Session K41: Superconducting Qubits: Gates and Coupling

Demonstration of a Multi-Qubit Gate for All-to-All Connected Superconducting Qubits

Exploring highly connected networks of qubits is invaluable for implementing various quantum codes and simulations. All-to-all connectivity allows for entangling qubits with reduced gate depth. In the trapped-ion qubit community, the Mølmer-Sørensen gate is routinely used to entangle over a dozen qubits with high fidelity. We implement a Mølmer-Sørensen-like interaction through the use of shared coplanar waveguide (CPW) resonators to couple multiple superconducting qubits. We present two-qubit and multi-qubit experiments and detail sources of errors and prospects for scalability.   

Engineering multi-qubit interactions between superconducting flux qubits

Nonpairwise multi-qubit interactions present a useful resource for quantum information processors. Their implementation would enable analog simulations of molecules and combinatorial optimization problems, and they could simplify error suppression and correction schemes. In this talk, we present a superconducting circuit architecture in which a coupling module mediates interactions between four flux qubits. The system Hamiltonian is estimated via multi-qubit pulse sequences that implement Ramsey-type interferometry between all neighboring excitation manifolds in the system. Interactions are determined with the coupler on and off, and we present evidence for multi-spin coupling mechanisms. Spectroscopic techniques, combined with numerical simulations of the circuit, permit an extrapolation of the interactions beyond the coherent regime of the qubits.   

Compiling Arbitrary Single-Qubit Gates Via the Phase-Shifts of Microwave Pulses

Realizing an arbitrary single-qubit gate is a precursor for many quantum computational tasks, including the conventional approach to universal quantum computing. For superconducting qubits, single-qubit gates are usually realized by microwave pulses along drive or flux lines. These pulses are calibrated to realize a particular single-qubit gate. However, it is clearly impractical to calibrate a pulse for every possible single-qubit gate  in SU(2). On the other hand, compiling arbitrary gates using a finite universal gate set will lead to unacceptably low fidelities. Here, we provide a compilation scheme for arbitrary single-qubit gates for which the three real parameters of the gate directly correspond to the phase shifts of microwave pulses, which can be made extremely accurate experimentally, that is also compatible with any two-qubit gate. Furthermore, we only require the calibration of the X_π and X_π/2 pulses, gates that are already necessary for tasks such as Clifford-based randomized benchmarking as well as measuring the T₁ and T₂ decoherence parameters.   

Towards a transmon qubit with gate-controlled Sn-InSb Josephson Junction

We report our experimental progress towards realizing gate tunable superconducting transmon qubit with the newly developed superconducting Sn shells on InSb nanowire as Josephson element. Gate tunable superconducting transmon qubits have previously been demonstrated with Al-InAs nanowire weak- link josephson junctions. These nanowire-based qubits are interesting for their gate tunability and high magnetic field compatibility. In our work, the readout circuit is made of high internal quality factor NbTiN co-planar waveguide resonators. With spectroscopic and time domain measurements we characterize and report on the relaxation and coherence times of these qubits.   

Design and Characterization of 3D-Integrated Superconducting Qubit Lattices

Superconducting qubits hold the promise of individual qubit control and readout, with broad tunability of qubit frequencies and coupling strengths. However, in-plane interconnect routing becomes prohibitive for even moderately sized lattices due to space constraints. Here, we incorporate flip-chip 3D integration technology in the design of mesoscale qubit lattices. This allows us to reduce interconnect density and enables the control and readout of all qubits in larger-scale processors. We report on the improvements to loss and crosstalk enabled by 3D integration.   

Floating tunable coupler for scalable quantum computing architectures

We propose a floating tunable coupler that does not rely on direct qubit-qubit coupling capacitances to achieve the zero-coupling condition. We show that the polarity of the qubit-coupler couplings can be engineered to offset the otherwise constant qubit-qubit coupling and attain the zero-coupling condition when the coupler frequency is above or below the qubit frequencies. We experimentally demonstrate these two operating regimes of the tunable coupler by implementing symmetric and asymmetric configurations of the superconducting pads of the coupler with respect to the qubits.  We demonstrate parametric-resonance iSWAP and CZ gates for both operating regimes of the tunable coupler with two-qubit interleaved randomized benchmarking fidelity exceeding 99%. We show a simple and scalable calibration method for both parametric-resonance and fast DC pulse enabled iSWAP gates.    

Towards High-Fidelity Gates in the Soft Zero-Pi Qubit

The soft zero-pi circuit [1, 2, 3] has shown experimental evidence of protection against relaxation and dephasing, making it a promising candidate for high-fidelity quantum processing. However, in the most recent realization, the small hybridization gap and weak drive coupling limited flux-noise insensitivity and gate speed. Here, we show recent advances in pushing the soft zero-pi further into its protected regime, especially through increasing the ratio of the charging energies for the two participating modes. Further, we discuss efforts to improve gate speed and characterize fidelity of the multi-level system through randomized benchmarking.

[1] A. Kitaev. arXiv:cond-mat/0609441 (2006).

[2] P. Brooks, A. Kitaev, J. Preskill. Phys. Rev. A 87, 052306 (2013).

[3] A. Gyenis, P. Mundada, A. Di Paolo et. al. PRX Quantum 2, 010339 (2021).   

A two-qubitentangling gate based on a two-spin gadget

The faster speed and operational convenience of two-qubit gate with flux bias control makes it an important candidate for future large-scale quantum computers based on high coherence flux qubits. We designed a two-qubit entangling gate using only flux bias control for flux qubits coupled with tunable couplers, based on a properly designed two-spin gadget which has small gaps during the evolution of energy levels. Starting from idle, by making an excursion to one small gap caused by anticrossing in our gadget, a CNOT-equivalent gate with a fidelity larger than 99.9% within 40ns can be realized. Moreover, we also use the Schrieffer-Wolff Transformation to translate the spin model Ising coefficients schedule to circuit model flux bias schedule for realistic flux qubit circuits coupled by a tunable rf-SQUID. Our two-qubit gate has implications in improving reverse annealing as well as realizing efficient two-qubit gates in flux qubit systems.   

Realization of a two-qubit gate using a coherently driven coupler

Fast and high-fidelity iSWAP and CZ gates can be realized using frequency-tunable transmons as nonlinear coupling elements between two superconducting qubits [1-4]. These gates are typically performed by flux-tuning the frequency of the coupling transmon which leads to a modification of the qubit-qubit coupling strength. In this work, we experimentally demonstrate that the interaction between two qubits can also be controlled by coherently driving the coupler. For a particular qubit frequency, there is no interaction when the coupler is in its ground state while high coupling rate is achieved when the coupler is excited. To perform an iSWAP gate in this configuration, we apply a resonant two-pi pulse on the coupler. The population transfer between qubits is maximal when the pulse duration matches the qubit coupling rate. Our coupling scheme could significantly reduce the complexity of superconducting quantum processors by eliminating the need for coupler flux tuning lines and the associated flux crosstalk and settling tails calibrations. 

[1] Li et al., Phys. Rev. Applied 14, 024070 (2020)

[2] Foxen et al., PRL 125 120504 (2020) 

[3] Collodo et al., PRL 125 240502 (2020) 

[4] Sung et al., PRX 11 021058 (2021)   

Speed limits for two-qubit gates with weakly anharmonic qubits

We consider the implementation of two-qubit gates when the physical systems used to realize the qubits are weakly anharmonic and therefore possess additional quantum states in the accessible energy range. We analyze the effect of the additional quantum states on the maximum achievable speed for quantum gates in the qubit state space. By calculating the minimum gate time using optimal control theory, we find that higher energy levels can help make two-qubit gates significantly faster than the reference value based on simple qubits. This speedup is a result of the higher coupling strength between higher energy levels. We then analyze the situation where the pulse optimization algorithm avoids pulses that excite the higher levels. We find that in this case the presence of the additional states can lead to a significant reduction in the maximum achievable gate speed. We also compare the optimal control gate times with those obtained using the cross-resonance/selective-darkening gate protocol. We find that the latter, with some parameter optimization, can be used to achieve a relatively fast implementation of the CNOT gate. These results can help the search for optimized gate implementations in realistic quantum computing architectures, such as those based on superconducting qubits. They also provide guidelines for desirable conditions on anharmonicity that would allow optimal utilization of the higher levels to achieve fast quantum gates.   

Ancilla-Error-Transparent Controlled-SWAP Gate

One of the big obstacles in quantum computing is engineering efficient and highly controllable quantum gates. A gate with a broad range of applications is the controlled-SWAP gate that can be used in universal quantum computing and various verification processes. This gate has been realized in circuit QED with a transmon-based ancilla to entangle two microwave fields (Gao et al. Nature 566, 509 (2019)) but its fidelity was limited by the ancilla errors, particularly transmon relaxation. To improve the gate performance, we propose a controlled beam splitter with a SNAIL-based Kerr-cat ancilla. Using the coherent states of the Kerr cat enables us to create a controlled-phase beam splitter operation on two microwave fields and biases the ancilla noise towards phase flips. This can then be combined with a deterministic beam splitter to generate a controlled beam splitter gate that is transparent to the dominant error channel preventing the propagation of the ancilla errors into the fields. This error transparency enables improved coherence compared to the transmon setup and allows improved performance of applications such as swap tests or quantum random access memory protocols.   

Achieving fast, high fidelity single qubit gates for the Kerr-Cat Qubit

The Kerr-Cat Qubit is a biased noise qubit realised by coherent states in an oscillator. We investigated the effect of a detuning and a single photon drive on this qubit. 

Both of which cause the coherent states │±α〉 defined by the two photon drive and Kerr nonlinearity to be no longer eigenstates of our Hamiltonian. 

For a small detuning and single photon drive strength the difference to the eigenstates is small enough so that these states are a good approximation of the eigenstates. 

However this limits us to the regime in which X and Z rotations which are realised by a detuning and a single photon drive respectively are slow. 

Increasing these terms will speed up the gates but will result in considerably lower fidelities as the coherent states are deformed over time. 

Using coherent states that are better approximations of eigenstates than │±α〉 can result in fast, high fidelity gates. 

These displaced states have a semi periodic deformation in them, which needs to be considered carefully and gives rise to a discrete set of detunings and Kerr nonlinearities that produce high fidelity rotations.   

Realizing high-fidelity and low-leakage gates in a fluxonium processor

High-fidelity quantum operations are critical for performing quantum error correction. Although impressive advancements have been made for the transmon qubit, further improvements in its fidelity are impeded by its decoherence. In addition, large leakage error caused by its weak nonlinearity can induce correlated errors that threaten quantum error correction. In contrast, with its low decoherence and large anharmonicity, fluxonium is an attractive qubit for fault-tolerance. Here, we perform on a fluxonium processor single-qubit gates with up to 99.98% fidelity and a two-qubit entangling gate with up to 99.72% fidelity. Our analysis shows that the leakage errors of these operations are substantially lower than those commonly observed in a transmon system. This result paves a clear path toward fault-tolerant quantum computing through fluxonium processors.   

Mode-selective coupling with low crosstalk between multi-mode coaxial transmons

We present experimental results on statically coupled two-mode coaxial transmon qubits in which we utilise spatial symmetries to introduce highly mode-selective coupling. This allows for intrinsic crosstalk suppression between the protected modes that can be used for computation, whilst still allowing for fast entanglement operations, using the directly coupled ancillary modes. We demonstrate an all-microwave activated conditional phase gate, generating a fast entanglement operation between computational modes. We show this gate can be driven in multiple regimes and allows for a wide range of resonance conditions that can be met. Through simultaneous readout of both computational and ancillary modes, we show minimal leakage outside of the computational basis due to the entanglement operation.   

Ultrastrong tunable coupler between superconducting LC resonators

We investigate the ultrastrong tunable coupler for coupling of superconducting resonators. Obtained coupling constant exceeds 1 GHz, and the wide range tunability is achieved both antiferromagnetics and ferromagnetics from -1086 MHz to 604 MHz. Ultrastrong coupler is composed of rf-SQUID and dc-SQUID as tunable junctions, which connected to resonators via shared aluminum thin film meander lines enabling such a huge coupling constant. The spectrum of the coupler obviously shows the breaking of the rotating wave approximation, and our circuit model treating the Josephson junction as a tunable inductance reproduces the experimental results well. The ultrastrong coupler is expected to be utilized in quantum annealing circuits and/or NISQ devices with dense connections between qubits.