METHODS, SYSTEMS, AND APPARATUS FOR PROGRAMMABLE QUANTUM PHOTONIC PROCESSING

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First Claim
1. A photonic device comprising:
 a semiconductor substrate;
a plurality of interconnected variable beam splitters, fabricated in the semiconductor substrate, configured to perform an arbitrary unitary optical transformation on at least one optical mode, the plurality of interconnected variable beam splitters having a plurality of input waveguides configured to receive the at least one optical mode and a plurality of output waveguides configured to output the at least one optical mode after the arbitrary unitary optical transformation;
a plurality of detectors, in optical communication with the plurality of output waveguides, configured to measure the at least one optical mode after the arbitrary unitary optical transformation; and
control circuitry, operably coupled to the plurality of interconnected variable beam splitters and to the plurality of detectors, configured to determine a density distribution of the at least one optical mode at the plurality of output waveguides and configured to adjust at least one setting of at least one variable beam splitter in the plurality of interconnected variable beam splitters so as to change the density distribution of the at least one optical mode at the plurality of output waveguides.
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Abstract
A programmable photonic integrated circuit implements arbitrary linear optics transformations in the spatial mode basis with high fidelity. Under a realistic fabrication model, we analyze programmed implementations of the CNOT gate, CPHASE gate, iterative phase estimation algorithm, state preparation, and quantum random walks. We find that programmability dramatically improves device tolerance to fabrication imperfections and enables a single device to implement a broad range of both quantum and classical linear optics experiments. Our results suggest that existing fabrication processes are sufficient to build such a device in the silicon photonics platform.
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1 Claim
 1. A photonic device comprising:
a semiconductor substrate; a plurality of interconnected variable beam splitters, fabricated in the semiconductor substrate, configured to perform an arbitrary unitary optical transformation on at least one optical mode, the plurality of interconnected variable beam splitters having a plurality of input waveguides configured to receive the at least one optical mode and a plurality of output waveguides configured to output the at least one optical mode after the arbitrary unitary optical transformation; a plurality of detectors, in optical communication with the plurality of output waveguides, configured to measure the at least one optical mode after the arbitrary unitary optical transformation; and control circuitry, operably coupled to the plurality of interconnected variable beam splitters and to the plurality of detectors, configured to determine a density distribution of the at least one optical mode at the plurality of output waveguides and configured to adjust at least one setting of at least one variable beam splitter in the plurality of interconnected variable beam splitters so as to change the density distribution of the at least one optical mode at the plurality of output waveguides.
1 Specification
This application is a continuation of U.S. application Ser. No. 15/716,196, filed Sep. 26, 2017, entitled “Programmable Quantum Processing,” which is a continuation of U.S. application Ser. No. 15/143,450, now U.S. Pat. No. 9,791,258, filed Apr. 29, 2016, entitled, “Methods, Systems, and Apparatus for Programmable Quantum Photonic Processing,” which is a continuation of U.S. application Ser. No. 14/732,012, filed Jun. 5, 2015, and entitled “METHODS, SYSTEMS, AND APPARATUS FOR PROGRAMMABLE QUANTUM PHOTONIC PROCESSING,” which in turn claims priority, under 35 U.S.C. § 119(e), from U.S. Application No. 62/008,870, filed Jun. 6, 2014, and entitled “A Programmable Photonic Integrated Network for Universal Linear Optics.” Each of these applications is hereby incorporated herein by reference in its entirety.
This invention was made with government support under Grant No. FA95501410052 awarded by the U.S. Air Force. The government has certain rights in the invention.
Conventional computers work by manipulating bits that exist in either a 0 state or a 1 state. In contrast, quantum computers encode information as quantum bits, or qubits, which can exist in 0 state, 1 state or a superposition of 0 and 1 states. In other words, qubits can be both 0 and 1 (and all points in between) at the same time. Qubits can be represented by atoms, ions, photons or electrons and their respective control devices that are working together to act as computer memory and a processor.
The superposition of qubits can give quantum computers inherent parallelism and allow a quantum computer to work on a large number of computations at once, while conventional computers work on one computation at a time. For example, a 30qubit quantum computer can equal the processing power of a conventional computer that could run at 10 teraflops (trillions of floatingpoint operations per second). As a comparison, today'"'"'s typical desktop computers run at speeds measured in gigaflops (billions of floatingpoint operations per second).
Quantum computers can also utilize another aspect of quantum mechanics known as entanglement, which can enables making measurement of the qubits indirectly to preserve their integrity (i.e., without changing their values). In quantum physics, if an outside force is applied to two atoms, the outside force can cause the two atoms to become entangled, and the second atom can take on the properties of the first atom. If left alone, one atom will spin in all directions. Once disturbed, one atom chooses one spin, or one value. At the same time, the second entangled atom chooses an opposite spin, or value. Therefore, the properties of one atom in an entangled pair can be derived by measuring the properties of the other atom in the entangled pair. This method avoids any direct measurement of the atom of interest, thereby avoiding changing or destroying the value of the qubit due to measurement.
Embodiments of the present invention include apparatus, systems, and methods of programmable quantum photonic processing. In one example, a photonic integrated circuit for performing quantum information processing includes a semiconductor substrate and a plurality of interconnected MachZehnder interferometers. The plurality of interconnected MachZehnder interferometers is fabricated in the semiconductor substrate to perform at least one linear optical transformation on a plurality of optical modes coupled into the plurality of interconnected MachZehnder interferometers. The photonic integrated circuit further includes a plurality of detectors, in optical communication with the plurality of MachZehnder interferometers, to measure an output state of the plurality of optical modes. Control circuitry, operably coupled to the interconnected MachZehnder interferometers and to the detectors, is configured to determine a fidelity of the output state of the optical modes to an ideal output state of the optical modes and to adjust a phase setting of at least one of the MachZehnder interferometers so as to increase the fidelity of the output state of the optical modes to the ideal output state of the optical modes.
In another example, a method of performing quantum information processing includes (A) coupling a plurality of optical modes into a plurality of interconnected MachZehnder interferometers fabricated in a semiconductor substrate so as to perform at least one linear optical transformation on the optical modes; (B) detecting the optical modes at an output of the interconnected MachZehnder interferometers; (C) determining a fidelity of the output state of the optical modes to an ideal output state of the optical modes; and (D) adjusting at least one phase of at least one of the MachZehnder interferometers so as to increase the fidelity of the output state of the optical modes to the ideal output state of the optical modes.
It should be appreciated that all combinations of the foregoing concepts and additional concepts discussed in greater detail below (provided such concepts are not mutually inconsistent) are contemplated as being part of the inventive subject matter disclosed herein. In particular, all combinations of claimed subject matter appearing at the end of this disclosure are contemplated as being part of the inventive subject matter disclosed herein. It should also be appreciated that terminology explicitly employed herein that also may appear in any disclosure incorporated by reference should be accorded a meaning most consistent with the particular concepts disclosed herein.
The skilled artisan will understand that the drawings primarily are for illustrative purposes and are not intended to limit the scope of the inventive subject matter described herein. The drawings are not necessarily to scale; in some instances, various aspects of the inventive subject matter disclosed herein may be shown exaggerated or enlarged in the drawings to facilitate an understanding of different features. In the drawings, like reference characters generally refer to like features (e.g., functionally similar and/or structurally similar elements).
Overview
Rapid advances in photonic integrated circuits (PIC) enable the experimental implementation of quantum information processing protocols using linear optics, including quantum simulation and boson sampling. PICs can contain a large number of optical components and can perform tunable, highfidelity quantum operations. Generation of highdimensional optical transformations can be a primary application of photonic integrated circuits in both the quantum and classical regimes. Examples include linear optics quantum gates, onetomany power splitters, and mixers for optical transceivers. However, these systems are typically custombuilt for each application and, in general, are not tuned insitu to combat fabrication errors. In other words, conventional systems are singlepurpose devices (i.e., not programmable or reconfigurable) in which only a small subset of linear optics transformations could be implemented.
A programmable linear quantum system can accelerate prototyping and scaling of quantum algorithms. Here, a programmable quantum photonic processor (QPP) that enables dynamic implementation of any unitary linear optics transformation on a set of input photons in a single device is disclosed. These transformations are realized using a network of dynamically tunable MachZehnder interferometers (MZIs) on a monolithic silicon PIC. Even a small QPP with eight waveguide modes can be programed to implement a variety of linear optics proposals, including the quantum iterative phase estimation algorithm (IPEA), sixmode CNOT gate, and discretetime quantum walk with disorder and decoherence, thereby demonstrating the versatility of this network. Dynamic optimization of circuit parameters can also compensate for fabrication defects, dramatically improving the fidelity of quantum gates to near unity.
The reconfigurability of the proposed QPP offers several advantages. First of all, the reconfigurability can be used to correct for fabrication imperfections, to perform process tomography at any stage of the network, and to enable rapid statistical averaging over multiple circuit realizations to investigate the role of disorder and noise in quantum random walks (QRW). Further, the ability to rapidly implement an arbitrary unitary optical transformation on a large set of spatial modes can greatly accelerate the development, optimization, and verification of linear optics quantum algorithms.
In general, the proposed programmable QPP can perform high fidelity operations and can be constructed using experimentally demonstrated devices fabricated in standard silicon photonics processes. The tiled unit cell of the QPP is a phasestable, waveguidebased MachZehnder interferometer (MZI) with an internal and external phase shifter. Even a small QPP, operating on 1020 spatial modes, could be programmed to implement a wide range of proposals including postselected photonic quantum gates, optical quantum simulation, and quantum random walks (QRW), as well as classical switching and transformation optics. The QPP can also be expanded to include integrated detectors and fast switches to implement scalable linear optical quantum computing (LOQC). The QPP can be further augmented with emerging integrated devices, including singlephoton detectors, singlephoton sources, lowphotonnumber nonlinear elements, and classical feedforward logic.
Hardware Model
The control circuitry 140 is configured to determine a fidelity of the output state 15 of the plurality of optical modes 10 to an ideal output state of the plurality of optical modes 10. The control circuitry is also configured to adjust a phase setting of at least one variable beam splitter in the plurality of interconnected variable beam splitters 120 so as to increase the fidelity of the output state 15 of the plurality of optical modes 10 to the ideal output state of the plurality of optical modes 10.
The semiconductor substrate 110 is in general transparent at the wavelength of the optical modes 10. Exemplary wavelengths of the optical modes 10 can be from visible to the midinfrared region, although other wavelengths can also be used. The semiconductor substrate 110 can also be machineable so as to form singlemode optical components (e.g., waveguides). Examples of suitable semiconductor substrate materials include, but are not limited to, silicon, gallium phosphide, silicon nitride, silicon oxynitride, gallium arsenide, gallium nitride, indium phosphide, lithium niobate, chalcogenides, and silicaonsilicon.
The interconnected variable beam splitters 120 can have adjustable reflectivity (or transmission) between 0 and 1. Such adjustable reflectivity can be implemented in various ways. In one example, the interconnected variable beam splitters 120 form Mach Zehnder Interferometers (MZIs), which further comprise directional couplers and phase shifters. In another example, the interconnected variable beam splitters 120 include waveguides and polarization optics and mechanical motion to change waveguide coupling so as to adjust a directional coupler splitting ratio.
The linear optical transformation that can be performed by the interconnected variable beam splitters 120 on the optical modes 10 include, but are not limited to modecrossings, identity operations, and mode mixing (combining the two input modes at different ratios). The optical modes 10 can be either spolarized or ppolarized, or a combination of spolarization and ppolarization. In other words, the QPP 100 or more specifically the interconnected variable beam splitters 120 can be configured to be polarization insensitive.
The plurality of interconnected variable beam splitters 120 can be configured to implement various optical circuits, including, for example, a CNOT gate, a CPHASE gate, an iterative phase estimation, a single qubit rotation, a quantum random walk, their combinations, or any circuits based on the above.
The detectors 130 can include any device that can send out identifiable signals with high probability if a photon hits the device. Similarly, if a signal is sent out from the device, it is mostly like due to a photon hitting the device. In this way, the detectors 130 can provide accurate and reliable data about the number and state of the photons that reach the detectors 130. Examples of detectors 130 include, but are not limited to, superconducting nanowire single photon detectors (SNSPD), IIIN type avalanche photodiodes (APD), Ge APDs, photomultiplier tubes (PMT), and transition edge sensors (TES).
The control circuitry 140 in the QPP 100 is configured to determine a fidelity of the output state 15 of the plurality of optical modes 10 to an ideal output state of the plurality of optical modes 10. Without being bound by any particular theory or mode of operation, in quantum information theory, fidelity can be defined as a measure of the “closeness” of two quantum states. In practice, fidelity can be calculated in terms of trace distance or HilbertSchmidt inner product of the two quantum states, which is given by F=V†V_{0}^{2}, where V_{0 }is the ideal transformation and V is the actual transformation. In general, higher fidelity in a quantum processor means the generated output state more closely resembles the desired output state.
Based, at least in part, on the determined fidelity of the output state 15, the control circuitry 140 is configured to change the phase setting of the interconnected variable beam splitters 120. For example, the control circuity 140 can be configured to change the time it takes for an optical mode 10 to travel from the beginning to the end of a physical phase shifter (e.g., 221a and 221b in
The optical modes 10 can be coupled into the plurality of interconnected variable beam splitters 120 via various ways. In one example, the optical modes 10 are generated onchip (e.g., by a light source fabricated on the same semiconductor substrate 110 or another substrate closely coupled to the semiconductor substrate 110), and the optical modes 10 are routed to the interconnected variable beam splitters 120 via waveguides. Light sources that can be fabricated on the semiconductor substrate 110 can include, but are not limited to, laser diodes, surface emitting lasers, quantum cascade lasers, or any other type of semiconductor layers known in the art. In another example, the optical modes 10 are generated offchip, in which case the optical modes 10 are routed to the waveguides in the interconnected variable beam splitters 120 through free space optics, optical fibers, etc. Optical fibers can be coupled to the waveguides in a number of ways, including fiber arrays coupled to arrays of grating couplers, fiber arrays coupled to arrays of edge couplers containing waveguide inverse tapers, fiber arrays coupled to modematching structures on the edge of the chip. Single fibers can be coupled to all of the same. The individual fibers can have numerical apertures matched to the numerical aperture of the waveguide for efficient coupling.
In one example, the QPP 100 as shown in
The two beam splitters 211a and 211b can be 50:50 beam splitters and can include, for example, directional couplers, multimode interferometers, stimulated Raman adiabatic passage (STIRAP) couplers, or other beam splitting means known in the art. The first phase shifter 221a, disposed on one arm of the MZI 201, adjusts an internal phase θ (between 0 and 2π) of light traveling through the arm and can control the coupling ratio of the top input arm and top output arm according to η=sin(θ)^{2}. The second phase shifter 221b adjusts an external phase Φ (between 0 and 2π) of light traveling in the top output arm and controls the relative phase of the two output arms of the MZI 201. Therefore, tuning the internal and external phase differences can adjust the splitting ratio and differential output phase, respectively, thereby allowing any beam splitter (i.e., any 2×2 unitary) to be implemented.
Linear Quantum Optical Computing
As illustrated in
Both losses and splitting ratios can be modeled with Gaussian distributions. The means (standard deviations) of optical losses and splitting ratios can be, for example, 5.16% and 50% (2.84% and 4.3%), respectively. While only two tunable phase shifters are considered here for each MZI, an additional phase shifter on each internal and external arm of the MZIs (e.g., see
Using the above modeling of losses and splitting ratios, specific gates in quantum photonic processors can be investigated. For example, a CNOT gate can be implemented in a network of waveguides, as shown in
acts as a mirror with transfer matrix
The schematic of unitMZI in this CNOT gate can be seen in, for example,
Experimental realizations of this postselected CNOT gate shown in
A nonlinear optimization can be split into characterization and tuning. Characterization generally involves determining, as a function of input voltages, the transformation performed by each MZI (unit cell) in the array. Once the transformation for each block (MZI) as a function of voltage is determined, the effect of cascading several of these blocks (MZIs) can then be simulated. More specifically, the knowledge of the transformation for each MZI can be used to calculate the transformation performed by a section of the QPP including multiple MZIs. Subsequent steps in the nonlinear optimization can take place as follows: 1) calculate the fidelity of the transformation resulting from a “naïve” programming of the array (what would be programmed into the QPP as if the fabrication was perfect); and 2) using this “naïve” setting as a starting point, implement a global nonlinear optimization to improve the fidelity of the transformation in this block. The available “knobs” (adjustable parameters) are the voltages/phases set in the QPP. Step 2) of the nonlinear process may be implemented by the NLopt software, which can be found at http.//abinitio.mit.edu/wiki/index.php/Citing_NLopt.
Quantum Simulation
Due to the stability and dynamic reconfigurability of the QPP, more complex circuits can be implemented well with the QPP. The ability to achieve high fidelity makes the QPP an attractive platform for photonic quantum simulation algorithms. Additionally, successive iterations of a single simulation can be rapidly updated based on prior measurements and different simulations can be programmed into one device.
As an example, an iterative phase estimation algorithm (IPEA) can be used for solving eigenvalue problems with applications in sensing and simulation.
More specifically, an IPEA can map a Hamiltonian to a unitary propagator, U, amenable to implementation in linear optics. Therefore, solving the eigenvalue problem
Uu>=e
^{i2πλ}
u>
is equivalent to calculating the energy levels of the Hamiltonian. By representing λ with a binary expansion of depth N, λ=Σ_{1}^{N}b_{i}2^{−i}, λ can be calculated by adaptive and iterative bitwise measurements. In the case of the QPP, this can be achieved by the application of different voltages across phase shifters. The least significant bit b_{N }can be calculated first using the circuit shown in
Applying a Hadamard transform sets the qubit deterministically in state 0 for b_{N}=0, and 1 for b_{N}=1. On subsequent iteration, k, the controlled unitary is set to U_{k}=(U_{N})^{2k/N }and ω_{k}=πΣ_{j=nk+1}^{N}b_{j}2^{njk }so that c is in state 0(1) if b_{k}=0 (b_{k}=1).
While only two qubits are used to simulate small molecules, such as H_{2}, many more qubits can be used to construct larger systems. The number of qubits scales to fifth order in the number of gates, further motivating the development of largescale, chipintegrated systems such as the QPP.
Quantum Random Walks: Introduction
The QPP is not limited to implementing the gate model of quantum computation; it also offers a unique opportunity to study other linear optics quantum information processing (QIP) schemes. Quantum walks, which describe the quantummechanical analogue of the classical random walk, can function as an alternative approach to QIP and for quantum simulation. Without being bound by any particular theory or mode of operation, a quantum walk can also be regarded as an experiment in which quantum particles, e.g., photons, can tunnel coherently into different locations or sites. Some promising applications include, but are not limited to, quantumwalk based search algorithms and Boson Sampling, where multipleparticle quantum walks can give rise to increased computation complexity. For example, quantum walks can be used to compute some matrix properties faster than a classical computer. In this context, a reconfigurable quantum walk with multiple quantum particles can provide a powerful and versatile platform for quantum information processing.
Quantum walks can also be useful to understand various physical and chemical mechanisms. As an example, quantum walks can simulate manyparticle transport in periodic and disordered systems, and can simulate biophysical processes such as optimal transfer in photosynthesis.
One challenge in random walks is disorder, which, in this context, can refer to the randomness of phase settings on the output of each step in the random walk. This may be extended to cover randomness in the probability in each step of moving left or right/up or down. For the single particle quantumwalk, timeindependent disorder can result in Anderson localization, while timedependent disorder can result in phasedecoherence and the emergence of classical randomwalklike dynamics. For two particles, periodic and disordered lattices may exhibit nontrivial quantum correlations. Much less is known about the interplay between manyparticle transport, entanglement, disorder and decoherence in quantum walks, and their dependence on different properties of the underlying graph such as the spatial and/or temporal correlations, other statistical properties of the disorder, or the existence of external driving fields. These issues can be investigated on the MZI array, where a time step corresponds to a column of the MZI array, and a spatial position corresponds to a row (see, e.g.,
A challenge in the study of quantum dynamics in disordered systems is that experiments studying only a single realization of disorder contain very little information and a specific realization can contain extreme arrangements leading to artifacts and nongeneral extreme events (see, e.g.,
The programmability of the QPP also enables detailed studies of single and multiphoton quantum random walks on a lattice with discrete, nearestneighbor coupling as shown in
Quantum Random Walks: State Preparation
The unit cell of the QPP (the MZI) in general does not necessarily implement a symmetric beam splitter and therefore realizes an asymmetric quantum walk. One possible method for realizing a symmetric quantum walk is disclosed here. With MZI phases set to θ=π/2 and φ=0, the following unitary (Hadamard) transformation is applied to the input modes (to a global phase),
Thus, photons incident from the left port (see,
Given two indistinguishable photons, this state can be prepared by the QPP.
In operation, one of the photons is launched into port R of a first type MZI 1110 and the other into port L of a second type MZI 1120—both of which are configured to implement “wires” with a variable output phase shift (θ=π while varying φ). To generate the NOON state described above, the second type MZI applies a relative phase shift of φ=π/2 while the first type MZI is set to apply φ=0 relative phase shift. All other MZIs 1130, marked in gray in
The first column (a.iiii) of
A QPP system can be characterized to extract sufficient information about each MZI to inform the optimizations described above. To start, a method is described that is algorithmically simple but involves augmenting the QPP unit cell to include detectors that can be “switched off” for example by using tunable ring resonators to create a switched drop filter. These detectors can be placed at the outputs of each MZI (e.g. the outputs at the top of
More specifically, the 2×2 transform of a given MZI is:
where γ_{1 }and γ_{3 }correspond to the losses in the θ and φ modulators, respectively, and γ_{2 }and γ_{4 }correspond to the other two (loss balancing, but otherwise inactive) modulators. V can be captured compactly as an arbitrary 2×2 complex matrix:
where x_{r}=x and x_{p}=arg(x) for x=a, b, c, or d, the x_{r}s are functions of θ, the x_{p}s are functions of both θ and φ. Then, the problem can be reduced to determining these eight real parameters as a function of the phases θ and φ.
The x_{r }elements can then be extracted directly using the embedded detectors; assuming that only one of the input optical powers P_{in,top }and P_{in,bottom }is nonzero for a given measurement:
a_{r}(θ)=√{square root over (P_{out,top}(θ)/P_{in,top})} (1)
b_{r}(θ)=√{square root over (P_{out,top}(θ)/P_{in,bottom})} (2)
c_{r}(θ)=√{square root over (P_{out,bottom}(θ)/P_{in,top})} (3)
d_{r}(θ)=√{square root over (P_{out,bottom}(θ)/P_{in,top})} (4)
Characterization of the array proceeds iteratively: a known optical power is inserted into each port of the array, and the corresponding matrix values are measured as a function of the relevant θ. This then allows the preparation of a known optical power at the inputs to the second layer, which, once characterized, allows for known optical powers at the third, etc. until the entire array is characterized.
This leaves the determination of the x_{p }parameters. Using the previous results, light can be routed in “wirepaths” (waveguides) throughout the QPP array, where the light travels along a single path from input to output. Externally, the light from this path can then be interfered on a beam splitter with a local oscillator, giving a phase. In a wire (waveguides), each MZI is either in the “identity” state or in the “swap” state, meaning there are 8 x_{p }free parameters per MZI. The total phase acquired along a wirepath can be a simple sum of the x_{p }elements along that path meaning that, so long as there are more wirepaths than x_{p }values, all of the x_{p }values can be determined by linear regression. In fact, in a given QPP, there are far more ways of constructing a “wire” through the array than there are free parameters (i.e. an overcomplete set of equations). For example, the QPP can have 60 MZIs (giving 480 x_{p }values) while there are 2976 wire paths from inputs to outputs in the example shown in
However, such wirepaths may not be true wires. Due to imperfections, there can be small amounts of light that travel along other paths yet still reach the target output port. This light can be isolated and removed from the calculations by varying the voltage applied to all modulators in the array not along the wirepath so that this spurious light appears in the Fourier transform of the output signal at a nonzero frequency. This can effectively tag the confounding light, allowing it to be removed from the result.
Once the x_{p }values have been found for the wirepaths, individual modulators can be varied to verify the change of the x_{p}s for intermediate settings of the modulators. Interior (0) modulators will affect which wirepath the light takes, but as the other modulators are held constant, this does not increase the complexity of the characterization.
Until now, this process has assumed switched detectors embedded into the array, which may increase the demands on the fabrication process and likely introduce extra complication. However, switched detectors can be removed in return for some added computational cost and characterization time. In particular, the phase settings necessary to create wirelike paths without any measurement of intermediate optical powers can be determined.
If light is input to only a single port of a QPP array, it normally can only reach a finite number of output ports in either lateral direction. If this lightcone of reachable ports for a given input MZI is considered, the topmost output mode can only be reached by light leaving the top output port of the first MZI; likewise, the bottommost output mode can only be reached by light leaving the bottom output port of the first MZI. By only putting light into one mode of the first MZI and monitoring the power at one of these edge modes, the MZI can be configured to be in the “identity” or “swap” configurations. This process can then proceed iteratively through the array, setting each MZI on the path to the appropriate configuration. The logarithms of the magnitudes of the x_{r }elements along a given path add, meaning a similar linear regression as discussed for the phases above can be performed, characterizing the entire array without the need for embedded detectors. The modulation scheme to remove spurious light from calculations is used here as well.
While thousands of measurements for the characterization may seem like a daunting experimental task, any QPP realized in practice can be computer controlled, meaning this process can be entirely automated. And, at the speeds of thermooptic modulators (>100 kHz), the characterization may take little time on any given chip.
Quantum operations on the QPP architecture are sensitive to fabrication defects. Even for singlequbit gates, the induced disorder quickly decreases the fidelity below acceptable limits. However, it is possible to apply numerical optimization techniques to adjust the applied phases to these devices postfabrication in an efficient manner, achieving extremely high fidelity operation of single gates. Moreover, even though the optimization is performed only locally for each gate, these improvements in fidelity are maintained at the global scale when cascading operations.
For this work, four different individual networks can be optimized: the postselected CNOT and CPHASE gates, as well as the singlequbit rotations necessary at the input and output of the iterative phase estimation algorithm.
The optimization process uses the computational basis transform applied by each MZI (a 4×4 complex, twophoton matrix, φ(U), that is a principal submatrix of the full unitary transform) and calculates the fitness of a given phase setting using the HilbertSchmidt norm. The optimization process is seeded with the set of phases for an ideal (desired) subblock of the QPP and uses a running timebounded combination of global and local optimization procedures. In order to improve the fidelity achieved using this procedure, buffer layers of MZIs can be added to the input and output of each gate, expanding the size of the network slightly.
The calculation of the computational basis transform is performed as follows. First, a vector corresponding to the phase of each modulator is selected by the optimization algorithm. These phases are used to generate the single particle unitary transform generated by the QPP subblock under consideration, incorporating fabrication errors. This is then used to calculate the matrix elements of the computational basis transform.
Quantum Random Walks: Simulation
Quantum walks with photons can simulate the transport of electrons in networks performing photosynthesis. Quantum walks with interacting particles can also be universal for quantum computation. In the discretetime QRW, a particle with an internal binary degree of freedom (a “coin”) is placed on the lattice. At each step of the walk, two operations occur: the internal state of the coin is prepared and the particle is shifted left or right (as indicated in
The propagation is studied for two indistinguishable photons on a QRW in the QPP. The initial state is φ_{i}=(20_{LR}+02_{LR})/√{square root over (2)}, where L and R are the two outputs of the first MZI of the QRW, MZI1. This state is prepared in the QPP by first launching indistinguishable photons into adjacent waveguides of neighboring MZIs set to (η, φ)=(1, 0) and (1, π/2). These MZIs produce the state e^{iπ/2}11 on the input waveguides of MZI1; the output then results in φ_{i }with the settings (η, φ)=(1/2, 0). Having prepared φ_{i}, the state is then evolved in the following 14 MZI layers of the QPP, where all internal phases θ are set to π/2. In these simulations, disorder is introduced by sampling the MZI output phases (φ) randomly from a uniform distribution on the interval [θ; Φ_{max}].
A lattice without disorder, i.e., Φ_{max}=0 is first considered. Simulation results for a realistic QPP are plotted in
As noted above, many questions remain regarding the impact of disorder on pathentanglement and the transport of multiphoton states. A single realization of disorder offers little information as it can contain extreme arrangements not representative of the majority of lattices with the same level of disorder. This can be seen by comparing a single realization of disorder (
A single QPP can generate many instances of disorder. Timedependent (independent) disorder can be realized with random phase settings along (orthogonal to) the direction of propagation. Applying weak timeindependent disorder (Φ_{max}=0.6π) to the lattice results in twophoton correlation and density functions that exhibit both bunched and localized characteristics (
Strong, timeindependent disorder in the QPP lattice (Φ_{max}=2π) reveals the characteristic exponential distributions of Anderson localization (
The QPP described here can be reconfigured by applying voltages across the phase shifters. A time step in a onedimensional QRW corresponds to a column of the QPP; a spatial position corresponds to a row (see
The phase shifters can include heaters (e.g.,
Directional couplers are fabricated with 200 nm nominal waveguide separation and a 17.5 μm interaction length and measured their transmission with respect to the transmission of straight waveguides. The loss in the directional coupler is minimal for the waveguide spacing. The splitting ratio is about 50.91%±1.94% at 1560 nm. This deviation may be attributed to variations in the measurement setup. The splitting ratio of the directional couplers has a standard error of 1.94% due to variations in the waveguide width and thickness. While this variation can occur gradually across a wafer, for example due to variations in the silicon device layer thickness, full randomness on each heater is assumed.
These results are then used to simulate the quantum random walk. The performance using the gate fidelity is quantified. Considering imperfections in the directional couplers and heaters, the fidelity of large gates is still very close to one.
Augmented QPP
The QPP may be augmented using, for example, highspeed switches, lowloss waveguides, onchip single photon sources, onchip singlephoton detectors and onchip electronics. First, enhancements in computational rates may be achieved with lowloss waveguides and by avoiding on and offchip coupling using integrated sources and detectors. Second, highspeed switches and integrated detectors enable feedforward for LOQC and multipass quantum networks, as shown in
The QPP can be placed inside of a loop; photons can be switched in and out of the loop by a modulator fast enough (e.g., approximately 1 MHz) to switch during the time it takes a photon to do a round trip in the QPP. Light gets injected into the QPP loop if the fast modulator is set to “pass.” If the modulator is left on the “pass” setting, light couples out of the loop after one pass through the loop. To keep light in the loop, the fast modulator is set to “no pass,” which both prevents light from entering the loop and prevents light from leaving the loop. Controlling this modulator enables control over how many passes the photon makes through the QPP. If the QPP imparts some unitary, U, then this control amounts to imparting U_{k }for a chosen k. The fast modulator could be a ring modulator based on carrier depletion or carrier injection, or any other fast modulator.
This multipass geometry is useful for studies of quantum random walks, which occur over extremely large interaction lengths. Multipass circuits enable short chips but long circuits. It is additionally useful in quantum information processing to calculate the powers of unitaries, e.g., for the iterative phase estimation algorithm. The multipass architecture enables this calculation.
Applications of Quantum Photonic Processors
Designing quantum algorithms using classical computers may be prohibitively challenging for large systems. Multiple photons can be injected into the QPP and the results may be used in a nonlinear algorithm such as that used above to calculate the next phase settings on the QPP to improve performance. In this way, the QPP can be used to design for new quantum information processing algorithms.
These algorithms are not limited to the spatial mode computational basis. Polarization control can be incorporated and by changing the MZI unit cell of the QPP, the QPP can process temporal and spectral modes as well. Unbalanced MZIs have one path between the directional couplers longer than the other. If the path imbalance is shorter than the coherence time of the light, then the MZI can be used as a spectrometer; the MZI array can be used as a broadband, highly tunable spectrometer, spectral filter and pulseshaper. This can be shown for small numbers of MZIs in a static geometry unlike that for the QPP. If the path imbalance in the MZI is longer than the coherence time of the light, then there is no selfinterference in the MZI, however the MZI can be used to select the time delay imparted on the photon—“long” or “short.” The QPP can therefore be able to shift photons in time and perform algorithms that make use of the temporal degreeoffreedom of the photons.
The QPP can be further enhanced through the use of nonlinear optical elements. Linear optics quantum computing relies on detector nonlinearities and postselection, which can only succeed probabilistically. Deterministic operation can be achieved if nonlinearities are added the gate itself. Potential nonlinear elements are cavitycoupled selfassembled quantum dots, graphene disks, and even trapped ions. All have been shown to be highly nonlinear elements that can be integrated onchip.
The QPP described above can be used for classical optics applications as well. The QPP may serve as a nonblocking, multiinput multioutput, transparent (i.e., all optical) switch, signal router, or highdimensional beam splitter. It can also process spatial modes used to encrypt or encode information. The complex unitary transformations that the QPP imparts on a large number of inputs makes it attractive for realizing large phased arrays, e.g., for LIDAR applications.
For applications that involve large temperature variations, components of the QPP can be made exceptionally temperature insensitive. For example, many CPUs and other main computer chips can heat up significantly during operation. A QPP near one of these chips would also experience temperature swings. Directional couplers could be replaced by multimode interferometers (MMI), or adiabatic couplers, which are also much less sensitive to fabrication imperfections. Temperature monitors could be incorporated onchip in the form of ringresonators, to dynamically adjust phase settings of the QPP to account for temperature drifts of the system.
Discussion
A QPP, fabricated in current silicon photonics processes, enables high fidelity, postselected quantum gates, quantum simulation, and quantum random walks. The promise of such a circuit for faulttolerant quantum computation in the context of LOQC is now considered. Faulttolerant quantum computation is possible if gate error probabilities are below some threshold. For postselected LOQC, this threshold can be as high as 1%. But considering limitations on overhead (e.g., <10^{4 }physical CNOT gates per qubit and gate), the desired error rate is normally much lower: 10^{−3 }to 10^{−4}. Due to advanced silicon fabrication processes and the optimization of gate settings presented above, the QPP enables achieving these error rates on a PIC.
Architectures for universal quantum computers based on LOQC may also involve efficient singlephoton sources, singlephoton detectors, and feedforward operations on the quantum state. Examples of these techniques include entangledphoton sources based on fourwave mixing and waveguideintegrated superconducting singlephoton detectors. The potential for multiplexing the emission of spontaneous singlephoton sources could enable highefficiency state preparation for quantum computation; lowlatency superconducting logic could enable feedforward required for scalable LOQC; and low photonnumber nonlinear elements could enable photonphoton interaction and deterministic quantum logic.
The highdimensional unitary transformations possible on the QPP could also enable a number of applications in classical optics, including multiinput multioutput, transparent, nonblocking switches, signal routers, highdimensional beam splitters, and large phased arrays, e.g., for LIDAR applications.
Conclusion
While various inventive embodiments have been described and illustrated herein, those of ordinary skill in the art will readily envision a variety of other means and/or structures for performing the function and/or obtaining the results and/or one or more of the advantages described herein, and each of such variations and/or modifications is deemed to be within the scope of the inventive embodiments described herein. More generally, those skilled in the art will readily appreciate that all parameters, dimensions, materials, and configurations described herein are meant to be exemplary and that the actual parameters, dimensions, materials, and/or configurations will depend upon the specific application or applications for which the inventive teachings is/are used. Those skilled in the art will recognize, or be able to ascertain using no more than routine experimentation, many equivalents to the specific inventive embodiments described herein. It is, therefore, to be understood that the foregoing embodiments are presented by way of example only and that, within the scope of the appended claims and equivalents thereto, inventive embodiments may be practiced otherwise than as specifically described and claimed. Inventive embodiments of the present disclosure are directed to each individual feature, system, article, material, kit, and/or method described herein. In addition, any combination of two or more such features, systems, articles, materials, kits, and/or methods, if such features, systems, articles, materials, kits, and/or methods are not mutually inconsistent, is included within the inventive scope of the present disclosure.
The abovedescribed embodiments can be implemented in any of numerous ways. For example, embodiments of designing and making the technology disclosed herein may be implemented using hardware, software or a combination thereof. When implemented in software, the software code can be executed on any suitable processor or collection of processors, whether provided in a single computer or distributed among multiple computers.
Further, it should be appreciated that a computer may be embodied in any of a number of forms, such as a rackmounted computer, a desktop computer, a laptop computer, or a tablet computer. Additionally, a computer may be embedded in a device not generally regarded as a computer but with suitable processing capabilities, including a Personal Digital Assistant (PDA), a smart phone or any other suitable portable or fixed electronic device.
Also, a computer may have one or more input and output devices. These devices can be used, among other things, to present a user interface. Examples of output devices that can be used to provide a user interface include printers or display screens for visual presentation of output and speakers or other sound generating devices for audible presentation of output. Examples of input devices that can be used for a user interface include keyboards, and pointing devices, such as mice, touch pads, and digitizing tablets. As another example, a computer may receive input information through speech recognition or in other audible format.
Such computers may be interconnected by one or more networks in any suitable form, including a local area network or a wide area network, such as an enterprise network, and intelligent network (IN) or the Internet. Such networks may be based on any suitable technology and may operate according to any suitable protocol and may include wireless networks, wired networks or fiber optic networks.
The various methods or processes (outlined herein may be coded as software that is executable on one or more processors that employ any one of a variety of operating systems or platforms. Additionally, such software may be written using any of a number of suitable programming languages and/or programming or scripting tools, and also may be compiled as executable machine language code or intermediate code that is executed on a framework or virtual machine.
In this respect, various inventive concepts may be embodied as a computer readable storage medium (or multiple computer readable storage media) (e.g., a computer memory, one or more floppy discs, compact discs, optical discs, magnetic tapes, flash memories, circuit configurations in Field Programmable Gate Arrays or other semiconductor devices, or other nontransitory medium or tangible computer storage medium) encoded with one or more programs that, when executed on one or more computers or other processors, perform methods that implement the various embodiments of the invention discussed above. The computer readable medium or media can be transportable, such that the program or programs stored thereon can be loaded onto one or more different computers or other processors to implement various aspects of the present invention as discussed above.
The terms “program” or “software” are used herein in a generic sense to refer to any type of computer code or set of computerexecutable instructions that can be employed to program a computer or other processor to implement various aspects of embodiments as discussed above. Additionally, it should be appreciated that according to one aspect, one or more computer programs that when executed perform methods of the present invention need not reside on a single computer or processor, but may be distributed in a modular fashion amongst a number of different computers or processors to implement various aspects of the present invention.
Computerexecutable instructions may be in many forms, such as program modules, executed by one or more computers or other devices. Generally, program modules include routines, programs, objects, components, data structures, etc. that perform particular tasks or implement particular abstract data types. Typically the functionality of the program modules may be combined or distributed as desired in various embodiments.
Also, data structures may be stored in computerreadable media in any suitable form. For simplicity of illustration, data structures may be shown to have fields that are related through location in the data structure. Such relationships may likewise be achieved by assigning storage for the fields with locations in a computerreadable medium that convey relationship between the fields. However, any suitable mechanism may be used to establish a relationship between information in fields of a data structure, including through the use of pointers, tags or other mechanisms that establish relationship between data elements.
Also, various inventive concepts may be embodied as one or more methods, of which an example has been provided. The acts performed as part of the method may be ordered in any suitable way. Accordingly, embodiments may be constructed in which acts are performed in an order different than illustrated, which may include performing some acts simultaneously, even though shown as sequential acts in illustrative embodiments.
All definitions, as defined and used herein, should be understood to control over dictionary definitions, definitions in documents incorporated by reference, and/or ordinary meanings of the defined terms.
The indefinite articles “a” and “an,” as used herein in the specification and in the claims, unless clearly indicated to the contrary, should be understood to mean “at least one.”
The phrase “and/or,” as used herein in the specification and in the claims, should be understood to mean “either or both” of the elements so conjoined, i.e., elements that are conjunctively present in some cases and disjunctively present in other cases. Multiple elements listed with “and/or” should be construed in the same fashion, i.e., “one or more” of the elements so conjoined. Other elements may optionally be present other than the elements specifically identified by the “and/or” clause, whether related or unrelated to those elements specifically identified. Thus, as a nonlimiting example, a reference to “A and/or B”, when used in conjunction with openended language such as “comprising” can refer, in one embodiment, to A only (optionally including elements other than B); in another embodiment, to B only (optionally including elements other than A); in yet another embodiment, to both A and B (optionally including other elements); etc.
As used herein in the specification and in the claims, “or” should be understood to have the same meaning as “and/or” as defined above. For example, when separating items in a list, “or” or “and/or” shall be interpreted as being inclusive, i.e., the inclusion of at least one, but also including more than one, of a number or list of elements, and, optionally, additional unlisted items. Only terms clearly indicated to the contrary, such as “only one of” or “exactly one of,” or, when used in the claims, “consisting of,” will refer to the inclusion of exactly one element of a number or list of elements. In general, the term “or” as used herein shall only be interpreted as indicating exclusive alternatives (i.e. “one or the other but not both”) when preceded by terms of exclusivity, such as “either,” “one of,” “only one of,” or “exactly one of” “Consisting essentially of,” when used in the claims, shall have its ordinary meaning as used in the field of patent law.
As used herein in the specification and in the claims, the phrase “at least one,” in reference to a list of one or more elements, should be understood to mean at least one element selected from any one or more of the elements in the list of elements, but not necessarily including at least one of each and every element specifically listed within the list of elements and not excluding any combinations of elements in the list of elements. This definition also allows that elements may optionally be present other than the elements specifically identified within the list of elements to which the phrase “at least one” refers, whether related or unrelated to those elements specifically identified. Thus, as a nonlimiting example, “at least one of A and B” (or, equivalently, “at least one of A or B,” or, equivalently “at least one of A and/or B”) can refer, in one embodiment, to at least one, optionally including more than one, A, with no B present (and optionally including elements other than B); in another embodiment, to at least one, optionally including more than one, B, with no A present (and optionally including elements other than A); in yet another embodiment, to at least one, optionally including more than one, A, and at least one, optionally including more than one, B (and optionally including other elements); etc.
In the claims, as well as in the specification above, all transitional phrases such as “comprising,” “including,” “carrying,” “having,” “containing,” “involving,” “holding,” “composed of,” and the like are to be understood to be openended, i.e., to mean including but not limited to. Only the transitional phrases “consisting of” and “consisting essentially of” shall be closed or semiclosed transitional phrases, respectively, as set forth in the United States Patent Office Manual of Patent Examining Procedures, Section 2111.03.