Storing Quantum Information in Schrödinger's Cats Peter J. Leek Science 342, 568 (2013); DOI: 10.1126/science.1245510
If you wish to distribute this article to others, you can order high-quality copies for your colleagues, clients, or customers by clicking here. Permission to republish or repurpose articles or portions of articles can be obtained by following the guidelines here. The following resources related to this article are available online at www.sciencemag.org (this information is current as of October 31, 2013 ): Updated information and services, including high-resolution figures, can be found in the online version of this article at: http://www.sciencemag.org/content/342/6158/568.full.html A list of selected additional articles on the Science Web sites related to this article can be found at: http://www.sciencemag.org/content/342/6158/568.full.html#related This article cites 14 articles, 3 of which can be accessed free: http://www.sciencemag.org/content/342/6158/568.full.html#ref-list-1
Science (print ISSN 0036-8075; online ISSN 1095-9203) is published weekly, except the last week in December, by the American Association for the Advancement of Science, 1200 New York Avenue NW, Washington, DC 20005. Copyright 2013 by the American Association for the Advancement of Science; all rights reserved. The title Science is a registered trademark of AAAS.
Downloaded from www.sciencemag.org on November 1, 2013
This copy is for your personal, non-commercial use only.
PERSPECTIVES APPLIED PHYSICS
Storing Quantum Information in Schrödinger’s Cats
Superposition states created with more than 100 photons enable the storage of multiple bits of quantum information.
Peter J. Leek
W
hen Schrödinger came up with his thought experiment connecting the fate of a cat in a box to the quantum-mechanical process of radioactive decay (1), he probably did not consider that the idea might one day be used in technology. However, the transfer of the state of a superconducting quantum bit (qubit) to a 100-photon light state to map and store the A
we experience is something that has been a puzzle ever since the early days of quantum theory. Researchers are increasingly able to create and control quantum states of larger, more complex objects than individual atoms and bridge this quantum-to-classical gap step by step, at the same time bringing new technologies like quantum computing ever closer (3). B
4
can then live undisturbed for milliseconds or more (7, 8). Recent work by Paik et al. has showed that it is possible to realize record lifetime superconducting qubits strongly coupled to microwave photons in a surprisingly simple device in which the qubits are housed inside a three-dimensional (3D) superconducting cavity (6). The setup bears some resemblance to that used in the recent Q
C
90°
Im(α)
2
0
Phase
180° 0°
I
–2
–4
270° –4
–2
0
2
4
Re(α)
contained quantum information, as reported by Vlastakis et al. on page 607 of this issue (2), is analogous to this iconic thought experiment. In contrast with the original version, however, the researchers are in complete control of the process and envision its use to store multiple bits of quantum information in a future quantum processor. Quantum mechanics is typically associated with very small things, like atoms, rather than large everyday objects (like cats), and the contrast between the strange quantum world of superpositions and entanglement and the familiar classical world that Department of Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford, OX1 3PU, UK. E-mail: peter. [email protected]
568
between. This state is related to a superposition of cats at four different positions on a circle (B) and is also closely related to a communications protocol called quadrature phase-shift keying (C), which combines together four signals that differ from each other by a 90° phase shift, shown here as points on the complex plane, where I is the in-phase component and Q is the quadrature component.
Creating large, complex quantum objects is a substantial challenge, because the fragile states easily lose their coherence (their quantum nature) through interaction with the surrounding environment, unless that environment is exquisitely well controlled. In solidstate systems like superconducting circuits (4), overcoming environmental decoherence has always been a major research challenge. Superconducting qubits are macroscopic in size, and particularly strongly coupled to their electromagnetic environment. Decisive steps forward in the field have been made by “hiding” qubits from the outside world by embedding them inside high-quality resonant cavities (5, 6), in which electromagnetic fields (or photons) can only reside if they have very specific resonant frequencies, and
pioneering experiments with Rydberg atom and microwave photon cavity quantum electrodynamics by Haroche and co-workers (7). The strong coupling and coherence possible in this new architecture, along with a new protocol for efficiently transferring qubit states to coherent light states ( 9), have now enabled Vlastakis et al. to create Schrödinger cats of an impressive size, consisting of up to 111 microwave photons trapped inside the 3D cavity. Controlled generation of modest-sized cat states has been demonstrated before, using trapped ions (10) and photons (11, 12), and also in superconducting circuits (13), but key to this new work is the efficiency and flexibility of the implemented protocol. It does not grow in complexity with the size of the generated
1 NOVEMBER 2013 VOL 342 SCIENCE www.sciencemag.org Published by AAAS
CREDIT: P. HUEY/SCIENCE
Four-state Schrodinger cats. (A) A superposition of four coherent light states, measured by Vlastakis et al. displays rich features in its Wigner function (plotted as a function of the real and imaginary parts of the superposition state α). The four coherent states appear as red smudges, and the sign of the quantum character of the superposition state is seen in the red-blue interference fringes in
PERSPECTIVES cat states and allows generation of states with any chosen amplitude and phase. The telltale sign of the quantum nature of the created states is seen by measuring a kind of phase diagram for the light, called the Wigner function (see the figure, panel A), which visualizes interference fringes between the superposed states, much like those observed in the classic double-slit experiment. Whereas Schrödinger’s original concept involved superpositions of two classical states (a dead and living cat), Vlastakis et al. demonstrate cats with up to four different states in superposition (see the figure, panel B). Extended further, this approach could be very useful in a quantum computer; with a coherent enough cavity, superpositions of many more than four states could be stored in it, making it an excellent candidate for a quantum memory. Interestingly, Vlastakis et al. point out that the methods they use are similar to those already in use in communications technol-
ogy, in a scheme known as phase-shift keying (PSK). Here, multiple bits of information on communications channels are stored by the same frequency carrier wave, but at different phases (two or four are typically used; see the figure, panel C) to increase data rates. In much the same way, quantum PSK could be useful in future quantum technology for efficient storage and communication of quantum data. The Schrödinger cat states may be useful not only in quantum memories but also in quantum metrology because of the interference patterns present in the phase space representation of the states (2, 14). Imagine measuring a point near the center of the diagram of the cat state shown in panel A of the figure. Just a small shift or rotation of the picture would give a large change in the measurement at that point (for example, a shift from a red to a blue spot). Such sensitive measurements are impossible with a classical state, in which these interference fringes
are simply not present. This example illustrates a key point of much of quantum information research, that coherent quantum systems often display behavior that has no classical counterpart and that may be exploited to realize transformative new technologies. References 1. E. Schrödinger, Naturwissenschaften 23, 807 (1935). 2. B. Vlastakis et al., Science 342, 607 (2013); 10.1126/ science.1243289 3. Special Issue on Quantum Information Processing, Science 339, 1163 (2013). 4. M. H. Devoret, R. J. Schoelkopf, Science 339, 1169 (2013). 5. A. Wallraff et al., Nature 431, 162 (2004). 6. H. Paik et al., Phys. Rev. Lett. 107, 240501 (2011). 7. S. Gleyzes et al., Nature 446, 297 (2007). 8. M. Reagor et al., Appl. Phys. Lett. 102, 192604 (2013). 9. Z. Leghtas et al., Phys. Rev. A 87, 042315 (2013). 10. D. Leibfried et al., Nature 438, 639 (2005). 11. A. Ourjoumtsev, H. Jeong, R. Tualle-Brouri, P. Grangier, Nature 448, 784 (2007). 12. S. Deléglise et al., Nature 455, 510 (2008). 13. M. Hofheinz et al., Nature 459, 546 (2009). 14. W. H. Zurek, Nature 412, 712 (2001). 10.1126/science.1245510
PHYSICS
Quantized Electronic Heat Flow Björn Sothmann and Christian Flindt
T
raffic laws impose strict limits on the maximum speed of cars on a highway. In nanoscale electronics, the laws of quantum physics similarly set an upper limit to the electrical conductance of a conductor. This was first demonstrated three decades ago (1, 2) on a quantum point contact—a narrow constriction connecting two electronic reservoirs. A similar prediction has been made for the maximal heat conductance of an electronic conductor (3, 4), but an experimental verification has so far been missing. On page 601 of this issue, Jezouin et al. (5) measure the quantum-limited electronic heat flow in a quantum point contact, paving the way for novel heat-control technologies at the nanoscale. In quantum electronics, electrons behave as waves. They may be spread out over a spatial region, and they may interfere with themselves, as well as with other electrons. Quantum electronics is typically implemented in two-dimensional electron gases captured at the interface between semiconducting materials. With a magnetic field Département de Physique Théorique, Université de Genève, 24 quai Ernest Ansermet, CH-1211 Genève 4, Switzerland. E-mail: [email protected] (B.S.)
A measurement of the quantum-limited heat flow in an electronic conductor opens a pathway to the nanoscale control of heat currents.
applied, the electrons in the gas move along the boundaries of the sample in directional edge states, which function as electronic
highways (6). The number of one-way lanes (or edge states) on the highway can be controlled with an external gate voltage. Each edge state is a conduction channel that can guide a stream of electrons toward a quantum point contact. The width of the quantum point contact can be adjusted to control Ge GQ the number of channels passing through it. Quantum point contacts constitute one of the fundamental building blocks in quantum electronics. A hallmark prediction in the field of mesoscopic physics is the quantization of the electrical conductance of a quantum point conSpeed limits on the highway. Quantum physics predicts an tact. The conductance quantifies upper limit to the electrical conductance (Ge), as well as the heat the current that runs in a conducconductance (GQ) of a single quantum channel. For electrons, the tor in response to a small voltage quantum-limited electrical conductance was measured nearly 30 applied across it. Each fully open years ago (1, 2). Now, Jezouin et al. have measured the quan- conduction channel in a quantum tum-limited heat conductance in a quantum point contact—the point contact contributes to the narrow constriction connecting two electronic reservoirs. Edge total conductance with one constates running along the boundaries of the sample function as duction quantum whose value is the lanes on an electronic highway. The number of edge states going through the quantum point contact can be controlled. determined by fundamental conHere, only the edge states in green pass through the quantum stants only (7). Specifically, the point contact, allowing Jezouin et al. to measure the maximal electronic conduction quantum is simply the square of the electronic heat conduction of a single electronic conduction channel.
www.sciencemag.org SCIENCE VOL 342 1 NOVEMBER 2013 Published by AAAS
569
If you wish to distribute this article to others, you can order high-quality copies for your colleagues, clients, or customers by clicking here. Permission to republish or repurpose articles or portions of articles can be obtained by following the guidelines here. The following resources related to this article are available online at www.sciencemag.org (this information is current as of October 31, 2013 ): Updated information and services, including high-resolution figures, can be found in the online version of this article at: http://www.sciencemag.org/content/342/6158/568.full.html A list of selected additional articles on the Science Web sites related to this article can be found at: http://www.sciencemag.org/content/342/6158/568.full.html#related This article cites 14 articles, 3 of which can be accessed free: http://www.sciencemag.org/content/342/6158/568.full.html#ref-list-1
Science (print ISSN 0036-8075; online ISSN 1095-9203) is published weekly, except the last week in December, by the American Association for the Advancement of Science, 1200 New York Avenue NW, Washington, DC 20005. Copyright 2013 by the American Association for the Advancement of Science; all rights reserved. The title Science is a registered trademark of AAAS.
Downloaded from www.sciencemag.org on November 1, 2013
This copy is for your personal, non-commercial use only.
PERSPECTIVES APPLIED PHYSICS
Storing Quantum Information in Schrödinger’s Cats
Superposition states created with more than 100 photons enable the storage of multiple bits of quantum information.
Peter J. Leek
W
hen Schrödinger came up with his thought experiment connecting the fate of a cat in a box to the quantum-mechanical process of radioactive decay (1), he probably did not consider that the idea might one day be used in technology. However, the transfer of the state of a superconducting quantum bit (qubit) to a 100-photon light state to map and store the A
we experience is something that has been a puzzle ever since the early days of quantum theory. Researchers are increasingly able to create and control quantum states of larger, more complex objects than individual atoms and bridge this quantum-to-classical gap step by step, at the same time bringing new technologies like quantum computing ever closer (3). B
4
can then live undisturbed for milliseconds or more (7, 8). Recent work by Paik et al. has showed that it is possible to realize record lifetime superconducting qubits strongly coupled to microwave photons in a surprisingly simple device in which the qubits are housed inside a three-dimensional (3D) superconducting cavity (6). The setup bears some resemblance to that used in the recent Q
C
90°
Im(α)
2
0
Phase
180° 0°
I
–2
–4
270° –4
–2
0
2
4
Re(α)
contained quantum information, as reported by Vlastakis et al. on page 607 of this issue (2), is analogous to this iconic thought experiment. In contrast with the original version, however, the researchers are in complete control of the process and envision its use to store multiple bits of quantum information in a future quantum processor. Quantum mechanics is typically associated with very small things, like atoms, rather than large everyday objects (like cats), and the contrast between the strange quantum world of superpositions and entanglement and the familiar classical world that Department of Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford, OX1 3PU, UK. E-mail: peter. [email protected]
568
between. This state is related to a superposition of cats at four different positions on a circle (B) and is also closely related to a communications protocol called quadrature phase-shift keying (C), which combines together four signals that differ from each other by a 90° phase shift, shown here as points on the complex plane, where I is the in-phase component and Q is the quadrature component.
Creating large, complex quantum objects is a substantial challenge, because the fragile states easily lose their coherence (their quantum nature) through interaction with the surrounding environment, unless that environment is exquisitely well controlled. In solidstate systems like superconducting circuits (4), overcoming environmental decoherence has always been a major research challenge. Superconducting qubits are macroscopic in size, and particularly strongly coupled to their electromagnetic environment. Decisive steps forward in the field have been made by “hiding” qubits from the outside world by embedding them inside high-quality resonant cavities (5, 6), in which electromagnetic fields (or photons) can only reside if they have very specific resonant frequencies, and
pioneering experiments with Rydberg atom and microwave photon cavity quantum electrodynamics by Haroche and co-workers (7). The strong coupling and coherence possible in this new architecture, along with a new protocol for efficiently transferring qubit states to coherent light states ( 9), have now enabled Vlastakis et al. to create Schrödinger cats of an impressive size, consisting of up to 111 microwave photons trapped inside the 3D cavity. Controlled generation of modest-sized cat states has been demonstrated before, using trapped ions (10) and photons (11, 12), and also in superconducting circuits (13), but key to this new work is the efficiency and flexibility of the implemented protocol. It does not grow in complexity with the size of the generated
1 NOVEMBER 2013 VOL 342 SCIENCE www.sciencemag.org Published by AAAS
CREDIT: P. HUEY/SCIENCE
Four-state Schrodinger cats. (A) A superposition of four coherent light states, measured by Vlastakis et al. displays rich features in its Wigner function (plotted as a function of the real and imaginary parts of the superposition state α). The four coherent states appear as red smudges, and the sign of the quantum character of the superposition state is seen in the red-blue interference fringes in
PERSPECTIVES cat states and allows generation of states with any chosen amplitude and phase. The telltale sign of the quantum nature of the created states is seen by measuring a kind of phase diagram for the light, called the Wigner function (see the figure, panel A), which visualizes interference fringes between the superposed states, much like those observed in the classic double-slit experiment. Whereas Schrödinger’s original concept involved superpositions of two classical states (a dead and living cat), Vlastakis et al. demonstrate cats with up to four different states in superposition (see the figure, panel B). Extended further, this approach could be very useful in a quantum computer; with a coherent enough cavity, superpositions of many more than four states could be stored in it, making it an excellent candidate for a quantum memory. Interestingly, Vlastakis et al. point out that the methods they use are similar to those already in use in communications technol-
ogy, in a scheme known as phase-shift keying (PSK). Here, multiple bits of information on communications channels are stored by the same frequency carrier wave, but at different phases (two or four are typically used; see the figure, panel C) to increase data rates. In much the same way, quantum PSK could be useful in future quantum technology for efficient storage and communication of quantum data. The Schrödinger cat states may be useful not only in quantum memories but also in quantum metrology because of the interference patterns present in the phase space representation of the states (2, 14). Imagine measuring a point near the center of the diagram of the cat state shown in panel A of the figure. Just a small shift or rotation of the picture would give a large change in the measurement at that point (for example, a shift from a red to a blue spot). Such sensitive measurements are impossible with a classical state, in which these interference fringes
are simply not present. This example illustrates a key point of much of quantum information research, that coherent quantum systems often display behavior that has no classical counterpart and that may be exploited to realize transformative new technologies. References 1. E. Schrödinger, Naturwissenschaften 23, 807 (1935). 2. B. Vlastakis et al., Science 342, 607 (2013); 10.1126/ science.1243289 3. Special Issue on Quantum Information Processing, Science 339, 1163 (2013). 4. M. H. Devoret, R. J. Schoelkopf, Science 339, 1169 (2013). 5. A. Wallraff et al., Nature 431, 162 (2004). 6. H. Paik et al., Phys. Rev. Lett. 107, 240501 (2011). 7. S. Gleyzes et al., Nature 446, 297 (2007). 8. M. Reagor et al., Appl. Phys. Lett. 102, 192604 (2013). 9. Z. Leghtas et al., Phys. Rev. A 87, 042315 (2013). 10. D. Leibfried et al., Nature 438, 639 (2005). 11. A. Ourjoumtsev, H. Jeong, R. Tualle-Brouri, P. Grangier, Nature 448, 784 (2007). 12. S. Deléglise et al., Nature 455, 510 (2008). 13. M. Hofheinz et al., Nature 459, 546 (2009). 14. W. H. Zurek, Nature 412, 712 (2001). 10.1126/science.1245510
PHYSICS
Quantized Electronic Heat Flow Björn Sothmann and Christian Flindt
T
raffic laws impose strict limits on the maximum speed of cars on a highway. In nanoscale electronics, the laws of quantum physics similarly set an upper limit to the electrical conductance of a conductor. This was first demonstrated three decades ago (1, 2) on a quantum point contact—a narrow constriction connecting two electronic reservoirs. A similar prediction has been made for the maximal heat conductance of an electronic conductor (3, 4), but an experimental verification has so far been missing. On page 601 of this issue, Jezouin et al. (5) measure the quantum-limited electronic heat flow in a quantum point contact, paving the way for novel heat-control technologies at the nanoscale. In quantum electronics, electrons behave as waves. They may be spread out over a spatial region, and they may interfere with themselves, as well as with other electrons. Quantum electronics is typically implemented in two-dimensional electron gases captured at the interface between semiconducting materials. With a magnetic field Département de Physique Théorique, Université de Genève, 24 quai Ernest Ansermet, CH-1211 Genève 4, Switzerland. E-mail: [email protected] (B.S.)
A measurement of the quantum-limited heat flow in an electronic conductor opens a pathway to the nanoscale control of heat currents.
applied, the electrons in the gas move along the boundaries of the sample in directional edge states, which function as electronic
highways (6). The number of one-way lanes (or edge states) on the highway can be controlled with an external gate voltage. Each edge state is a conduction channel that can guide a stream of electrons toward a quantum point contact. The width of the quantum point contact can be adjusted to control Ge GQ the number of channels passing through it. Quantum point contacts constitute one of the fundamental building blocks in quantum electronics. A hallmark prediction in the field of mesoscopic physics is the quantization of the electrical conductance of a quantum point conSpeed limits on the highway. Quantum physics predicts an tact. The conductance quantifies upper limit to the electrical conductance (Ge), as well as the heat the current that runs in a conducconductance (GQ) of a single quantum channel. For electrons, the tor in response to a small voltage quantum-limited electrical conductance was measured nearly 30 applied across it. Each fully open years ago (1, 2). Now, Jezouin et al. have measured the quan- conduction channel in a quantum tum-limited heat conductance in a quantum point contact—the point contact contributes to the narrow constriction connecting two electronic reservoirs. Edge total conductance with one constates running along the boundaries of the sample function as duction quantum whose value is the lanes on an electronic highway. The number of edge states going through the quantum point contact can be controlled. determined by fundamental conHere, only the edge states in green pass through the quantum stants only (7). Specifically, the point contact, allowing Jezouin et al. to measure the maximal electronic conduction quantum is simply the square of the electronic heat conduction of a single electronic conduction channel.
www.sciencemag.org SCIENCE VOL 342 1 NOVEMBER 2013 Published by AAAS
569
