Measurement-Induced State Transitions in a Superconducting Qubit: Within the Rotating Wave Approximation

  1. Mostafa Khezri,
  2. Alex Opremcak,
  3. Zijun Chen,
  4. Andreas Bengtsson,
  5. Theodore White,
  6. Ofer Naaman,
  7. Rajeev Acharya,
  8. Kyle Anderson,
  9. Markus Ansmann,
  10. Frank Arute,
  11. Kunal Arya,
  12. Abraham Asfaw,
  13. Joseph C Bardin,
  14. Alexandre Bourassa,
  15. Jenna Bovaird,
  16. Leon Brill,
  17. Bob B. Buckley,
  18. David A. Buell,
  19. Tim Burger,
  20. Brian Burkett,
  21. Nicholas Bushnell,
  22. Juan Campero,
  23. Ben Chiaro,
  24. Roberto Collins,
  25. Alexander L. Crook,
  26. Ben Curtin,
  27. Sean Demura,
  28. Andrew Dunsworth,
  29. Catherine Erickson,
  30. Reza Fatemi,
  31. Vinicius S. Ferreira,
  32. Leslie Flores-Burgos,
  33. Ebrahim Forati,
  34. Brooks Foxen,
  35. Gonzalo Garcia,
  36. William Giang,
  37. Marissa Giustina,
  38. Raja Gosula,
  39. Alejandro Grajales Dau,
  40. Michael C. Hamilton,
  41. Sean D. Harrington,
  42. Paula Heu,
  43. Jeremy Hilton,
  44. Markus R. Hoffmann,
  45. Sabrina Hong,
  46. Trent Huang,
  47. Ashley Huff,
  48. Justin Iveland,
  49. Evan Jeffrey,
  50. Julian Kelly,
  51. Seon Kim,
  52. Paul V. Klimov,
  53. Fedor Kostritsa,
  54. John Mark Kreikebaum,
  55. David Landhuis,
  56. Pavel Laptev,
  57. Lily Laws,
  58. Kenny Lee,
  59. Brian J. Lester,
  60. Alexander T. Lill,
  61. Wayne Liu,
  62. Aditya Locharla,
  63. Erik Lucero,
  64. Steven Martin,
  65. Matt McEwen,
  66. Anthony Megrant,
  67. Xiao Mi,
  68. Kevin C. Miao,
  69. Shirin Montazeri,
  70. Alexis Morvan,
  71. Matthew Neeley,
  72. Charles Neill,
  73. Ani Nersisyan,
  74. Jiun How Ng,
  75. Anthony Nguyen,
  76. Murray Nguyen,
  77. Rebecca Potter,
  78. Chris Quintana,
  79. Charles Rocque,
  80. Pedram Roushan,
  81. Kannan Sankaragomathi,
  82. Kevin J. Satzinger,
  83. Christopher Schuster,
  84. Michael J. Shearn,
  85. Aaron Shorter,
  86. Vladimir Shvarts,
  87. Jindra Skruzny,
  88. W. Clarke Smith,
  89. George Sterling,
  90. Marco Szalay,
  91. Douglas Thor,
  92. Alfredo Torres,
  93. Bryan W. K. Woo,
  94. Z. Jamie Yao,
  95. Ping Yeh,
  96. Juhwan Yoo,
  97. Grayson Young,
  98. Ningfeng Zhu,
  99. Nicholas Zobrist,
  100. and Daniel Sank
Superconducting qubits typically use a dispersive readout scheme, where a resonator is coupled to a qubit such that its frequency is qubit-state dependent. Measurement is performed
by driving the resonator, where the transmitted resonator field yields information about the resonator frequency and thus the qubit state. Ideally, we could use arbitrarily strong resonator drives to achieve a target signal-to-noise ratio in the shortest possible time. However, experiments have shown that when the average resonator photon number exceeds a certain threshold, the qubit is excited out of its computational subspace, which we refer to as a measurement-induced state transition. These transitions degrade readout fidelity, and constitute leakage which precludes further operation of the qubit in, for example, error correction. Here we study these transitions using a transmon qubit by experimentally measuring their dependence on qubit frequency, average photon number, and qubit state, in the regime where the resonator frequency is lower than the qubit frequency. We observe signatures of resonant transitions between levels in the coupled qubit-resonator system that exhibit noisy behavior when measured repeatedly in time. We provide a semi-classical model of these transitions based on the rotating wave approximation and use it to predict the onset of state transitions in our experiments. Our results suggest the transmon is excited to levels near the top of its cosine potential following a state transition, where the charge dispersion of higher transmon levels explains the observed noisy behavior of state transitions. Moreover, occupation in these higher energy levels poses a major challenge for fast qubit reset.

Readout of a quantum processor with high dynamic range Josephson parametric amplifiers

  1. T. C. White,
  2. Alex Opremcak,
  3. George Sterling,
  4. Alexander Korotkov,
  5. Daniel Sank,
  6. Rajeev Acharya,
  7. Markus Ansmann,
  8. Frank Arute,
  9. Kunal Arya,
  10. Joseph C Bardin,
  11. Andreas Bengtsson,
  12. Alexandre Bourassa,
  13. Jenna Bovaird,
  14. Leon Brill,
  15. Bob B. Buckley,
  16. David A. Buell,
  17. Tim Burger,
  18. Brian Burkett,
  19. Nicholas Bushnell,
  20. Zijun Chen,
  21. Ben Chiaro,
  22. Josh Cogan,
  23. Roberto Collins,
  24. Alexander L. Crook,
  25. Ben Curtin,
  26. Sean Demura,
  27. Andrew Dunsworth,
  28. Catherine Erickson,
  29. Reza Fatemi,
  30. Leslie Flores-Burgos,
  31. Ebrahim Forati,
  32. Brooks Foxen,
  33. William Giang,
  34. Marissa Giustina,
  35. Alejandro Grajales Dau,
  36. Michael C. Hamilton,
  37. Sean D. Harrington,
  38. Jeremy Hilton,
  39. Markus Hoffmann,
  40. Sabrina Hong,
  41. Trent Huang,
  42. Ashley Huff,
  43. Justin Iveland,
  44. Evan Jeffrey,
  45. Mária Kieferová,
  46. Seon Kim,
  47. Paul V. Klimov,
  48. Fedor Kostritsa,
  49. John Mark Kreikebaum,
  50. David Landhuis,
  51. Pavel Laptev,
  52. Lily Laws,
  53. Kenny Lee,
  54. Brian J. Lester,
  55. Alexander Lill,
  56. Wayne Liu,
  57. Aditya Locharla,
  58. Erik Lucero,
  59. Trevor McCourt,
  60. Matt McEwen,
  61. Xiao Mi,
  62. Kevin C. Miao,
  63. Shirin Montazeri,
  64. Alexis Morvan,
  65. Matthew Neeley,
  66. Charles Neill,
  67. Ani Nersisyan,
  68. Jiun How Ng,
  69. Anthony Nguyen,
  70. Murray Nguyen,
  71. Rebecca Potter,
  72. Chris Quintana,
  73. Pedram Roushan,
  74. Kannan Sankaragomathi,
  75. Kevin J. Satzinger,
  76. Christopher Schuster,
  77. Michael J. Shearn,
  78. Aaron Shorter,
  79. Vladimir Shvarts,
  80. Jindra Skruzny,
  81. W. Clarke Smith,
  82. Marco Szalay,
  83. Alfredo Torres,
  84. Bryan Woo,
  85. Z. Jamie Yao,
  86. Ping Yeh,
  87. Juhwan Yoo,
  88. Grayson Young,
  89. Ningfeng Zhu,
  90. Nicholas Zobrist,
  91. Yu Chen,
  92. Anthony Megrant,
  93. Julian Kelly,
  94. and Ofer Naaman
We demonstrate a high dynamic range Josephson parametric amplifier (JPA) in which the active nonlinear element is implemented using an array of rf-SQUIDs. The device is matched to the
50 Ω environment with a Klopfenstein-taper impedance transformer and achieves a bandwidth of 250-300 MHz, with input saturation powers up to -95 dBm at 20 dB gain. A 54-qubit Sycamore processor was used to benchmark these devices, providing a calibration for readout power, an estimate of amplifier added noise, and a platform for comparison against standard impedance matched parametric amplifiers with a single dc-SQUID. We find that the high power rf-SQUID array design has no adverse effect on system noise, readout fidelity, or qubit dephasing, and we estimate an upper bound on amplifier added noise at 1.6 times the quantum limit. Lastly, amplifiers with this design show no degradation in readout fidelity due to gain compression, which can occur in multi-tone multiplexed readout with traditional JPAs.

Extensive characterization of a family of efficient three-qubit gates at the coherence limit

  1. Christopher W. Warren,
  2. Jorge Fernández-Pendás,
  3. Shahnawaz Ahmed,
  4. Tahereh Abad,
  5. Andreas Bengtsson,
  6. Janka Biznárová,
  7. Kamanasish Debnath,
  8. Xiu Gu,
  9. Christian Križan,
  10. Amr Osman,
  11. Anita Fadavi Roudsari,
  12. Per Delsing,
  13. Göran Johansson,
  14. Anton Frisk Kockum,
  15. Giovanna Tancredi,
  16. and Jonas Bylander
While all quantum algorithms can be expressed in terms of single-qubit and two-qubit gates, more expressive gate sets can help reduce the algorithmic depth. This is important in the
presence of gate errors, especially those due to decoherence. Using superconducting qubits, we have implemented a three-qubit gate by simultaneously applying two-qubit operations, thereby realizing a three-body interaction. This method straightforwardly extends to other quantum hardware architectures, requires only a „firmware“ upgrade to implement, and is faster than its constituent two-qubit gates. The three-qubit gate represents an entire family of operations, creating flexibility in quantum-circuit compilation. We demonstrate a gate fidelity of 97.90%, which is near the coherence limit of our device. We then generate two classes of entangled states, the GHZ and W states, by applying the new gate only once; in comparison, decompositions into the standard gate set would have a two-qubit gate depth of two and three, respectively. Finally, we combine characterization methods and analyze the experimental and statistical errors on the fidelity of the gates and of the target states.

Measurement and control of a superconducting quantum processor with a fully-integrated radio-frequency system on a chip

  1. Mats O. Tholén,
  2. Riccardo Borgani,
  3. Giuseppe Ruggero Di Carlo,
  4. Andreas Bengtsson,
  5. Christian Križan,
  6. Marina Kudra,
  7. Giovanna Tancredi,
  8. Jonas Bylander,
  9. Per Delsing,
  10. Simone Gasparinetti,
  11. and David B. Haviland
We describe a digital microwave platform called Presto, designed for measurement and control of multiple quantum bits (qubits) and based on the third-generation radio-frequency system
on a chip. Presto uses direct digital synthesis to create signals up to 9 GHz on 16 synchronous output ports, while synchronously analyzing response on 16 input ports. Presto has 16 DC-bias outputs, 4 inputs and 4 outputs for digital triggers or markers, and two continuous-wave outputs for synthesizing frequencies up to 15 GHz. Scaling to a large number of qubits is enabled through deterministic synchronization of multiple Presto units. A Python application programming interface configures a firmware for synthesis and analysis of pulses, coordinated by an event sequencer. The analysis integrates template matching (matched filtering) and low-latency (184 – 254 ns) feedback to enable a wide range of multi-qubit experiments. We demonstrate Presto’s capabilities with experiments on a sample consisting of two superconducting qubits connected via a flux-tunable coupler. We show single-shot readout and active reset of a single qubit; randomized benchmarking of single-qubit gates showing 99.972% fidelity, limited by the coherence time of the qubit; and calibration of a two-qubit iSWAP gate.

Nonequilibrium heat transport and work with a single artificial atom coupled to a waveguide: emission without external driving

  1. Yong Lu,
  2. Neill Lambert,
  3. Anton Frisk Kockum,
  4. Ken Funo,
  5. Andreas Bengtsson,
  6. Simone Gasparinetti,
  7. Franco Nori,
  8. and Per Delsing
We observe the continuous emission of photons into a waveguide from a superconducting qubit without the application of an external drive. To explain this observation, we build a two-bath
model where the qubit couples simultaneously to a cold bath (the waveguide) and a hot bath (a secondary environment). Our results show that the thermal-photon occupation of the hot bath is up to 0.14 photons, 35 times larger than the cold waveguide, leading to nonequilibrium heat transport with a power of up to 132 zW, as estimated from the qubit emission spectrum. By adding more isolation between the sample output and the first cold amplifier in the output line, the heat transport is strongly suppressed. Our interpretation is that the hot bath may arise from active two-level systems being excited by noise from the output line. We also apply a coherent drive, and use the waveguide to measure thermodynamic work and heat, suggesting waveguide spectroscopy is a useful means to study quantum heat engines and refrigerators. Finally, based on the theoretical model, we propose how a similar setup can be used as a noise spectrometer which provides a new solution for calibrating the background noise of hybrid quantum systems.

Quantum efficiency, purity and stability of a tunable, narrowband microwave single-photon source

  1. Yong Lu,
  2. Andreas Bengtsson,
  3. Jonathan J. Burnett,
  4. Baladitya Suri,
  5. Sankar Raman Sathyamoorthy,
  6. Hampus Renberg Nilsson,
  7. Marco Scigliuzzo,
  8. Jonas Bylander,
  9. Göran Johansson,
  10. and Per Delsing
We demonstrate an on-demand source of microwave single photons with 71–99% intrinsic quantum efficiency. The source is narrowband (300unite{kHz}) and tuneable over a 600 MHz
range around 5.2 GHz. Such a device is an important element in numerous quantum technologies and applications. The device consists of a superconducting transmon qubit coupled to the open end of a transmission line. A π-pulse excites the qubit, which subsequently rapidly emits a single photon into the transmission line. A cancellation pulse then suppresses the reflected π-pulse by 33.5 dB, resulting in 0.005 photons leaking into the photon emission channel. We verify strong antibunching of the emitted photon field and determine its Wigner function. Non-radiative decay and 1/f flux noise both affect the quantum efficiency. We also study the device stability over time and identify uncorrelated discrete jumps of the pure dephasing rate at different qubit frequencies on a time scale of hours, which we attribute to independent two-level system defects in the device dielectrics, dispersively coupled to the qubit.

Resolving catastrophic error bursts from cosmic rays in large arrays of superconducting qubits

  1. Matt McEwen,
  2. Lara Faoro,
  3. Kunal Arya,
  4. Andrew Dunsworth,
  5. Trent Huang,
  6. Seon Kim,
  7. Brian Burkett,
  8. Austin Fowler,
  9. Frank Arute,
  10. Joseph C Bardin,
  11. Andreas Bengtsson,
  12. Alexander Bilmes,
  13. Bob B. Buckley,
  14. Nicholas Bushnell,
  15. Zijun Chen,
  16. Roberto Collins,
  17. Sean Demura,
  18. Alan R. Derk,
  19. Catherine Erickson,
  20. Marissa Giustina,
  21. Sean D. Harrington,
  22. Sabrina Hong,
  23. Evan Jeffrey,
  24. Julian Kelly,
  25. Paul V. Klimov,
  26. Fedor Kostritsa,
  27. Pavel Laptev,
  28. Aditya Locharla,
  29. Xiao Mi,
  30. Kevin C. Miao,
  31. Shirin Montazeri,
  32. Josh Mutus,
  33. Ofer Naaman,
  34. Matthew Neeley,
  35. Charles Neill,
  36. Alex Opremcak,
  37. Chris Quintana,
  38. Nicholas Redd,
  39. Pedram Roushan,
  40. Daniel Sank,
  41. Kevin J. Satzinger,
  42. Vladimir Shvarts,
  43. Theodore White,
  44. Z. Jamie Yao,
  45. Ping Yeh,
  46. Juhwan Yoo,
  47. Yu Chen,
  48. Vadim Smelyanskiy,
  49. John M. Martinis,
  50. Hartmut Neven,
  51. Anthony Megrant,
  52. Lev Ioffe,
  53. and Rami Barends
Scalable quantum computing can become a reality with error correction, provided coherent qubits can be constructed in large arrays. The key premise is that physical errors can remain
both small and sufficiently uncorrelated as devices scale, so that logical error rates can be exponentially suppressed. However, energetic impacts from cosmic rays and latent radioactivity violate both of these assumptions. An impinging particle ionizes the substrate, radiating high energy phonons that induce a burst of quasiparticles, destroying qubit coherence throughout the device. High-energy radiation has been identified as a source of error in pilot superconducting quantum devices, but lacking a measurement technique able to resolve a single event in detail, the effect on large scale algorithms and error correction in particular remains an open question. Elucidating the physics involved requires operating large numbers of qubits at the same rapid timescales as in error correction, exposing the event’s evolution in time and spread in space. Here, we directly observe high-energy rays impacting a large-scale quantum processor. We introduce a rapid space and time-multiplexed measurement method and identify large bursts of quasiparticles that simultaneously and severely limit the energy coherence of all qubits, causing chip-wide failure. We track the events from their initial localised impact to high error rates across the chip. Our results provide direct insights into the scale and dynamics of these damaging error bursts in large-scale devices, and highlight the necessity of mitigation to enable quantum computing to scale.

Primary thermometry of propagating microwaves in the quantum regime

  1. Marco Scigliuzzo,
  2. Andreas Bengtsson,
  3. Jean-Claude Besse,
  4. Andreas Wallraff,
  5. Per Delsing,
  6. and Simone Gasparinetti
The ability to control and measure the temperature of propagating microwave modes down to very low temperatures is indispensable for quantum information processing, and may open opportunities
for studies of heat transport at the nanoscale, also in the quantum regime. Here we propose and experimentally demonstrate primary thermometry of propagating microwaves using a transmon-type superconducting circuit. Our device operates continuously, with a sensitivity down to 4×10−4 photons/Hz−−−√ and a bandwidth of 40 MHz. We measure the thermal occupation of the modes of a highly attenuated coaxial cable in a range of 0.001 to 0.4 thermal photons, corresponding to a temperature range from 35 mK to 210 mK at a frequency around 5 GHz. To increase the radiation temperature in a controlled fashion, we either inject calibrated, wideband digital noise, or heat the device and its environment. This thermometry scheme can find applications in benchmarking and characterization of cryogenic microwave setups, temperature measurements in hybrid quantum systems, and quantum thermodynamics.

Multi-level Quantum Noise Spectroscopy

  1. Youngkyu Sung,
  2. Antti Vepsäläinen,
  3. Jochen Braumüller,
  4. Fei Yan,
  5. Joel I-Jan Wang,
  6. Morten Kjaergaard,
  7. Roni Winik,
  8. Philip Krantz,
  9. Andreas Bengtsson,
  10. Alexander J. Melville,
  11. Bethany M. Niedzielski,
  12. Mollie E. Schwartz,
  13. David K. Kim,
  14. Jonilyn L. Yoder,
  15. Terry P. Orlando,
  16. Simon Gustavsson,
  17. and William D. Oliver
System noise identification is crucial to the engineering of robust quantum systems. Although existing quantum noise spectroscopy (QNS) protocols measure an aggregate amount of noise
affecting a quantum system, they generally cannot distinguish between the underlying processes that contribute to it. Here, we propose and experimentally validate a spin-locking-based QNS protocol that exploits the multi-level energy structure of a superconducting qubit to achieve two notable advances. First, our protocol extends the spectral range of weakly anharmonic qubit spectrometers beyond the present limitations set by their lack of strong anharmonicity. Second, the additional information gained from probing the higher-excited levels enables us to identify and distinguish contributions from different underlying noise mechanisms.

Quantum approximate optimization of the exact-cover problem on a superconducting quantum processor

  1. Andreas Bengtsson,
  2. Pontus Vikstål,
  3. Christopher Warren,
  4. Marika Svensson,
  5. Xiu Gu,
  6. Anton Frisk Kockum,
  7. Philip Krantz,
  8. Christian Križan,
  9. Daryoush Shiri,
  10. Ida-Maria Svensson,
  11. Giovanna Tancredi,
  12. Göran Johansson,
  13. Per Delsing,
  14. Giulia Ferrini,
  15. and Jonas Bylander
Present-day, noisy, small or intermediate-scale quantum processors—although far from fault-tolerant—support the execution of heuristic quantum algorithms, which might enable
a quantum advantage, for example, when applied to combinatorial optimization problems. On small-scale quantum processors, validations of such algorithms serve as important technology demonstrators. We implement the quantum approximate optimization algorithm (QAOA) on our hardware platform, consisting of two transmon qubits and one parametrically modulated coupler. We solve small instances of the NP-complete exact-cover problem, with 96.6\% success probability, by iterating the algorithm up to level two.