Superconducting qubits

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Superconducting qubits have seized an early lead in commercial quantum computing activity. Being first to demonstrate technical quantum supremacy means they are well placed to search for NISQ quantum advantage. However there are significant challenges to be faced in scaling up these systems in the extreme cryogenic environments they require.

At milli-Kelvin temperatures, resistance-free current oscillates in a circuit loop with only discrete energy levels. Inserting a Josephson junction spreads out the energy levels and allows the circuit to be operated as an effective two-level quantum system. Qubits can be defined on the basis of quantised charge or magnetic flux. The design most common in commercial development for gate-model quantum computing is the transmon, a charge qubit with an added shunt capacitor to control noise.

A key difference in the approaches being taken by early commercial players is how exactly they choose to drive 2Q gates and the different implications for fidelity and control wiring this brings. New entrants have plenty of reason to believe there is still everything to play for in this technology.

For a detailed recent review of superconducting qubit technology see [ ] or [ ].

SWOT Analysis

Strengths

  • High 2Q gate fidelities above 99%.
  • Fast gate speeds, typically 20-200ns.
  • Microfrabricated devices using standard lithographic processes.

Opportunities

  • First mover advantage in the current commercial ecosystem; small devices have been successfully demonstrated up to 53 qubits.
  • 2D device layouts are a nature fit with common error correcting codes.
  • Very flexible qubit engineering possibilities: tunable qubits have so far offered faster, higher fidelity gates; fixed frequency qubits promise few control lines; tunable couplers extend control options. New options continue to emerge.
  • New quantum plane geometries are emerging, offering low crosstalk, flexibility and scalability, e.g. Coaxmon from OQC.
  • New control plane options emerging e.g. SFQ from SeeQC.
  • New qubit designs may point the way to longer lifetimes, e.g.3D Transmons  [ ], Fluxonium [ ] or Zero-Pi [ ].
  • New architectures for continuous variable quantum computing are possible, opening up new approaches to quantum error correction and new opportunities in quantum simulation (C. S. Wang et al. 2020)

Weaknesses

  • Extreme cryogenic cooling is required, typically to 20mK using dilution refrigerators.
  • Only modest qubit coherence lifetimes, typically 20-200μs (though mitigated by the fast gate speeds).
  • Individual qubit footprint is moderately large, typically 100μm.
  • Qubits vary at fabrication introducing a potential source of error.
  • The materials science of noise processes is not fully understood.
  • Interconnects must operate at microwave frequencies. Such technology is in its infancy, though first steps have been demonstrated (Pogorzalek et al. 2019).

Threats

  • Scaling puts pressure on the management of heat dissipation from control electronics; very low cooling power is available at 20mK.
  • The point may be reached where further significant improvement in fidelities require new material science advances to support better fabrication process.
  • Large scale FTQC probably requires the coherent networking of processors across multiple dilution refrigerators. The footprint for FTQC installations could be very large.

Key Players and Approaches

A key difference between current commercial approaches is whether tunable or fixed frequency transmons are used and how the 2Q gate is driven. Let’s look at the main approaches in turn.

Tunable Qubits with CZ gates

In addition to a microwave control line used for 1Q gates, each qubit has a dedicated ‘flux-bias’ line used to tune the resonant frequency of the qubit and thus drive 2Q gates.

Notable Commercial Players/consortia: Google, Origin Quantum, QuTech, IQM, QCI, SeeQC

  • Good 2Q fidelities in lab, 99.4% [ ], recently 99.7% reported [ ].
  • Good 2Q fidelities maintained in 53Q device,  99.64 %(indiviual) 99.38% (simultaneous), [ ], combined with very fast 12ns gate times. (Google Sycamore is an impressive device!)
  • First to claim technical quantum supremacy; giving first crack at demonstrating NISQ quantum advantage in a practical application.
  • 4-way connectivity offers early opportunities to demonstrate surface code QEC operations. Work at QuTech is underway to demonstrate surface-17 operations [ ].
  • Flexible design possibilities. IQM are focussing on tailoring designs for specific NISQ applications, with the potential to bring in other gate techniques and analogue blocks as required.
  • Driving qubits away from their operational ‘sweet spot’ reduces coherence lifetime. Google quotes ‘idle frequency’ coherence lifetimes (T2) of only 15us [ ], the net lifetimes including interactions will be lower. Ultimately this could limit fidelity improvement.
  • Tunable qubits require an additional control line and introduce an additional source of noise; frequency transitions risk sweeping though neighbouring qubit resonances on the way.
  • Tunable couplers required to maintain fidelities by turning off idle interactions have introduced yet another control line; further complicating wiring.

Arguably the biggest quantum news so far this year has been the departure of John Martinis from the Google Quantum AI team, just as it basks in its quantum supremacy success. Seasoned investors will not find it surprising that two senior individuals can part ways over issues of authority and priorities, as Martinis has done with Neven Hartmut, his boss at Google [ ]. An understanding of the technical roadmap issues perhaps makes it more understandable that Martinis should cite a disagreement about ‘wiring technology’ to illustrate the split. Such issues go to the heart of balancing NISQ and FTQC priorities

Google remains well placed to exploit its current NISQ leadership, though early results point to practical quantum advantage being outside reach without further increases in device size [ ]. Speaking at QT Digital Week, Alan Ho confirmed that provision of certified random numbers remains on the Google roadmap. Fact Based Insight sees this as a potential first genuine application. Google is targeting 2Q gate fidelities of 99.9% and a 1000Q device. Google are looking for a small number of ‘customer collaborators’ to partner with in the search for sector specific applications.

At IQT New York, Seeqc CEO John Levy summarised plans to develop a hybrid application specific quantum computer. This is expected to be based on tunable qubits, but leveraging their unique SFQ technology to address the control wiring dilemma. This could constitute a revolutionary step forward, but it remains at an early stage of development.

QCI was cofounded by a leading pioneer of the CZ gate. However might we see an early QCI device that leverages Rob Schoelkopf’s more recent work on 3D transmons and bosonic quantum simulation [ ]?

Fixed-Frequency Qubits with CR gates

To avoid the potential drawbacks of flux tunability, all-microwave 2Q gates have also been developed. The resonant point of such ‘fixed frequency’ qubits is set at fabrication.

Notable Commercial Players/Consortia:  IBM, OpenSuperQ, OQC

  • Good 2Q gate fidelities in lab,  99.1% [ ].
  • A growing family of devices have been demonstrated from 5Q to 28Q, the best demonstrating QV of 32 [ ].
  • Heavy hex layout of latest 53Q designs emphasise compatibility with the low 3-way connectivity required by the colour code (a family of quantum error correcting codes)[ ].
  • Optimal control techniques point to much faster 2Q gates of 10-30ns  [ ]; this would open up the possibility of consequentially improved 2Q gate fidelities
  • The market leading penetration of the IBM Q ecosystem brings in other players to assist control and compilation optimisation; developers will build experience with specifically this native gate set.
  • New connection geometries promise to further minimise the amount of control circuitry required on the quantum plane, for example OQC’s coaxmon design.
  • The flexibility remains to introduce some tunable components as part of the overall architecture.
  • Current gate times are slower than tunable qubits, 160-180ns (Sheldon et al. 2016; McKay et al. 2016); current fidelities are also significantly lower.
  • Device fabrication is complicated by the need to avoid ‘frequency collisions’ between nearby qubits.

It’s interesting to note that recent improvements in the performance of IBM devices to achieve QV 32 have been achieved as much by control software enhancements (target rotary pulses) as by hardware enhancements [ ].

IBM can arguably claim to have the superconducting hardware roadmap most advanced along the path to FTQC. They also have the leading NISQ software ecosystem. Avoiding these becoming misaligned will be a continuing challenge for the team and the available resources over the coming years.

Mixed Fixed and Tunable qubits with parametric gates

Hybrid schemes that combine fixed frequency and tunable qubits are also a promising approach. A tunable qubit is modulated to drive the required gate, but this is done ‘parametrically’ so that on average it remains at the ‘sweet spot’ for longer coherence lifetime.

Notable Commercial Players/Consortia: Rigetti

  • Good 2Q gate fidelities in lab  99.2% [ ]; Parametric operation recovered coherence lifetimes (T2) of 20μs.
  • Fabrication optimisations at Rigetti’s own foundry have allowed qubit state lifetimes (T1) up to 110μs [ ].
  • Successful families of device have been developed up to the latest 31Q Aspen-8 series.
  • Parametric techniques have also been used to implement √SWAP gates [ ] and, with the aim of minimising NISQ application gate-count, flexible XY gates with median fidelity of 97.3% [ ].
  • Potential ‘middle way’ in terms of trading off control requirements.
  • Demonstrated gate speeds are only moderate, 176ns [ ], not yet faster than all fixed frequency schemes.
  • Aspen-8 2Q gate fidelity only 95.66% (avg) at launch [ ].

The Rigetti platform combines features designed for a particular focus on supporting hybrid quantum classical NISQ algorithms: pre-compilation of parameterised quantum circuits, fast qubit reset to allow faster iterations and low-latency due to the co-location of quantum and conventional backends [ ].

Speaking recently at QT Digital Week, Andrew Bestwick, Director of Quantum Device Architecture, outlined plans for 100Q+ modular devices in early 2021 formed by linking together multiple Aspen-class chips. Fact Based Insight sees improving 2Q gate fidelities as a key test for Rigetti’s roadmap.

Quantum computing can be a small world. Chad Rigetti previously worked on quantum computers at IBM before founding his own eponymous startup in 2013. More recently, in 2017 Alexei Marchenkov left Rigetti to found Bleximo, which intends to focus on application specific superconducting quantum computers.

Flux qubits for quantum annealing

A very different approach has been to use a large array of flux qubits to simulate an ‘energy landscape’. Problems that require finding the lowest point in this landscape can then be solved by evolving the state of the machine to match the required landscape. Quantum fluctuations can help the system avoid local minima to find the true minimum solution.

Notable Commercial Players: D-Wave Systems

  • Flux qubits offer an interaction structure natively suited to quantum annealing.
  • D-Wave commercially offers a 2000Q system and has announced the first sale of its new 5000Q system for delivery later this year.
  • Quantum annealing natively solves Ising model quantum simulation problems and the QUBO hard optimisation problems. A wide variety of other types of problem can also be mapped to these classes [ ].
  • A strength of D-Wave’s approach has been the active engagement with a wide variety of potential early adopters on practical business problems. This has led to a series of showcase demonstrations, notably at Volkswagen and Denso.
  • The monolithic integration of control electronics with the qubits has allowed these systems to scale rapidly, but this comes at the expense of significant lower qubit quality; coherence lifetimes are only in the 10-100ns range [ ].
  • Quantum annealing is a step on the roadmap to an approach to universal quantum computation known as adiabatic quantum computing. However the path by which annealing can evolve into true adiabatic evolution is not theoretically well understood.
  • Currently quantum annealing faces competition from special purpose conventional systems optimised to implement ‘simulated annealing’, or other conventional algorithms inspired by quantum annealing.

Academic criticism of this approach stems largely from the observation that current D-Wave devices can only implement ‘stochastic Hamiltonians’ and that these can in principle be efficiently simulated by conventional computers [ ]. However D-Wave have recently demonstrated roadmap technology that appears to take them beyond this constraint [ ].

Qilimanjaro, a Spanish spinout, is a new addition to the quantum annealing camp. Expect it to benefit from participation in the EU AVaQus project.

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David Shaw

About the Author

David Shaw has worked extensively in consulting, market analysis & advisory businesses across a wide range of sectors including Technology, Healthcare, Energy and Financial Services. He has held a number of senior executive roles in public and private companies. David studied Physics at Balliol College, Oxford and has a PhD in Particle Physics from UCL. He is a member of the Institute of Physics. Follow David on Twitter and LinkedIn