dots in a two-by-two grid and thereby realize the first two-dimensional qubit array with semiconductor qubits, a crucial step toward quantum error correction and practical quantum algorithms. We achieve these results by defining qubits based on hole states in strained planar germanium quantum wells, enabling a high degree of control, well defined qubit states, and fast, all-electrical qubit driving.
We perform one, two, three, and four qubit logic for all qubit combinations, realizing a compact and high-connectivity circuit. Furthermore, we show that the hole coherence can be extended up to 100 ms using refocusing pulses and employ this to perform a quantum circuit executed on the full four-qubit system. These results mark an important step for scaling up spin qubits in two dimensions and position planar germanium as a prime candidate for practical quantum applications.

This research represented a big simplification of the germanium spin-qubit platform. The researchers did so by incorporating enough spin-orbit coupling such that they didn't need a micromagnet in order to do microwave manipulations, allowing them to create an array rather than just a 2-qubit interaction.

Presenter: Ciaran Ryan-Anderson (Honeywell Intl)
Abstract: Mid-circuit measurement and active feed-forward are essential ingredients to fault-tolerant quantum error correction, and the QCCD architecture naturally lends itself to these operational primitives. Ion-transport operations allow for individual qubits to be spatially isolated, where they may be safely interrogated and reinitialized with focused laser beams without damaging idling qubits. Here we present experimental characterizations of these operations including both primitive as well as algorithmic benchmarking results. We will also discuss our results’ implications for the QCCD architecture’s capabilities.

It has been really awesome to see the steady progress they have made from their original H0 device. We appreciated the clear communication of the effort they have dedicated to methodically solving each problem in turn and sharing the results.

Presenter: Prof Andrew Houck (Princeton University)
Abstract: We employ tantalum transmon qubits with coherence times above 0.3 ms to demonstrate the importance of materials engineering in realizing a superconducting quantum processor. In this talk we characterize the regions and mechanisms of loss in state-of-the-art two-dimensional qubits. To do so, we efficiently iterate our fabrication procedure using materials spectroscopy. We correlate the spectroscopic results with time domain measurements to enable rapid screening of new materials and processing techniques. We further elucidate the dominant loss sources by characterizing time, frequency, geometry, and temperature fluctuations of coherence. Our fabrication techniques can be easily employed in standard industry and academic cleanrooms, and integrated into existing quantum processor architectures.

It's always great to see new innovations in this field using novel materials. Prof Houck did a great job outlining why this type of creative exploration was necessary and the results are not only quite impressive, they are easily implemented in other labs. We also enjoyed seeing your co-author, the cat. Unfortunately, he was a little blurry, but we just assume this means he has very precise momentum.

Presenter: Uros Delic (University of Vienna)
Abstract: Owing to its excellent isolation from the thermal environment, an optically levitated silica nanoparticle in ultra-high vacuum has been proposed to observe quantum behavior of massive objects at room temperature, with applications ranging from sensing to testing fundamental physics. As a first step towards quantum state preparation of the nanoparticle motion, both cavity and feedback cooling methods have been used to attempt cooling to its motional ground state, albeit with many technical difficulties. We have recently developed a new experimental interface, which combines stable (and arbitrary) trapping potentials of optical tweezers with the cooling performance of optical cavities, and demonstrated operation at desired experimental conditions [1]. In order to overcome still existent technical problems we implemented a new cooling method – cavity cooling by coherent scattering – which we employ to demonstrate ground state cooling of the nanoparticle motion [2, 3]. In this talk I will present our latest experimental result on motional ground state cooling of a levitated nanoparticle and discuss next steps toward macroscopic quantum states.
1. Delic, Grass et al., QST 5 (2), 025006
2. Delic et al., Phys. Rev. Lett. 122, 123602
3. Delic et al., Science 367, 892-895
Figuring out why this result is cool is left as an exercise to the reader. :)