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ch11_circles1.js
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ch11_circles1.js
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// Programming Quantum Computers
// by Eric Johnston, Nic Harrigan and Mercedes Gimeno-Segovia
// O'Reilly Media
// To run this online, go to http://oreilly-qc.github.io?p=12-X
// PERFORMANCE NOTE: Increasing any of the following parameters by 1 will
// cause the program to take either 2x longer or 4x longer.
// For example: if the numbers are 6,2,1,10 and the program takes 10 seconds to run,
// then increasing them to 12,8,6,16 will cause the program to take approximately 2,700 years.
// ...so when experimenting here it's best to start with small changes.
var res_full_bits = 6; // Number of bits in x,y in the complete image. 8 means the image is 256x256
var res_aa_bits = 2; // Number of bits in x,y per sub-pixel tile. 2 means tiles are 4x4
var num_counter_bits = 1; // The effective bit depth of the result.
var accum_bits = 10; // Scratch qubits for the shader. More scratch bits means we can do more complicated math
var res_full = 1 << res_full_bits; // The x and y size of the full image, before sampling.
var res_aa = 1 << res_aa_bits; // The x and y size of each subpixel tile.
var res_tiles = res_full / res_aa; // The number of tiles which make up one image row or column.
var qss_full_lookup_table = null;
var qss_count_to_hits = [];
var do_shortcut_qss = false; // Use classical sampling based on the ideal result to approximate the QSS result
var do_monte_carlo = true; // Generate the MonteCarlo image
// The main function draws the full-size image for reference, then constructs the QSS lookup table,
// and then finally uses QSS to draw the sampled image.
function main()
{
setup_display_boxes();
// Draw the whole image, so we can see what we're sampling.
draw_reference_res_images();
// Create the QSS lookup table
// This can be done beforehand and saved for use with multiple QSS images
create_qss_lookup_table();
do_qss_image();
draw_confidence_map();
}
// The quantum pixel shader is the function which is called for each iteration.
// When drawing the full-size image, this is called per sub-pixel.
function shader_quantum(qx, qy, tx, ty, qacc, condition, out_color)
{
var num_bins = 16;
var hbin = 0|(num_bins * tx / res_tiles);
var vbin = 0|(num_bins * ty / res_tiles);
var ball_pos = [2, 2];
var ball_radius = 1;
var is_ball = hbin >= (ball_pos[0] - ball_radius) && hbin < (ball_pos[0] + ball_radius)
&& vbin >= (ball_pos[1] - ball_radius) && vbin < (ball_pos[1] + ball_radius);
var is_sky = (vbin & 4) == 0 && !is_ball;
var is_ground = !is_ball && !is_sky;
if (1 || is_ball)
{
// drawing a circle is tricky, because we want x^2+y^2<r^2, but we don't have
// a great way to accumulate the squared sum of tx*res+qx. Instead,
// we can make use of (a+b)^2 = a^2+2ab+b^2.
var tiles_per_bin = res_tiles / num_bins;
var bx = ball_pos[0] * tiles_per_bin;
var by = ball_pos[1] * tiles_per_bin;
var br = ball_radius * tiles_per_bin * res_aa;
var dx = tx - bx;
var dy = ty - by;
if (dx < 0) dx = -(dx + 1);
if (dy < 0) dy = -(dy + 1);
dx *= res_aa;
dy *= res_aa;
qacc.add(dx * dx + dy * dy - br * br);
if (tx < bx)
qx.not();
if (ty < by)
qy.not();
for (var i = 0; i < dx; ++i)
qacc.addShifted(qx, 1);
for (var i = 0; i < dy; ++i)
qacc.addShifted(qy, 1);
qacc.addSquared(qx);
qacc.addSquared(qy);
// qacc.add(dx + dy - br);
var acc_sign_bit = 1 << (accum_bits - 1);
var mask = qacc.bits(acc_sign_bit);
mask.orEquals(condition);
xor_color(null, mask, out_color);
// qacc.subtract(dx + dy - br);
qacc.subtractSquared(qx);
qacc.subtractSquared(qy);
for (var i = 0; i < dx; ++i)
qacc.subtractShifted(qx, 1); // todo make this shifted again
for (var i = 0; i < dy; ++i)
qacc.subtractShifted(qy, 1);
qacc.subtract(dx * dx + dy * dy - br * br);
if (tx < bx)
qx.not();
if (ty < by)
qy.not();
}
if (0 && is_sky)
{
// sky
if (0) {
qacc.addShifted(ty, ty_shift);
qacc.addShifted(qy, qy_shift);
xor_color(null, mask, out_color);
qacc.subtractShifted(ty, ty_shift);
qacc.subtractShifted(qy, qy_shift);
} else {
// just gray sky
qx.cnot(qy, 0x1);
var mask = qx.bits(0x1);
mask.orEquals(condition);
xor_color(null, mask, out_color);
qx.cnot(qy, 0x1);
}
}
if (0 && is_ground)
{
// perspective checkerboard
var tile_shift = res_aa_bits;
var y_offset = res_full >> 2;
if (ty >= (res_tiles >> 1))
y_offset += res_full >> 1;
var x_offset = (res_full) >> 1;
var left_side = (tx < (res_tiles >> 1));
var slopes = [[1,0],[0,1],[0,2]]; // checkerboard vertical edge slopes
if (left_side)
slopes = [[0,0],[0,1],[0,2]];
// Draw checkerboard perspective
for (var slope = 0; slope < slopes.length; ++slope)
{
var num = slopes[slope][0];
var denom = slopes[slope][1];
// mirror horiz
x_offset = 0;
txx = tx % (res_tiles >> 1);
if (left_side)
{
txx = (res_tiles >> 1) - txx;
qx.not();
}
qacc.add((txx << (tile_shift + num)) - (x_offset << num));
qacc.addShifted(qx, num);
qacc.subtract((ty << (tile_shift + denom)) - (y_offset << denom));
qacc.subtractShifted(qy, denom);
var acc_sign_bit = 1 << (accum_bits - 1);
var mask = qacc.bits(acc_sign_bit);
mask.orEquals(condition);
xor_color(null, mask, out_color);
qacc.addShifted(qy, denom);
qacc.add((ty << (tile_shift + denom)) - (y_offset << denom));
qacc.subtractShifted(qx, num);
qacc.subtract((txx << (tile_shift + num)) - (x_offset << num));
if (left_side)
{
txx = (res_tiles >> 1) - txx;
qx.not();
}
}
// Draw checkerboard parallel
for (var band = 0; band < 6; ++band)
{
var band_bit = 1 << (band + 1);
qacc.subtract((ty << (tile_shift)) - (y_offset));
qacc.subtract(qy);
var acc_bit =qacc.bits(~(band_bit - 1));
var mask = acc_bit;
mask.orEquals(condition);
xor_color(null, mask, out_color);
qacc.add(qy);
qacc.add((ty << (tile_shift)) - (y_offset));
}
}
}
// Flip num_terms_to_flip terms of quantum reg x, conditional on condition
function flip_n_terms(x, num_terms_to_flip, condition)
{
// This is a simple brute-force way to do it, but as this function
// is only used to build the look-up tables, that's ok.
var terms_flipped = 0;
for (var i = 0; i < num_terms_to_flip; ++i)
{
x.not(i);
x.cphase(180, ~0, condition);
x.not(i);
}
}
function create_qss_lookup_table()
{
qc.clearOutput();
qc.disableAnimation();
qc.disableRecording();
qc.reset((res_aa_bits + res_aa_bits) + num_counter_bits);
var qxy = qint.new(res_aa_bits + res_aa_bits, 'qxy');
var qcount = qint.new(num_counter_bits, 'count');
var num_subpixels = 1 << (res_aa_bits + res_aa_bits);
qss_full_lookup_table = null;
for (var hits = 0; hits <= num_subpixels; ++hits)
create_table_column(hits, qxy, qcount);
var cw = qss_full_lookup_table;
qss_count_to_hits = [];
for (var count = 0; count < cw.length; ++count)
{
var best_hits = 0;
var best_prob = 0;
for (var hits = 0; hits < cw[0].length; ++hits)
{
if (best_prob < cw[count][hits])
{
best_prob = cw[count][hits];
best_hits = hits;
}
}
qss_count_to_hits.push(best_hits);
}
// Draw the cw table
if (qss_full_lookup_table && display_cwtable)
{
var disp = display_cwtable;
var ysize = cw.length;
var xsize = cw[0].length;
disp.setup(xsize, ysize, 16);
for (var y = 0; y < ysize; ++y)
for (var x = 0; x < xsize; ++x)
disp.pixel(x, y, cw[y][x]);
disp.span.innerHTML = 'QSS Probability Table<br/>' +
'horiz = '+num_subpixels+' hits<br/>' +
'vert = '+(1 << num_counter_bits)+' sample rows';
}
}
function draw_confidence_map()
{
// Draw the confidence map
if (ideal_result && qss_raw_result)
{
var cw = qss_full_lookup_table;
display_confidence.label('Confidence Map');
for (var ty = 0; ty < res_tiles; ++ty)
{
for (var tx = 0; tx < res_tiles; ++tx)
{
var ysize = cw.length;
var xsize = cw[0].length;
var qss_out = qss_raw_result[ty][tx];
// Given the QSS result, find the confidence
var row_total = 0;
var row_max = 0;
for (var x = 0; x < xsize; ++x)
{
var val = cw[qss_out][x];
row_total += val;
if (val > row_max)
row_max = val;
}
var confidence = row_max / row_total;
display_confidence.pixel(tx, ty, confidence);
}
}
}
}
function create_table_column(color, qxy, qcount)
{
var num_subpixels = 1 << (res_aa_bits + res_aa_bits);
var true_count = color;
// Put everything into superposition
qc.write(0);
qcount.hadamard();
qxy.hadamard();
for (var i = 0; i < num_counter_bits; ++i)
{
var reps = 1 << i;
var condition = qcount.bits(reps);
var mask_with_condition = qxy.bits().or(condition);
for (var j = 0; j < reps; ++j)
{
flip_n_terms(qxy, true_count, condition);
grover_iteration(qxy.bits(), mask_with_condition);
}
}
invQFT(qcount);
// Construct the translation table
var table = [];
for (var i = 0; i < (1 << num_counter_bits); ++i)
table.push(qcount.peekProbability(i));
if (qss_full_lookup_table == null)
{
qss_full_lookup_table = [];
for (var i = 0; i < (1 << num_counter_bits); ++i)
{
qss_full_lookup_table.push([]);
for (var j = 0; j < num_subpixels; ++j)
qss_full_lookup_table[i].push(0);
}
}
for (var col = 0; col < (1 << num_counter_bits); ++col)
qss_full_lookup_table[col][true_count] = table[col];
}
///////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////
var ideal_result = null;
var qss_raw_result = null;
function draw_reference_res_images()
{
qc.clearOutput();
qc.disableAnimation();
qc.disableRecording();
var bits = res_aa_bits;
var disable_simulation = 30; // overload the qubits to disable the quantum sim and fall back to digital
var total_qubits = 2 * bits + accum_bits + 1 + disable_simulation; // +30 is to disable sim
qc.reset(total_qubits);
var qx = qint.new(bits, 'qx');
var qy = qint.new(bits, 'qy');
var qacc = qint.new(accum_bits, 'scratch');
var color = qint.new(1, 'color');
qc.write(0);
if (qacc)
qacc.write(0);
var num_monte_carlo_samples = (1 << num_counter_bits) - 1;
var num_subpixels = res_aa * res_aa;
var total_pixel_error = 0;
var num_zero_error_pixels = 0;
ideal_result = [];
for (var ty = 0; ty < res_tiles; ++ty)
{
ideal_result.push([]);
console.log('full-res row ' + ty + ' of ' + res_tiles);
for (var tx = 0; tx < res_tiles; ++tx)
{
// Do full-res reference, and also ideal sampling
var tile_ideal_sum = 0;
for (var y = 0; y < res_aa; ++y)
{
for (var x = 0; x < res_aa; ++x)
{
qx.write(x);
qy.write(y);
color.write(0);
shader_quantum(qx, qy, tx, ty, qacc, null, color);
var subpixel_value = color.read();
var full_x = (tx << res_aa_bits) + x;
var full_y = (ty << res_aa_bits) + y;
display_qfull_res.pixel(full_x, full_y, subpixel_value);
tile_ideal_sum += subpixel_value;
}
}
ideal_result[ty].push(tile_ideal_sum);
display_ground_truth.pixel(tx, ty, tile_ideal_sum / num_subpixels);
if (do_monte_carlo)
{
// Do Monte Carlo sampling
var tile_monte_carlo_sum = 0;
for (var sample = 0; sample < num_monte_carlo_samples; ++sample)
{
var x = random_int(res_aa);
var y = random_int(res_aa);
qx.write(x);
qy.write(y);
color.write(0);
shader_quantum(qx, qy, tx, ty, qacc, null, color);
tile_monte_carlo_sum += color.read();
}
display_monte_carlo.pixel(tx, ty, tile_monte_carlo_sum / num_monte_carlo_samples);
var normalized_mc_sum = Math.round(num_subpixels * tile_monte_carlo_sum / num_monte_carlo_samples);
var pixel_error = Math.abs(normalized_mc_sum - tile_ideal_sum);
if (pixel_error)
total_pixel_error += pixel_error;
else
num_zero_error_pixels++;
}
}
}
if (do_monte_carlo)
{
var average_pixel_error_percent = Math.round(100 * total_pixel_error / (res_tiles * res_tiles * num_subpixels));
var zero_error_pixels_percent = Math.round(100 * num_zero_error_pixels / (res_tiles * res_tiles));
display_monte_carlo.label('Monte Carlo result<br/>'+num_monte_carlo_samples+' samples/tile<br/>'
+res_tiles+'x'+res_tiles+' pixels<br/>'
+'avg pixel error: '+average_pixel_error_percent+'%<br/>'
+'zero-error pixels: '+zero_error_pixels_percent+'%<br/>');
}
display_qfull_res.label('Full-resolution reference<br/>'+res_full+'x'+res_full+' pixels');
display_ground_truth.label('Ideal sampling reference<br/>'+res_tiles+'x'+res_tiles+' pixels');
qc.qReg.disableSimulation = false;
}
// Return a random int [0,range)
function random_int(range)
{
return Math.floor(Math.random() * range) % range;
}
function qss_tile(sp)
{
if (do_shortcut_qss && ideal_result)
{
var cw = qss_full_lookup_table;
var ysize = cw.length;
var xsize = cw[0].length;
var true_val = ideal_result[sp.ty][sp.tx];
// Given the true val, simulate a QSS reult
var total_prob = 0;
for (var y = 0; y < ysize; ++y)
total_prob += cw[y][true_val];
var dice = Math.random() * total_prob;
var qss_out = 0;
var prob = 0;
for (var y = 0; y < ysize; ++y)
{
prob += cw[y][true_val];
if (prob >= dice)
{
qss_out = y;
break;
}
}
sp.readVal = qss_out;
sp.hits = qss_count_to_hits[sp.readVal];
sp.color = sp.hits / (res_aa * res_aa);
return sp.color;
}
sp.qx.write(0);
sp.qy.write(0);
sp.counter.write(0);
sp.qx.hadamard();
sp.qy.hadamard();
sp.counter.hadamard();
for (var cbit = 0; cbit < num_counter_bits; ++cbit)
{
var iters = 1 << cbit;
var qxy_bits = sp.qx.bits().or(sp.qy.bits());
var condition = sp.counter.bits(iters);
var mask_with_condition = qxy_bits.or(condition);
for (var i = 0; i < iters; ++i)
{
shader_quantum(sp.qx, sp.qy, sp.tx, sp.ty, sp.qacc, condition, sp.qcolor);
grover_iteration(qxy_bits, mask_with_condition);
}
}
invQFT(sp.counter);
sp.readVal = sp.counter.read();
sp.hits = qss_count_to_hits[sp.readVal];
sp.color = sp.hits / (res_aa * res_aa);
return sp.color;
}
// This one is the best so far.
function do_qss_image()
{
var sp = {};
qc.clearOutput();
qc.disableAnimation();
qc.disableRecording();
var total_qubits = 2 * res_aa_bits + num_counter_bits + accum_bits;
qc.reset(total_qubits);
sp.qx = qint.new(res_aa_bits, 'qx');
sp.qy = qint.new(res_aa_bits, 'qy');
sp.counter = qint.new(num_counter_bits, 'counter');
sp.qacc = qint.new(accum_bits, 'scratch');
var total_pixel_error = 0;
var num_zero_error_pixels = 0;
qss_raw_result = [];
sp.qacc.write(0);
for (sp.ty = 0; sp.ty < res_tiles; ++sp.ty)
{
qss_raw_result.push([]);
console.log('QSS row ' + sp.ty + ' of ' + res_tiles);
for (sp.tx = 0; sp.tx < res_tiles; ++sp.tx)
{
qss_tile(sp);
qss_raw_result[sp.ty].push(sp.readVal);
display_qss.pixel(sp.tx, sp.ty, sp.color);
if (ideal_result)
{
var pixel_error = Math.abs(sp.hits - ideal_result[sp.ty][sp.tx]);
if (pixel_error)
total_pixel_error += pixel_error;
else
num_zero_error_pixels++;
}
}
}
var num_qss_iterations = (1 << num_counter_bits) - 1;
if (ideal_result)
{
var num_subpixels = res_aa * res_aa;
var average_pixel_error_percent = Math.round(100 * total_pixel_error / (res_tiles * res_tiles * num_subpixels));
var zero_error_pixels_percent = Math.round(100 * num_zero_error_pixels / (res_tiles * res_tiles));
display_qss.label('QSS result<br/>'+num_qss_iterations+' iterations/tile<br/>'
+res_tiles+'x'+res_tiles+' pixels<br/>'
+'avg pixel error: '+average_pixel_error_percent+'%<br/>'
+'zero-error pixels: '+zero_error_pixels_percent+'%<br/>');
}
else
{
display_qss.label('QSS result<br/>'+num_qss_iterations+' iterations/tile<br/>'
+res_tiles+'x'+res_tiles+' pixels<br/>');
}
}
function grover_iteration(mask, mask_with_condition)
{
qc.codeLabel('Grover iteration');
qc.hadamard(mask);
qc.not(mask);
qc.cphase(180, mask_with_condition);
qc.not(mask);
qc.hadamard(mask);
}
function invQFT(x)
{
var bits = x.numBits;
qc.codeLabel('inverse QFT');
for (var i = 0; i < bits; ++i)
{
var bit1 = bits - (i + 1);
var mask1 = 1 << bit1;
x.hadamard(mask1);
var theta = -90.0;
for (var j = i + 1; j < bits; ++j)
{
var bit2 = bits - (j + 1);
var mask2 = 1 << bit2;
x.cphase(theta, mask1 + mask2);
theta *= 0.5;
}
}
}
var display_ground_truth = null;
var display_monte_carlo = null;
var display_qfull_res = null;
var display_qss = null;
var display_confidence = null;
var display_cwtable = null;
function setup_display_boxes()
{
display_ground_truth = new DisplayBox('display_ground_truth');
display_monte_carlo = new DisplayBox('display_monte_carlo');
display_qfull_res = new DisplayBox('display_qfull_res');
display_qss = new DisplayBox('display_qss');
display_confidence = new DisplayBox('display_confidence');
display_cwtable = new DisplayBox('display_cwtable');
display_ground_truth.setup(res_tiles, res_tiles, res_aa);
display_monte_carlo.setup(res_tiles, res_tiles, res_aa);
display_qfull_res.setup(res_full, res_full, 1);
display_qss.setup(res_tiles, res_tiles, res_aa);
display_confidence.setup(res_tiles, res_tiles, res_aa);
display_cwtable.setup(res_tiles, res_tiles, res_aa);
}
function xor_color(qq, condition, out_color)
{
if (qq)
{
if (out_color)
out_color.cnot(qq, ~0, condition);
else
qq.cphase(180, ~0, condition);
}
else
{
if (out_color)
out_color.cnot(null, ~0, condition);
else
qc.cphase(180, condition);
}
}
function DisplayBox(canvas_name)
{
this.canvas = document.getElementById(canvas_name);
this.span = document.getElementById(canvas_name + '_span');
this.ctx = this.canvas.getContext('2d');
this.resolution_x = this.canvas.width;
this.resolution_y = this.canvas.height;
this.clear = function()
{
this.ctx.fillStyle = '#afafdf';
this.ctx.fillRect(0, 0, this.canvas.width, this.canvas.height);
}
this.setup = function(resolution_x, resolution_y, ss_scale)
{
this.resolution_x = resolution_x;
this.resolution_y = resolution_y;
this.canvas.width = this.resolution_x * ss_scale;
this.canvas.height = this.canvas.width * this.resolution_y / this.resolution_x;
}
this.pixel = function(x, y, color)
{
var gamma_correct = false;
if (gamma_correct)
{
var inv_gamma = 1.0 / 2.2;
color = Math.pow(color, inv_gamma);
}
var bright = (255 * color).toFixed(0);
var w = this.canvas.width / this.resolution_x;
var h = this.canvas.height / this.resolution_y;
var x1 = x * w;
var y1 = y * h;
this.ctx.fillStyle = 'rgb('+bright+','+bright+','+bright+')';
this.ctx.fillRect(x1, y1, w, h);
}
this.pixelRGB = function(x, y, color)
{
var inv_gamma = 1.0 / 2.2;
var r = Math.pow(color[0], inv_gamma);
var g = Math.pow(color[1], inv_gamma);
var b = Math.pow(color[2], inv_gamma);
r = (255 * r).toFixed(0);
g = (255 * g).toFixed(0);
b = (255 * b).toFixed(0);
var w = this.canvas.width / this.resolution_x;
var h = this.canvas.height / this.resolution_y;
var x1 = x * w;
var y1 = y * h;
this.ctx.fillStyle = 'rgb('+r+','+g+','+b+')';
this.ctx.fillRect(x1, y1, w, h);
}
this.label = function(text)
{
this.span.innerHTML = text;
}
this.get_bw_pixels = function(width, height)
{
var imgd = this.ctx.getImageData(0, 0, this.canvas.width, this.canvas.height);
var pix = imgd.data;
var out_bytes = new Array();
var src_row_index = 0;
var src_col_pitch = 4 * this.canvas.width / width;
var src_row_pitch = src_col_pitch * width * this.canvas.height / height;
for (var row = 0; row < height; ++row)
{
var src_index = src_row_index;
for (var col = 0; col < width; ++col)
{
out_bytes.push(pix[src_index]);
src_index += src_col_pitch;
}
src_row_index += src_row_pitch;
}
}
}
main();